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Journal articles on the topic 'Small space-Time scales'
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1
Andresen, Bjarne, and Christopher Essex. "Thermodynamics at Very Long Time and Space Scales." Entropy 22, no. 10 (September 28, 2020): 1090. http://dx.doi.org/10.3390/e22101090.
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Any observation, and hence concept, is limited by the time and length scale of the observer and his instruments. Originally, we lived on a timescale of minutes and a length scale of meters, give or take an order of magnitude or two. Therefore, we devloped laboratory sized concepts, like volume, pressure, and temperature of continuous media. The past 150 years we managed to observe on the molecular scale and similarly nanoseconds timescale, leading to atomic physics that requires new concepts. In this paper, we are moving in the opposite direction, to extremely large time and length scales. We call this regime “slow time”. Here, we explore which laboratory concepts still apply in slow time and which new ones may emerge. E.g., we find that temperature no longer exists and that a new component of entropy emerges from long time averaging of other quantities. Just as finite-time thermodynamics developed from the small additional constraint of a finite process duration, here we add a small new condition, the very long timescale that results in a loss of temporal resolution, and again look for new structure.
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Caltagirone, Jean-Paul. "Non-Fourier heat transfer at small scales of time and space." International Journal of Heat and Mass Transfer 160 (October 2020): 120145. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2020.120145.
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Mandapaka, P. V., P. Lewandowski, W. E. Eichinger, and W. F. Krajewski. "Multiscaling analysis of high resolution space-time lidar-rainfall." Nonlinear Processes in Geophysics 16, no. 5 (September 24, 2009): 579–86. http://dx.doi.org/10.5194/npg-16-579-2009.
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Abstract. In this study, we report results from scaling analysis of 2.5 m spatial and 1 s temporal resolution lidar-rainfall data. The high resolution spatial and temporal data from the same observing system allows us to investigate the variability of rainfall at very small scales ranging from few meters to ~1 km in space and few seconds to ~30 min in time. The results suggest multiscaling behaviour in the lidar-rainfall with the scaling regime extending down to the resolution of the data. The results also indicate the existence of a space-time transformation of the form t~Lz at very small scales, where t is the time lag, L is the spatial averaging scale and z is the dynamic scaling exponent.
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Berndtsson, Ronny, Kenji Jinno, Akira Kawamura, Magnus Larson, and Janusz Niemczynowicz. "Some Eulerian and Lagrangian statistical properties of rainfall at small space-time scales." Journal of Hydrology 153, no. 1-4 (January 1994): 339–55. http://dx.doi.org/10.1016/0022-1694(94)90198-8.
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Tzou, D. Y. "A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales." Journal of Heat Transfer 117, no. 1 (February 1, 1995): 8–16. http://dx.doi.org/10.1115/1.2822329.
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A universal constitutive equation between the heat flux vector and the temperature gradient is proposed to cover the fundamental behaviors of diffusion (macroscopic in both space and time), wave (macroscopic in space but microscopic in time), phonon–electron interactions (microscopic in both space and time), and pure phonon scattering. The model is generalized from the dual-phase-lag concept accounting for the lagging behavior in the high-rate response. While the phase lag of the heat flux captures the small-scale response in time, the phase lag of the temperature gradient captures the small-scale response in space. The universal form of the energy equation facilitates identifications of the physical parameters governing the transition from one mechanism (such as diffusion or wave) to another (the phonon–electron interaction).
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Jinno, Kenji, Akira Kawamura, Ronny Berndtsson, Magnus Larson, and Janusz Niemczynowicz. "Real-time rainfall prediction at small space-time scales using a two-dimensional stochastic advection-diffusion model." Water Resources Research 29, no. 5 (May 1993): 1489–504. http://dx.doi.org/10.1029/92wr02849.
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Hatch, D. R., F. Jenko, V. Bratanov, and A. Bañón Navarro. "Phase space scales of free energy dissipation in gradient-driven gyrokinetic turbulence." Journal of Plasma Physics 80, no. 4 (May 6, 2014): 531–51. http://dx.doi.org/10.1017/s0022377814000154.
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A reduced four-dimensional (integrated over perpendicular velocity) gyrokinetic model of slab ion temperature gradient-driven turbulence is used to study the phase-space scales of free energy dissipation in a turbulent kinetic system over a broad range of background gradients and collision frequencies. Parallel velocity is expressed in terms of Hermite polynomials, allowing for a detailed study of the scales of free energy dynamics over the four-dimensional phase space. A fully spectral code – the DNA code – that solves this system is described. Hermite free energy spectra are significantly steeper than would be expected linearly, causing collisional dissipation to peak at large scales in velocity space even for arbitrarily small collisionality. A key cause of the steep Hermite spectra is acritical balance– an equilibration of the parallel streaming time and the nonlinear correlation time – that extends to high Hermite numbern. Although dissipation always peaks at large scales in all phase space dimensions, small-scale dissipation becomes important in an integrated sense when collisionality is low enough and/or nonlinear energy transfer is strong enough. Toroidal full-gyrokinetic simulations using theGenecode are used to verify results from the reduced model. Collision frequencies typically found in present-day experiments correspond to turbulence regimes slightly favoring large-scale dissipation, while turbulence in low-collisionality systems like ITER and space and astrophysical plasmas is expected to rely increasingly on small-scale dissipation mechanisms. This work is expected to inform gyrokinetic reduced modeling efforts like Large Eddy Simulation and gyrofluid techniques.
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KOGAN, YAN I. "THE R→α′/R SPACE-TIME DUALITY FROM THE 2+1 POINT OF VIEW." Modern Physics Letters A 06, no. 06 (February 28, 1991): 501–15. http://dx.doi.org/10.1142/s0217732391000518.
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The duality between the large and small compactification radii in string theory (bosonic) is considered in the open topological membrane theory. The 2+1 analog of this R→α′/R duality is the duality between large and small scales in the corresponding topologically massive gauge theory with the spontaneous breaking of gauge invariance. This 2+1 duality is a consequence of the equivalence between the Chern-Simons theory with the mass term and the topologically massive gauge theory.
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Fiscaletti, D., B. Ganapathisubramani, and G. E. Elsinga. "Amplitude and frequency modulation of the small scales in a jet." Journal of Fluid Mechanics 772 (May 8, 2015): 756–83. http://dx.doi.org/10.1017/jfm.2015.227.
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The present study is an experimental investigation of the relationship between the large- and small-scale motions in the far field of an air jet at high Reynolds number. In the first part of our investigation, the analysis is based on time series of hot-wire anemometry (HWA), which are converted into space series after applying the Taylor hypothesis. By using a spectral filter, two signals are constructed, one representative of the large-scale motions ($2{\it\lambda}_{T}-L$, where ${\it\lambda}_{T}$ is the Taylor length scale, and $L$ is the integral length scale) and the other representative of the small-scale motions ($1.5{-}5{\it\eta}$, where ${\it\eta}$ is the Kolmogorov length scale). The small-scale signal is found to be modulated both in amplitude and in frequency by the energy-containing scales in an analogous way, both at the centreline and around the centreline. In particular, for positive fluctuations of the large-scale signal, the small-scale signal is locally stronger in amplitude (amplitude modulation), and it locally exhibits a higher number of local maxima and minima (frequency modulation). The extent of this modulation is quantified based on the strength of the large-scale fluctuations. The response of the small-scale motions to amplitude modulation can be considered instantaneous, being on the order of one Kolmogorov time scale. In the second part of our investigation we use long-range ${\it\mu}$PIV to study the behaviour of the small-scale motions in relation to their position in either high-speed or low-speed regions of the flow. The spatially resolved velocity vector fields allow us to quantify amplitude modulation directly in physical space. From this direct estimation in physical space, amplitude modulation is only 25 % of the value measured from HWA. The remaining 75 % comes from the fixed spectral band filter used to obtain the large- and small-scale signals, which does not consider the local convection velocity. A very similar overestimation of amplitude modulation when quantified in the time-frame is also obtained analytically. Furthermore, the size of the structures of intense vorticity does not change significantly in relation to the large-scale velocity fluctuation, meaning that there is no significant spatial frequency modulation. The remaining amplitude modulation in space can be explained as a statistical coupling between the strength of the structures of vorticity and their preferential location inside large-scale high-velocity regions. Finally, the implications that the present findings have on amplitude and frequency modulation in turbulent boundary layers (TBLs) are discussed.
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Wisniewski, W. Z. "Small telescopes and research from space." Symposium - International Astronomical Union 118 (1986): 323–24. http://dx.doi.org/10.1017/s0074180900151708.
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The number of artificial satellites dedicated to astrophysical research is increasing rapidly. Nearly 30 satellites currently under development or in the early planning stages will be in orbit within 10–12 years and will have more sensitive detectors and better data-processing technology as a result of current research. Many of the galactic and extragalactic objects discovered by the new technology are variable on surprisingly short time scales ranging from sub-seconds to many months. The new variable objects include but are not confined to: neutron and binary stars; quasars (and associated active centers of galaxies); newborn infrared stars and associated clouds; the coronal activity of main sequence stars; cataclysmic variables (white dwarfs in binaries); and novae, supernovae and remnants. We now realize that the short time-scale variations of many unusual stars and active galactic nuclei demand that ground and space data be taken as close in time as possible and that they be carefully planned and coordinated.
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Lohmann, Gerald. "Irradiance Variability Quantification and Small-Scale Averaging in Space and Time: A Short Review." Atmosphere 9, no. 7 (July 15, 2018): 264. http://dx.doi.org/10.3390/atmos9070264.
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The ongoing world-wide increase of installed photovoltaic (PV) power attracts notice to weather-induced PV power output variability. Understanding the underlying spatiotemporal volatility of solar radiation is essential to the successful outlining and stable operation of future power grids. This paper concisely reviews recent advances in the characterization of irradiance variability, with an emphasis on small spatial and temporal scales (respectively less than about 10 km and 1 min), for which comprehensive data sets have recently become available. Special attention is given to studies dealing with the quantification of variability using such unique data, the analysis and modeling of spatial smoothing, and the evaluation of temporal averaging.
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Falgarone, Edith. "Small Scale Structure in Nearby Molecular Gas." International Astronomical Union Colloquium 166 (1997): 251–60. http://dx.doi.org/10.1017/s0252921100071074.
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AbstractRecent observations at high angular resolution of molecular clouds of low column density have revealed the presence of a conspicuous net of small scale filamentary structures, visible in the 12CO rotational lines only. In addition, the existence of unresolved structure at scales as small as ~ 200 AU in space and/or velocity space is inferred from the spectral properties of the 12CO and 13CO emission. The resolved structures are part of the hierarchy of structures observed in molecular gas in the Solar Neighborhood and appear as non self-gravitating elements confined by an ambient pressure P0/kB ~ 3 × 104cm−3 K. We show why these structures might have their origin in the intermittent structures of turbulence in which viscous dissipation is concentrated in space and time.
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ARECCHI, F. T., S. BOCCALETTI, G. GIACOMELLI, G. P. PUCCIONI, P. L. RAMAZZA, and S. RESIDORI. "BOUNDARY DOMINATED VERSUS BULK DOMINATED REGIME IN OPTICAL SPACE-TIME COMPLEXITY." International Journal of Bifurcation and Chaos 04, no. 05 (October 1994): 1281–95. http://dx.doi.org/10.1142/s0218127494000976.
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By increasing the aspect ratio of an optical cavity with a photorefractive crystal, we observe the transition from a boundary-controlled regime, where the size of the transverse patterns scales with the aspect ratio, to a bulk-controlled regime where the pattern size is independent of the aspect ratio. In this new regime, the size corresponds to an intrinsic correlation length imposed by diffusion processes within the material. Such a new behavior is explained by the wave-number dependence of the gain within the instability region. Model equations provide good agreement with the two asymptotic cases of small aspect ratio (diffraction limited regime) and large aspect ratio (diffusion limited regime).
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Chen, Nan, Honghu Liu, and Fei Lu. "Shock trace prediction by reduced models for a viscous stochastic Burgers equation." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 4 (April 2022): 043109. http://dx.doi.org/10.1063/5.0084955.
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Viscous shocks are a particular type of extreme event in nonlinear multiscale systems, and their representation requires small scales. Model reduction can thus play an essential role in reducing the computational cost for the prediction of shocks. Yet, reduced models typically aim to approximate large-scale dominating dynamics, which do not resolve the small scales by design. To resolve this representation barrier, we introduce a new qualitative characterization of the space–time locations of shocks, named the “shock trace,” via a space–time indicator function based on an empirical resolution-adaptive threshold. Unlike exact shocks, the shock traces can be captured within the representation capacity of the large scales, thus facilitating the forecast of the timing and locations of the shocks utilizing reduced models. Within the context of a viscous stochastic Burgers equation, we show that a data-driven reduced model, in the form of nonlinear autoregression (NAR) time series models, can accurately predict the random shock traces, with relatively low rates of false predictions. Furthermore, the NAR model, which includes nonlinear closure terms to approximate the feedback from the small scales, significantly outperforms the corresponding Galerkin truncated model in the scenario of either noiseless or noisy observations. The results illustrate the importance of the data-driven closure terms in the NAR model, which account for the effects of the unresolved dynamics brought by nonlinear interactions.
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Yeung, P. K., James G. Brasseur, and Qunzhen Wang. "Dynamics of direct large-small scale couplings in coherently forced turbulence: concurrent physical- and Fourier-space views." Journal of Fluid Mechanics 283 (January 25, 1995): 43–95. http://dx.doi.org/10.1017/s0022112095002230.
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As discussed in a recent paper by Brasseur & Wei (1994), scale interactions in fully developed turbulence are of two basic types in the Fourier-spectral view. The cascade of energy from large to small scales is embedded within ‘local-to-non-local’ triadic interactions separated in scale by a decade or less. ‘Distant’ triadic interactions between widely disparate scales transfer negligible energy between the largest and smallest scales, but directly modify the structure of the smallest scales in relationship to the structure of the energy-dominated large scales. Whereas cascading interactions tend to isotropize the small scales as energy moves through spectral shells from low to high wavenumbers, distant interactions redistribute energy within spectral shells in a manner that leads to anisotropic redistributions of small-scale energy and phase in response to anisotropic structure in the large scales. To study the role of long-range interactions in small-scale dynamics, Yeung & Brasseur (1991) carried out a numerical experiment in which the marginally distant triads were purposely stimulated through a coherent narrow-band anisotropic forcing at the large scales readily interpretable in both the Fourier- and physical-space views. It was found that, after one eddy turnover time, the smallest scales rapidly became anisotropic as a direct consequence of the marginally distant triadic group in a manner consistent with the distant triadic equations. Because these asymptotic equations apply in the infinite Reynolds number limit, Yeung & Brasseur argued that the observed long-range effects should be applicable also at high Reynolds numbers.We continue the analysis of forced simulations in this study, focusing (i) on the detailed three-dimensional restructuring of the small scales as predicted by the asymptotic triadic equations, and (ii) on the relationship between Fourier- and physical-space evolution during forcing. We show that the three-dimensional restructuring of small-scale energy and vorticity in Fourier space from large-scale forcing is predicted in some detail by the distant triadic equations. We find that during forcing the distant interactions alter small-scale structure in two ways: energy is redistributed anisotropically within high-wavenumber spectral shells, and phase correlations are established at the small scales by the distant interactions. In the numerical experiments, the long-range interactions create two pairs of localized volumes of concentrated energy in three-dimensional Fourier space at high wavenumbers in which the Fourier modes are phase coupled. Each pair of locally phase-correlated volumes of Fourier modes separately corresponds to aligned vortex tubes in physical space in two orthogonal directions. We show that the dynamics of distant interactions in creating small-scale anisotropy may be described in physical space by differential advection and distortion of small-scale vorticity by the coherent large-scale energy-containing eddies, producing anisotropic alignment of small-scale vortex tubes.Scaling arguments indicate a disparity in timescale between distant triadic interactions and energy-cascading local-to-non-local interactions which increases with scale separation. Consequently, the small scales respond to forcing initially through the distant interactions. However, as energy cascades from the large-scale to the small-scale Fourier modes, the stimulated distant interactions become embedded within a sea of local-to-non-local energy cascading interactions which reduce (but do not eliminate) small-scale anisotropy at later times. We find that whereas the small-scale structure is still anisotropic at these later times, the second-order velocity moment tensor is insensitive to this anisotropy. Third-order moments, on the other hand, do detect the anisotropy. We conclude that whereas a single statistical measure of anisotropy can be used to indicate the presence of anisotropy, a null result in that measure does not necessarily imply that the signal is isotropic. The results indicate that non-equilibrium non-stationary turbulence is particularly sensitive to long-range interactions and deviations from local isotropy.
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Steinke, S., S. Eikenberg, U. Löhnert, G. Dick, D. Klocke, P. Di Girolamo, and S. Crewell. "Assessment of small-scale integrated water vapour variability during HOPE." Atmospheric Chemistry and Physics Discussions 14, no. 16 (September 8, 2014): 22837–79. http://dx.doi.org/10.5194/acpd-14-22837-2014.
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Abstract. The spatio-temporal variability of integrated water vapour (IWV) on small-scales of less than 10 km and hours is assessed with data from the two months of the High Definition Clouds and Precipitation for advancing Climate Prediction (HD(CP)2) Observational Prototype Experiment (HOPE). The statistical intercomparison of the unique set of observations during HOPE (microwave radiometer (MWR), Global Positioning System (GPS), sunphotometer, radiosondes, Raman Lidar, infrared and near infrared Moderate Resolution Imaging Spectroradiometer (MODIS) on the satellites Aqua and Terra) measuring close together reveals a good agreement in terms of standard deviation (≤ 1 kg m−2) and correlation coefficient (≥ 0.98). The exception is MODIS, which appears to suffer from insufficient cloud filtering. For a case study during HOPE featuring a typical boundary layer development, the IWV variability in time and space on scales of less than 10 km and less than 1 h is investigated in detail. For this purpose, the measurements are complemented by simulations with the novel ICOsahedral Non-hydrostatic modelling framework (ICON) which for this study has a horizontal resolution of 156 m. These runs show that differences in space of 3–4 km or time of 10–15 min induce IWV variabilities in the order of 4 kg m−2. This model finding is confirmed by observed time series from two MWRs approximately 3 km apart with a comparable temporal resolution of a few seconds. Standard deviations of IWV derived from MWR measurements reveal a high variability (> 1 kg m−2) even at very short time scales of a few minutes. These cannot be captured by the temporally lower resolved instruments and by operational numerical weather prediction models such as COSMO-DE (an application of the Consortium for Small-scale Modelling covering Germany) of Deutscher Wetterdienst, which is included in the comparison. However, for time scales larger than 1 h, a sampling resolution of 15 min is sufficient to capture the mean standard deviation of IWV. The present study shows that instrument sampling plays a major role when climatological information, in particular the mean diurnal cycle of IWV, is determined.
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Steinke, S., S. Eikenberg, U. Löhnert, G. Dick, D. Klocke, P. Di Girolamo, and S. Crewell. "Assessment of small-scale integrated water vapour variability during HOPE." Atmospheric Chemistry and Physics 15, no. 5 (March 9, 2015): 2675–92. http://dx.doi.org/10.5194/acp-15-2675-2015.
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Abstract. The spatio-temporal variability of integrated water vapour (IWV) on small scales of less than 10 km and hours is assessed with data from the 2 months of the High Definition Clouds and Precipitation for advancing Climate Prediction (HD(CP)2) Observational Prototype Experiment (HOPE). The statistical intercomparison of the unique set of observations during HOPE (microwave radiometer (MWR), Global Positioning System (GPS), sun photometer, radiosondes, Raman lidar, infrared and near-infrared Moderate Resolution Imaging Spectroradiometer (MODIS) on the satellites Aqua and Terra) measuring close together reveals a good agreement in terms of random differences (standard deviation ≤1 kg m−2) and correlation coefficient (≥ 0.98). The exception is MODIS, which appears to suffer from insufficient cloud filtering. For a case study during HOPE featuring a typical boundary layer development, the IWV variability in time and space on scales of less than 10 km and less than 1 h is investigated in detail. For this purpose, the measurements are complemented by simulations with the novel ICOsahedral Nonhydrostatic modelling framework (ICON), which for this study has a horizontal resolution of 156 m. These runs show that differences in space of 3–4 km or time of 10–15 min induce IWV variabilities on the order of 0.4 kg m−2. This model finding is confirmed by observed time series from two MWRs approximately 3 km apart with a comparable temporal resolution of a few seconds. Standard deviations of IWV derived from MWR measurements reveal a high variability (> 1 kg m−2) even at very short time scales of a few minutes. These cannot be captured by the temporally lower-resolved instruments and by operational numerical weather prediction models such as COSMO-DE (an application of the Consortium for Small-scale Modelling covering Germany) of Deutscher Wetterdienst, which is included in the comparison. However, for time scales larger than 1 h, a sampling resolution of 15 min is sufficient to capture the mean standard deviation of IWV. The present study shows that instrument sampling plays a major role when climatological information, in particular the mean diurnal cycle of IWV, is determined.
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Krocak, Makenzie J., and Harold E. Brooks. "Climatological Estimates of Hourly Tornado Probability for the United States." Weather and Forecasting 33, no. 1 (January 3, 2018): 59–69. http://dx.doi.org/10.1175/waf-d-17-0123.1.
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Abstract While there has been an abundance of research dedicated to the seasonal climatology of severe weather, very little has been done to study hazardous weather probabilities on smaller scales. To this end, local hourly climatological estimates of tornadic event probabilities were developed using storm reports from NOAA’s Storm Prediction Center. These estimates begin the process of analyzing tornado frequencies on a subdaily scale. Characteristics of the local tornado climatology are investigated, including how the diurnal cycle varies in space and time. Hourly tornado probabilities are peaked for both the annual and diurnal cycles in the plains, whereas the southeast United States has a more variable pattern. Areas that have similar total tornado threats but differ in the distribution of that threat are highlighted. Additionally, areas that have most of the tornado threat concentrated in small time frames both annually and diurnally are compared to areas that have a low-level threat at all times. These differences create challenges related to staffing requirements and background understanding of the tornado threat unique to each region. This work is part of a larger effort to provide background information for probabilistic forecasts of hazardous weather that are meaningful over broad time and space scales, with a focus on scales broader than the typical time and space scales of the events of interest (including current products on the “watch” scale). A large challenge remains to continue describing probabilities as the time and space scales of the forecast become comparable to the scale of the event.
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Macêdo, Antônio, Iván González, Ernesto Raposo, Leonardo Menezes, and Anderson Gomes. "Turbulent Intermittency in a Random Fiber Laser." Atoms 7, no. 2 (April 9, 2019): 43. http://dx.doi.org/10.3390/atoms7020043.
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In fluid turbulence, intermittency is the emergence of non-Gaussian tails in the distribution of velocity increments in small space and/or time scales. Intermittence is thus expected to gradually disappear as one moves from small to large scales. Here we study the turbulent-like intermittency effect experimentally observed in the distribution of intensity fluctuations in a disordered continuous-wave-pumped erbium-doped-based random fiber laser with specially-designed random fiber Bragg gratings. The intermittency effect is investigated as a crossover in the distribution of intensity increments from a heavy-tailed distribution (for short time scales), to a Gaussian distribution (for large time scales). The results are theoretically supported by a hierarchical stochastic model that incorporates Kolmogorov’s theory of turbulence. In particular, the discrete version of the hierachical model allows a general direct interpretation of the number of relevant scales in the photonic hierarchy as the order of the transitions induced by the non-linearities in the medium. Our results thus provide further statistical evidence for the interpretation of the turbulence-like emission previously observed in this system.
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Birkin, Mark, Kirk Harland, Nicolas Malleson, Philip Cross, and Martin Clarke. "An Examination of Personal Mobility Patterns in Space and Time Using Twitter." International Journal of Agricultural and Environmental Information Systems 5, no. 3 (July 2014): 55–72. http://dx.doi.org/10.4018/ijaeis.2014070104.
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New sources of data relating to personal mobility and activity patterns are now providing a unique opportunity to explore movement patterns at increasing scales of spatial and temporal refinement. In this article, a corpus of messages from the Twitter social networking platform are examined. An elementary classification of users is proposed on the basis of frequency of use in space and time. The behaviour of different user groups is investigated across small areas in the major conurbation of Leeds. Substantial variations can be detected in the configuration of individual networks. An interpretation of the patterns which result is provided in terms of the underlying demographic structures, and the basic form and function of the urban area.
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Caldwell, Robert R. "A gravitational puzzle." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1957 (December 28, 2011): 4998–5002. http://dx.doi.org/10.1098/rsta.2011.0284.
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The challenge to understand the physical origin of the cosmic acceleration is framed as a problem of gravitation. Specifically, does the relationship between stress–energy and space–time curvature differ on large scales from the predictions of general relativity. In this article, we describe efforts to model and test a generalized relationship between the matter and the metric using cosmological observations. Late-time tracers of large-scale structure, including the cosmic microwave background, weak gravitational lensing, and clustering are shown to provide good tests of the proposed solution. Current data are very close to proving a critical test, leaving only a small window in parameter space in the case that the generalized relationship is scale free above galactic scales.
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Hu, W., and B. C. Si. "Estimating spatially distributed soil water content at small watershed scales based on decomposition of temporal anomaly and time stability analysis." Hydrology and Earth System Sciences Discussions 12, no. 7 (July 3, 2015): 6467–503. http://dx.doi.org/10.5194/hessd-12-6467-2015.
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Abstract. Soil water content (SWC) at watershed scales is crucial to rainfall–runoff response. A model was used to decompose spatiotemporal SWC into time-stable pattern (i.e., temporal mean), space-invariant temporal anomaly, and space-variant temporal anomaly. This model was compared with a previous model that decomposes spatiotemporal SWC into spatial mean and spatial anomaly. The space-variant temporal anomaly or spatial anomaly was further decomposed using the empirical orthogonal function for estimating spatially distributed SWC. These two models are termed temporal anomaly (TA) model and spatial anomaly (SA) model, respectively. We aimed to test the hypothesis that underlying (i.e., time-invariant) spatial patterns exist in the space-variant temporal anomaly at the small watershed scale, and to examine the advantages of the TA model over the SA model in terms of estimation of spatially distributed SWC. For this purpose, a SWC dataset of near surface (0–0.2 m) and root zone (0–1.0 m) from a small watershed scale in the Canadian prairies was analyzed. Results showed that underlying spatial patterns exist in the space-variant temporal anomaly because of the permanent controls of "static" factors such as depth to the CaCO3 layer and organic carbon content. Combined with time stability analysis, the TA model improved estimation of spatially distributed SWC over the SA model because the latter failed to capture the space-variant temporal anomaly which accounted for non-negligible amounts of spatial variance in SWC. The outperformance was greater when SWC deviated from intermediate conditions, especially for dry conditions. Therefore, the TA model has potential to construct a spatially distributed SWC at watershed scales from remote sensed SWC.
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Bugmann, Harald. "Vom Kleinen zum Grossen in der langfristigen Walddynamik: Die Bedeutung verschiedener Massstabsebenen | Moving from the small to large in longterm forest dynamics: the importance of scaling issues." Schweizerische Zeitschrift fur Forstwesen 152, no. 5 (May 1, 2001): 193–98. http://dx.doi.org/10.3188/szf.2001.0193.
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The dynamics of forest ecosystems span very large ranges of time and space, from milliseconds to millennia and from square millimeters to the entire globe. Experiments and observations,however, are typically performed on small patches of land and for relatively short time spans. Thus, the problem arises as to how forest science can answer questions related to the development of forests under the impacts of changes in the socio-economic, political, physical and chemical environment in the 21st century. The concept of scale and the transition between different scales, so-called scaling, are introduced, and methods for the scaling of ecological information are discussed. Scaling questions can be answered by direct observation or experimentation,but such studies tend to be very expensive because they be performed over long periods of time and on several spatial scales. As an alternative, mathematical models that are based on hierarchy theory can be used to address scaling issues. Three examples are used to illustrate how ecological information can be scaled from small areas and short times to larger areas and long periods. Problems arising with hierarchy theory are also addressed.
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Carreira, Cátia, Júlia Porto Silva Carvalho, Samantha Talbot, Isabel Pereira, and Christian Lønborg. "Small-scale distribution of microbes and biogeochemistry in the Great Barrier Reef." PeerJ 8 (October 21, 2020): e10049. http://dx.doi.org/10.7717/peerj.10049.
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Microbial communities distribute heterogeneously at small-scales (mm-cm) due to physical, chemical and biological processes. To understand microbial processes and functions it is necessary to appreciate microbes and matter at small scales, however, few studies have determined microbial, viral, and biogeochemical distribution over space and time at these scales. In this study, the small-scale spatial and temporal distribution of microbes (bacteria and chlorophyll a), viruses, dissolved inorganic nutrients and dissolved organic carbon were determined at five locations (spatial) along the Great Barrier Reef (Australia), and over 4 consecutive days (temporal) at a coastal location. Our results show that: (1) the parameters show high small-scale heterogeneity; (2) none of the parameters measured explained the bacterial abundance distributions at these scales spatially or temporally; (3) chemical (ammonium, nitrate/nitrite, phosphate, dissolved organic carbon, and total dissolved nitrogen) and biological (chl a, and bacterial and viral abundances) measurements did not reveal significant relationships at the small scale; and (4) statistically significant differences were found between sites/days for all parameter measured but without a clear pattern.
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Kepert, Jeffrey D. "Time and Space Scales in the Tropical Cyclone Boundary Layer, and the Location of the Eyewall Updraft." Journal of the Atmospheric Sciences 74, no. 10 (September 22, 2017): 3305–23. http://dx.doi.org/10.1175/jas-d-17-0077.1.
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Abstract The transient response of the tropical cyclone boundary layer is studied using linearized and nonlinear models, with particular focus on the frictionally forced vertical motion. The impulsively started, linearized tropical cyclone boundary layer is shown to adjust to its equilibrium solution via a series of decaying oscillations with the inertial period . In the nonlinear case, the oscillation period is slightly lengthened by inward advection of the slower-evolving flow from larger radii, but the oscillations decay more quickly. In an idealized cyclone with small sinusoidal oscillations superimposed on the gradient wind, the equilibrium nonlinear boundary layer acts as a low-pass filter with pass length scaling as , where is the 10-m frictional inflow. This filter is absent from the linearized boundary layer. The eyewall frictional updraft is similarly displaced inward of the radius of maximum winds (RMW) by a distance that scales with , owing to nonlinear overshoot of the inflowing air as it crosses the relatively sharp increase in I near the eyewall. This displacement is smaller (other things being equal) when the RMW is small, and greater when it is large, including in secondary eyewalls. The dependence of this distance on may explain, at least partially, why observed RMW are seldom less than 20 km, why storms with relatively peaked radial profiles of wind speed can intensify more rapidly, and why some secondary eyewalls initially contract rapidly with little intensification, then contract more slowly while intensifying.
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Hu, W., and B. C. Si. "Estimating spatially distributed soil water content at small watershed scales based on decomposition of temporal anomaly and time stability analysis." Hydrology and Earth System Sciences 20, no. 1 (February 2, 2016): 571–87. http://dx.doi.org/10.5194/hess-20-571-2016.
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Abstract. Soil water content (SWC) is crucial to rainfall-runoff response at the watershed scale. A model was used to decompose the spatiotemporal SWC into a time-stable pattern (i.e., temporal mean), a space-invariant temporal anomaly, and a space-variant temporal anomaly. The space-variant temporal anomaly was further decomposed using the empirical orthogonal function (EOF) for estimating spatially distributed SWC. This model was compared to a previous model that decomposes the spatiotemporal SWC into a spatial mean and a spatial anomaly, with the latter being further decomposed using the EOF. These two models are termed the temporal anomaly (TA) model and spatial anomaly (SA) model, respectively. We aimed to test the hypothesis that underlying (i.e., time-invariant) spatial patterns exist in the space-variant temporal anomaly at the small watershed scale, and to examine the advantages of the TA model over the SA model in terms of the estimation of spatially distributed SWC. For this purpose, a data set of near surface (0–0.2 m) and root zone (0–1.0 m) SWC, at a small watershed scale in the Canadian Prairies, was analyzed. Results showed that underlying spatial patterns exist in the space-variant temporal anomaly because of the permanent controls of static factors such as depth to the CaCO3 layer and organic carbon content. Combined with time stability analysis, the TA model improved the estimation of spatially distributed SWC over the SA model, especially for dry conditions. Further application of these two models demonstrated that the TA model outperformed the SA model at a hillslope in the Chinese Loess Plateau, but the performance of these two models in the GENCAI network (∼ 250 km2) in Italy was equivalent. The TA model can be used to construct a high-resolution distribution of SWC at small watershed scales from coarse-resolution remotely sensed SWC products.
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Zhang, Rui, and Keming Ma. "New Prospects to Systematically Improve the Particulate Matter Removal Efficiency of Urban Green Spaces at Multi-Scales." Forests 14, no. 2 (January 18, 2023): 175. http://dx.doi.org/10.3390/f14020175.
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Previous studies on the removal of airborne particulate matter (PM) by plants have mostly focused on the individual scale, hence there is a lack of systematic understanding of how to improve the PM removal effect of green spaces (GS) at multi-scales. We provide new insights into an integrated model, which integrates the utilization efficiency of vertical space and time into the multi-cycle PM removal model developed in our previous study. By analyzing the variabilities of the influencing factors at different scales, directions to improve this function at multiple scales can be proposed. According to the planning of urban GS, five scales were divided. At the species scale, plants should not only have the characteristics to match the local climate, but also a high utilization efficiency of time and space. At the community scale, increasing the hierarchy and structural complexity can help improve the utilization of vertical space. At the patch and landscape scales, the factor affecting the PM removal efficiency of GS lie in precipitation frequency, and large/small green patches with low/high landscape fragmentation in climates with low/high precipitation frequency are recommended. At the urban scale, it is necessary to increase the degree of temporal and spatial distribution matching between PM and GS. These findings can improve urban GS planning to contribute to the removal of airborne PM.
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Koenig, T., D. Studer, D. Hubl, L. Melie, and W. K. Strik. "Brain connectivity at different time-scales measured with EEG." Philosophical Transactions of the Royal Society B: Biological Sciences 360, no. 1457 (May 29, 2005): 1015–24. http://dx.doi.org/10.1098/rstb.2005.1649.
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We present an overview of different methods for decomposing a multichannel spontaneous electroencephalogram (EEG) into sets of temporal patterns and topographic distributions. All of the methods presented here consider the scalp electric field as the basic analysis entity in space. In time, the resolution of the methods is between milliseconds (time-domain analysis), subseconds (time- and frequency-domain analysis) and seconds (frequency-domain analysis). For any of these methods, we show that large parts of the data can be explained by a small number of topographic distributions. Physically, this implies that the brain regions that generated one of those topographies must have been active with a common phase. If several brain regions are producing EEG signals at the same time and frequency, they have a strong tendency to do this in a synchronized mode. This view is illustrated by several examples (including combined EEG and functional magnetic resonance imaging (fMRI)) and a selective review of the literature. The findings are discussed in terms of short-lasting binding between different brain regions through synchronized oscillations, which could constitute a mechanism to form transient, functional neurocognitive networks.
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CASUSO, E. "INTEGRAL TREATMENT FOR TIME EVOLUTION: THE GENERAL INTERACTIVITY." International Journal of Modern Physics A 14, no. 20 (August 10, 1999): 3239–52. http://dx.doi.org/10.1142/s0217751x99001524.
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Assuming that the unpredictability associated with many dynamical systems is an artefact of the differential treatment of their time evolution, we propose here an integral treatment as an alternative. We make the assumption that time is two-dimensional, and that the time distribution in the past of observables characterizing the dynamical system, is some characteristic "projection" of its time distribution in the future. We show here how this method can be used to predict the time evolution of several dynamically complex systems over long time intervals. The present work can be considered as the natural next step to the assumption of nonderivability for subatomic dynamical systems to explain the connection between Quantum Mechanics and General Relativity. Here we propose that matter and space–time are not only nonderivable but also show structural discontinuity. Starting with this premise we use continuity and derivability, but only as a first order approximation to reality. Extrapolation to very large or very small scales, or to predictions over long time scales for many natural systems on intermediate scales (human scales), may lead to chaotic behavior, or to nondeterministic or probabilistic theories.
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Djadaojee, Lionel, Albane Douillet, and Jules Grucker. "Stimulated Brillouin gain spectroscopy in a confined spatio-temporal domain (30 μm, 170 ns)." European Physical Journal Applied Physics 89, no. 3 (March 2020): 30701. http://dx.doi.org/10.1051/epjap/2020200012.
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The Brillouin gain spectrum of a test sample (liquid acetone at room temperature) on scales simultaneously confined in space (~30 μm) and time (~170 ns) is reported. This is done using a pulsed stimulated Brillouin scattering gain spectrometer in a θ ≈ 90° crossing beam configuration. After having identified and corrected for different sources of background signals, we obtained a Brillouin gain spectrum allowing an accurate measurement (MHz range) of the Brillouin frequency (few GHz). This is of interest for probing acoustic properties of transparent media subjected to repetitive fast transient phenomena on small length scales.
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Morabito, L. K., and J. Silk. "Reaching small scales with low-frequency imaging: applications to the Dark Ages." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2188 (November 23, 2020): 20190571. http://dx.doi.org/10.1098/rsta.2019.0571.
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The initial conditions for the density perturbations in the early Universe, which dictate the large-scale structure and distribution of galaxies we see today, are set during inflation. Measurements of primordial non-Gaussianity are crucial for distinguishing between different inflationary models. Current measurements of the matter power spectrum from the cosmic microwave background only constrain this on scales up to k ∼ 0.1 Mpc −1 . Reaching smaller angular scales (higher values of k ) can provide new constraints on non-Gaussianity. A powerful way to do this is by measuring the HI matter power spectrum at z ≳ 30 . In this paper, we investigate what values of k can be reached for the Low-Frequency Array (LOFAR), which can achieve ≲ 1″ resolution at approximately 50 MHz. Combining this with a technique to isolate the spectrally smooth foregrounds to a wedge in k ∥ – k ⊥ space, we demonstrate what values of k we can feasibly reach within observational constraints. We find that LOFAR is approximately five orders of magnitude away from the desired sensitivity, for 10 years of integration time. This article is part of a discussion meeting issue ‘Astronomy from the Moon: the next decades’.
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Qiu, Yutong, and Carl Kingsford. "Constructing small genome graphs via string compression." Bioinformatics 37, Supplement_1 (July 1, 2021): i205—i213. http://dx.doi.org/10.1093/bioinformatics/btab281.
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Abstract Motivation The size of a genome graph—the space required to store the nodes, node labels and edges—affects the efficiency of operations performed on it. For example, the time complexity to align a sequence to a graph without a graph index depends on the total number of characters in the node labels and the number of edges in the graph. This raises the need for approaches to construct space-efficient genome graphs. Results We point out similarities in the string encoding mechanisms of genome graphs and the external pointer macro (EPM) compression model. We present a pair of linear-time algorithms that transform between genome graphs and EPM-compressed forms. The algorithms result in an upper bound on the size of the genome graph constructed in terms of an optimal EPM compression. To further reduce the size of the genome graph, we propose the source assignment problem that optimizes over the equivalent choices during compression and introduce an ILP formulation that solves that problem optimally. As a proof-of-concept, we introduce RLZ-Graph, a genome graph constructed based on the relative Lempel–Ziv algorithm. Using RLZ-Graph, across all human chromosomes, we are able to reduce the disk space to store a genome graph on average by 40.7% compared to colored compacted de Bruijn graphs constructed by Bifrost under the default settings. The RLZ-Graph scales well in terms of running time and graph sizes with an increasing number of human genome sequences compared to Bifrost and variation graphs produced by VGtoolkit. Availability The RLZ-Graph software is available at: https://github.com/Kingsford-Group/rlzgraph. Supplementary information Supplementary data are available at Bioinformatics online.
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Webber, S., and M. R. Jeffrey. "Loss of Determinacy at Small Scales, with Application to Multiple Timescale and Nonsmooth Dynamics." International Journal of Bifurcation and Chaos 31, no. 03 (March 15, 2021): 2150041. http://dx.doi.org/10.1142/s0218127421500413.
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A singularity is described that creates a forward time loss of determinacy in a two-timescale system, in the limit where the timescale separation is large. We describe how the situation can arise in a dynamical system of two fast variables and three slow variables or parameters, with weakly coupling between the fast variables. A wide set of initial conditions enters the [Formula: see text]-neighborhood of the singularity, and explodes back out of it to fill a large region of phase space, all in finite time. The scenario has particular significance in the application to piecewise-smooth systems, where it arises in the blow up of dynamics at a discontinuity and is followed by abrupt recollapse of solutions to “hide” the loss of determinacy, and yet leave behind a remnant of it in the global dynamics. This constitutes a generalization of a “micro-slip” phenomenon found recently in spring-coupled blocks, whereby coupled oscillators undergo unpredictable stick-slip-stick sequences instigated by a higher codimension form of the singularity. The indeterminacy is localized to brief slips events, but remains evident in the indeterminate sequencing of near-simultaneous slips of multiple blocks.
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Dimitriadis, Panayiotis, Theano Iliopoulou, G. Fivos Sargentis, and Demetris Koutsoyiannis. "Spatial Hurst–Kolmogorov Clustering." Encyclopedia 1, no. 4 (September 29, 2021): 1010–25. http://dx.doi.org/10.3390/encyclopedia1040077.
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The stochastic analysis in the scale domain (instead of the traditional lag or frequency domains) is introduced as a robust means to identify, model and simulate the Hurst–Kolmogorov (HK) dynamics, ranging from small (fractal) to large scales exhibiting the clustering behavior (else known as the Hurst phenomenon or long-range dependence). The HK clustering is an attribute of a multidimensional (1D, 2D, etc.) spatio-temporal stationary stochastic process with an arbitrary marginal distribution function, and a fractal behavior on small spatio-temporal scales of the dependence structure and a power-type on large scales, yielding a high probability of low- or high-magnitude events to group together in space and time. This behavior is preferably analyzed through the second-order statistics, and in the scale domain, by the stochastic metric of the climacogram, i.e., the variance of the averaged spatio-temporal process vs. spatio-temporal scale.
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Zhao, Sijian, and Qiao Zhang. "Risk Assessment of Crops Induced by Flood in the Three Northeastern Provinces of China on Small Space-and-Time Scales." Journal of Risk Analysis and Crisis Response 2, no. 3 (2012): 201. http://dx.doi.org/10.2991/jrarc.2012.2.3.7.
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Pfeffer, Julia, Cédric Champollion, Guillaume Favreau, Bernard Cappelaere, Jacques Hinderer, Marie Boucher, Yahaya Nazoumou, et al. "Evaluating surface and subsurface water storage variations at small time and space scales from relative gravity measurements in semiarid Niger." Water Resources Research 49, no. 6 (June 2013): 3276–91. http://dx.doi.org/10.1002/wrcr.20235.
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Génot, V., P. Louarn, and F. Mottez. "Alfvén wave interaction with inhomogeneous plasmas: acceleration and energy cascade towards small-scales." Annales Geophysicae 22, no. 6 (June 14, 2004): 2081–96. http://dx.doi.org/10.5194/angeo-22-2081-2004.
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Abstract. Investigating the process of electron acceleration in auroral regions, we present a study of the temporal evolution of the interaction of Alfvén waves (AW) with a plasma inhomogeneous in a direction transverse to the static magnetic field. This type of inhomogeneity is typical of the density cavities extended along the magnetic field in auroral acceleration regions. We use self-consistent Particle In Cell (PIC) simulations which are able to reproduce the full nonlinear evolution of the electromagnetic waves, as well as the trajectories of ions and electrons in phase space. Physical processes are studied down to the ion Larmor radius and electron skin depth scales. We show that the AW propagation on sharp density gradients leads to the formation of a significant parallel (to the magnetic field) electric field (E-field). It results from an electric charge separation generated on the density gradients by the polarization drift associated with the time varying AW E-field. Its amplitude may reach a few percents of the AW E-field. This parallel component accelerates electrons up to keV energies over a distance of a few hundred Debye lengths, and induces the formation of electron beams. These beams trigger electrostatic plasma instabilities which evolve toward the formation of nonlinear electrostatic structures (identified as electron holes and double layers). When the electrostatic turbulence is fully developed we show that it reduces the further wave/particle exchange. This sequence of mechanisms is analyzed with the program WHAMP, to identify the instabilities at work and wavelet analysis techniques are used to characterize the regime of energy conversions (from electromagnetic to electrostatic structures, from large to small length scales). This study elucidates a possible scenario to account for the particle acceleration and the wave dissipation in inhomogeneous plasmas. It would consist of successive phases of acceleration along the magnetic field, the development of an electrostatic turbulence, the thermalization and the heating of the plasma. Space plasma physics (charged particle motion and acceleration; numerical studies).
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Price, Victoria E., Peter J. Auster, and Laura Kracker. "Use of High-Resolution DIDSON Sonar to Quantify Attributes of Predation at Ecologically Relevant Space and Time Scales." Marine Technology Society Journal 47, no. 1 (January 1, 2013): 33–46. http://dx.doi.org/10.4031/mtsj.47.1.6.
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AbstractPredator-prey interactions of large vagile fishes are difficult to study in the ocean due to limitations in the space and time requirements for observations. Small-scale direct underwater observations by divers (ca. <10 m radius) and large-scale hydroacoustic surveys (10 s m2 to 100 s km2) are traditional approaches for surveying fish. However, large piscivorous predators identify and attack prey at the scale of meters to tens of meters. Dual-Frequency Identification Sonar (or DIDSON) is a high-resolution acoustic camera operating in the MHz range that provides detailed continuous video-like imaging of objects up to a range of 30 m. This technology can be used to observe predator-prey interactions at ecologically relevant space and time scales often missed by traditional methods. Here we establish an approach for quantifying predation-related behaviors from DIDSON records. Metrics related to predator and prey group size, prey responses to predation, predation rate, predator strategies, and the nonrandom use of landscape features by both predator and prey are described. In addition, relationships between patterns in these attributes are tested and issues regarding sampling strategies for future studies are discussed. We suggest that approaches combining direct visual observation and acoustic sampling at multiple scales are required to quantify variation in these relationships across underwater landscapes.
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Yoccoz, N. G., and R. A. Ims. "Spatial population dynamics of small mammals: some methodological and practical issues." Animal Biodiversity and Conservation 27, no. 1 (June 1, 2004): 427–35. http://dx.doi.org/10.32800/abc.2004.27.0427.
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Small mammals have been widely used to further our understanding of spatial and temporal population dynamical patterns, because their dynamics exhibit large variations, both in time (multi-annual cycles vs. seasonal variation only) and space (regional synchrony, travelling waves). Small mammals have therefore been the focus of a large number of empirical and statistical (analysis of time-series) studies, mostly based on trapping indices. These studies did not take into account sampling variability associated with the use of counts or estimates of population size. In this paper, we use our field study focusing on population dynamics and demography of small mammals in North Norway at three spatial scales (0.1, 10 and 100 km) to illustrate some methodological and practical issues. We first investigate the empirical patterns of spatial population dynamics, focusing on correlation among time-series of population abundance at increasing spatial scales. We then assess using simulated data the bias of estimates of spatial correlation induced by using either population indices such as the number of individuals captured (i.e., raw counts) or estimates of population size derived from statistical modeling of capture-recapture data. The problems encountered are similar to those described when assessing density-dependence in time-series -a special case of the consequence of measurement error for estimates of regression coefficients- but are to our knowledge ignored in the ecological literature. We suggest some empirical solutions as well as more rigorous approaches.
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Yuan, Yuman, Hongyang Bai, Panfeng Wu, Hongwei Guo, Tianyu Deng, and Weiwei Qin. "An Intelligent Detection Method for Small and Weak Objects in Space." Remote Sensing 15, no. 12 (June 18, 2023): 3169. http://dx.doi.org/10.3390/rs15123169.
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In the case of a boom in space resource development, space debris will increase dramatically and cause serious problems for the spacecraft in orbit. To address this problem, a novel context sensing-YOLOv5 (CS-YOLOv5) is proposed for small and weak space object detection, which could realize the extraction of local context information and the enhancement and fusion of spatial information. To enhance the expression ability of feature information and the identification ability of the network, we propose the cross-layer context fusion module (CCFM) through multiple branches in parallel to learn the context information of different scales. At the same time, to map the small-scale features sequentially to the features of the previous layer, we design the adaptive weighting module (AWM) to assist the CCFM in further enhancing the expression of features. Additionally, to solve the problem that the spatial information of small objects is easily lost, we designed the spatial information enhancement module (SIEM) to adaptively learn the weak spatial information of small objects that need to be protected. To further enhance the generalization ability of CS-YOLOv5, we propose a contrast mosaic data augmentation to enrich the diversity of the sample. Extensive experiments are conducted on self-built datasets, which strongly prove the effectiveness of our method in space object detection.
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Zakharov, Sergey V. "EVOLUTION OF A MULTISCALE SINGULARITY OF THE SOLUTION OF THE BURGERS EQUATION IN THE 4-DIMENSIONAL SPACE–TIME." Ural Mathematical Journal 8, no. 1 (July 29, 2022): 136. http://dx.doi.org/10.15826/umj.2022.1.012.
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The solution of the Cauchy problem for the vector Burgers equation with a small parameter of dissipation \(\varepsilon\) in the \(4\)-dimensional space-time is studied: $$ \mathbf{u}_t + (\mathbf{u}\nabla) \mathbf{u} = \varepsilon \triangle \mathbf{u}, \quad u_{\nu} (\mathbf{x}, -1, \varepsilon) = - x_{\nu} + 4^{-\nu}(\nu + 1) x_{\nu}^{2\nu + 1}, $$ With the help of the Cole–Hopf transform \(\mathbf{u} = - 2 \varepsilon \nabla \ln H,\) the exact solution and its leading asymptotic approximation, depending on six space-time scales, near a singular point are found. A formula for the growth of partial derivatives of the components of the vector field \(\mathbf{u}\) on the time interval from the initial moment to the singular point, called the formula of the gradient catastrophe, is established: $$ \frac{\partial u_{\nu} (0, t, \varepsilon)}{\partial x_{\nu}} = \frac{1}{t} \left[ 1 + O \left( \varepsilon |t|^{- 1 - 1/\nu} \right) \right]\!, \quad \frac{t}{\varepsilon^{\nu /(\nu + 1)} } \to -\infty, \quad t \to -0.$$The asymptotics of the solution far from the singular point, involving a multistep reconstruction of the space-time scales, is also obtained: $$ u_{\nu} (\mathbf{x}, t, \varepsilon) \approx - 2 \left( \frac{t}{\nu + 1} \right)^{1/2\nu} \tanh \left[ \frac{x_{\nu}}{\varepsilon} \left( \frac{t}{\nu + 1} \right)^{1/2\nu} \right]\!, \quad \frac{t}{\varepsilon^{\nu /(\nu + 1)} } \to +\infty. $$
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Uteng, Stig, Thomas Haugland Johansen, Jose Ignacio Zaballos, Samuel Ortega, Lasse Holmström, Gustavo M. Callico, Himar Fabelo, and Fred Godtliebsen. "Early Detection of Change by Applying Scale-Space Methodology to Hyperspectral Images." Applied Sciences 10, no. 7 (March 27, 2020): 2298. http://dx.doi.org/10.3390/app10072298.
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Given an object of interest that evolves in time, one often wants to detect possible changes in its properties. The first changes may be small and occur in different scales and it may be crucial to detect them as early as possible. Examples include identification of potentially malignant changes in skin moles or the gradual onset of food quality deterioration. Statistical scale-space methodologies can be very useful in such situations since exploring the measurements in multiple resolutions can help identify even subtle changes. We extend a recently proposed scale-space methodology to a technique that successfully detects such small changes and at the same time keeps false alarms at a very low level. The potential of the novel methodology is first demonstrated with hyperspectral skin mole data artificially distorted to include a very small change. Our real data application considers hyperspectral images used for food quality detection. In these experiments the performance of the proposed method is either superior or on par with a standard approach such as principal component analysis.
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Buscaglia, G. C., and M. Jai. "Homogenization of the Generalized Reynolds Equation for Ultra-Thin Gas Films and Its Resolution by FEM." Journal of Tribology 126, no. 3 (June 28, 2004): 547–52. http://dx.doi.org/10.1115/1.1739410.
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We address the numerical modeling of roughness or texture effects in ultra-thin gas films. Rarefaction (high Knudsen number) effects are dealt with using the Generalized Reynolds Equation, and a homogenization procedure is proposed to rigorously account for arbitrary roughness/texture shapes. The presentation is focused on head-disk magnetic storage devices, but the techniques proposed are general. Some details of the implementation, along with numerical tests, are included. By removing the small space and time scales from the problem, the methodology allows for efficient modeling of slider bearings with small-scale features.
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Harutyunian, Haik A. "Are the “Physically Bound Systems” beyond the Cosmological Expansion Effect? (A provocative musing on the given theme)." Proceedings of the International Astronomical Union 9, S304 (October 2013): 391–94. http://dx.doi.org/10.1017/s1743921314004384.
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AbstractInfluence of the dark energy at small scales is considered. Interaction and energy exchange between ordinary matter and dark energy is proposed as a working hypothesis. Some observational facts are put into the base of this consideration: the large rate of lunar retreat and the acceleration of cosmic expansion which proves the energy exchange between ordinary matter and dark energy. If the possibility of the space and matter expansion at the scales under consideration is accepted one can show that the dark energy transformed into the object's potential energy is enough to generate cluster of galaxies over the Hubble time due to matter ejection mechanism.
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Li, Yijia, Jing Wang, Zhengfang Wang, Qingmei Sui, and Ziming Xiong. "Microseismic P-Wave Travel Time Computation and 3D Localization Based on a 3D High-Order Fast Marching Method." Sensors 21, no. 17 (August 29, 2021): 5815. http://dx.doi.org/10.3390/s21175815.
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The travel time computation of microseismic waves in different directions (particularly, the diagonal direction) in three-dimensional space has been found to be inaccurate, which seriously affects the localization accuracy of three-dimensional microseismic sources. In order to solve this problem, this research study developed a method of calculating the P-wave travel time based on a 3D high-order fast marching method (3D_H_FMM). This study focused on designing a high-order finite-difference operator in order to realize the accurate calculation of the P-wave travel time in three-dimensional space. The method was validated using homogeneous velocity models and inhomogeneous layered media velocity models of different scales. The results showed that the overall mean absolute error (MAE) of the two homogenous models using 3D_H_FMM had been reduced by 88.335%, and 90.593% compared with the traditional 3D_FMM. On that basis, the three-dimensional localization of microseismic sources was carried out using a particle swarm optimization algorithm. The developed 3D_H_FMM was used to calculate the travel time, then to conduct the localization of the microseismic source in inhomogeneous models. The mean error of the localization results of the different positions in the three-dimensional space was determined to be 1.901 m, and the localization accuracy was found to be superior to that of the traditional 3D_FMM method (mean absolute localization error: 3.447 m) with the small-scaled inhomogeneous model.
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JEJJALA, VISHNU, and DJORDJE MINIC. "WHY THERE IS SOMETHING SO CLOSE TO NOTHING: TOWARDS A FUNDAMENTAL THEORY OF THE COSMOLOGICAL CONSTANT." International Journal of Modern Physics A 22, no. 10 (April 20, 2007): 1797–818. http://dx.doi.org/10.1142/s0217751x07036336.
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The cosmological constant problem is turned around to argue for a new foundational physics postulate underlying a consistent quantum theory of gravity and matter, such as string theory. This postulate is a quantum equivalence principle which demands a consistent gauging of the geometric structure of canonical quantum theory. We argue that string theory can be formulated to accommodate such a principle, and that in such a theory the observed cosmological constant is a fluctuation about a zero value. This fluctuation arises from an uncertainty relation involving the cosmological constant and the effective volume of space–time. The measured, small vacuum energy is dynamically tied to the large "size" of the universe, thus violating naive decoupling between small and large scales. The numerical value is related to the scale of cosmological supersymmetry breaking, supersymmetry being needed for a nonperturbative stability of local Minkowski space–time regions in the classical regime.
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Roland, Per E. "Space-Time Dynamics of Membrane Currents Evolve to Shape Excitation, Spiking, and Inhibition in the Cortex at Small and Large Scales." Neuron 94, no. 5 (June 2017): 934–42. http://dx.doi.org/10.1016/j.neuron.2017.04.038.
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KARATAS, Cengiz, Gazanfer UNAL, and Adil YILMAZ. "Co-movement and Forecasting Analysis of Major Real Estate Markets by Wavelet Coherence and Multiple Wavelet Coherence." Chinese Journal of Urban and Environmental Studies 05, no. 02 (June 2017): 1750010. http://dx.doi.org/10.1142/s2345748117500105.
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Wavelet coherence of time series provides valuable information about dynamic correlation and its impact on time scales. Here, the authors analyze the wavelet coherence of major real estate markets data, and take the USA, Hong Kong of China, Canada, Japan, and Developed Europe real estate market prices as time series. The wavelet coherence results show relationships among these markets, the correlations between the two and three markets (by multiple wavelet coherence) and how these relationships vary in the time-frequency space. These relationships allow the authors to build VARMA models of real estate data which produce forecasts with small errors.
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Litinski, Daniel. "A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery." Quantum 3 (March 5, 2019): 128. http://dx.doi.org/10.22331/q-2019-03-05-128.
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Given a quantum gate circuit, how does one execute it in a fault-tolerant architecture with as little overhead as possible? In this paper, we discuss strategies for surface-code quantum computing on small, intermediate and large scales. They are strategies for space-time trade-offs, going from slow computations using few qubits to fast computations using many qubits. Our schemes are based on surface-code patches, which not only feature a low space cost compared to other surface-code schemes, but are also conceptually simple~--~simple enough that they can be described as a tile-based game with a small set of rules. Therefore, no knowledge of quantum error correction is necessary to understand the schemes in this paper, but only the concepts of qubits and measurements.
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CATRAKIS, HARIS J., ROBERTO C. AGUIRRE, and JESUS RUIZ-PLANCARTE. "Area–volume properties of fluid interfaces in turbulence: scale-local self-similarity and cumulative scale dependence." Journal of Fluid Mechanics 462 (July 10, 2002): 245–54. http://dx.doi.org/10.1017/s0022112002008911.
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Area–volume properties of fluid interfaces are investigated to quantify the scale-local and cumulative structure. An area–volume density g3(λ) and ratio Ω3(λ) are introduced to examine the interfacial behaviour as a function of scale λ or across a range of scales, respectively. These measures are demonstrated on mixed-fluid interfaces from whole-field ∼10003 three-dimensional space–time concentration measurements in turbulent jets above the mixing transition, at Re ∼ 20000 and Sc ∼ 2000, recorded by laser-induced-fluorescence and digital-imaging techniques, with Taylor's hypothesis applied. The cumulative structure is scale dependent in Ω3(λ), with a dimension D3(λ) that increases with increasing scale. In contrast, the scale-local structure exhibits self-similarity in g3(λ) with an exponent αg ≈1.3 for these interfaces. The scale dependence in the cumulative structure arises from the large scales, while the self-similarity corresponds to the small-scale area–volume contributions. The small scales exhibit the largest area–volume density and provide the dominant contributions to the total area–volume ratio, which corresponds to ∼10 times the area of a purely large-scale interface for the present flow conditions. The self-similarity in the scale-local structure at small scales provides the key ingredient to extrapolate the area–volume behaviour to higher Reynolds numbers.