Journal articles: 'Classical range succession model'

1

Steer, Philippe, Thomas Croissant, Edwin Baynes, and Dimitri Lague. "Statistical modelling of co-seismic knickpoint formation and river response to fault slip." Earth Surface Dynamics 7, no. 3 (July 24, 2019): 681–706. http://dx.doi.org/10.5194/esurf-7-681-2019.

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Abstract. Most landscape evolution models adopt the paradigm of constant and uniform uplift. It results that the role of fault activity and earthquakes on landscape building is understood under simplistic boundary conditions. Here, we develop a numerical model to investigate river profile development subjected to fault displacement by earthquakes and erosion. The model generates earthquakes, including mainshocks and aftershocks, that respect the classical scaling laws observed for earthquakes. The distribution of seismic and aseismic slip can be partitioned following a spatial distribution of mainshocks along the fault plane. Slope patches, such as knickpoints, induced by fault slip are then migrated at a constant rate upstream a river crossing the fault. A major result is that this new model predicts a uniform distribution of earthquake magnitude rupturing a river that crosses a fault trace and in turn a negative exponential distribution of knickpoint height for a fully coupled fault, i.e. with only co-seismic slip. Increasing aseismic slip at shallow depths, and decreasing shallow seismicity, censors the magnitude range of earthquakes cutting the river towards large magnitudes and leads to less frequent but higher-amplitude knickpoints, on average. Inter-knickpoint distance or time between successive knickpoints follows an exponential decay law. Using classical rates for fault slip (15 mm year−1) and knickpoint retreat (0.1 m year−1) leads to high spatial densities of knickpoints. We find that knickpoint detectability, relatively to the resolution of topographic data, decreases with river slope that is equal to the ratio between fault slip rate and knickpoint retreat rate. Vertical detectability is only defined by the precision of the topographic data that sets the lower magnitude leading to a discernible offset. Considering a retreat rate with a dependency on knickpoint height leads to the merging of small knickpoints into larger ones and larger than the maximum offset produced by individual earthquakes. Moreover, considering simple scenarios of fault burial by intermittent sediment cover, driven by climatic changes or linked to earthquake occurrence, leads to knickpoint distributions and river profiles markedly different from the case with no sediment cover. This highlights the potential role of sediments in modulating and potentially altering the expression of tectonic activity in river profiles and surface topography. The correlation between the topographic profiles of successive parallel rivers cutting the fault remains positive for distance along the fault of less than half the maximum earthquake rupture length. This suggests that river topography can be used for paleo-seismological analysis and to assess fault slip partitioning between aseismic and seismic slip. Lastly, the developed model can be coupled to more sophisticated landscape evolution models to investigate the role of earthquakes on landscape dynamics.

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Lee, Seung-Joon, George T. Yates, and T. Yaotsu Wu. "Experiments and analyses of upstream-advancing solitary waves generated by moving disturbances." Journal of Fluid Mechanics 199 (February 1989): 569–93. http://dx.doi.org/10.1017/s0022112089000492.

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In this joint theoretical, numerical and experimental study, we investigate the phenomenon of forced generation of nonlinear waves by disturbances moving steadily with a transcritical velocity through a layer of shallow water. The plane motion considered here is modelled by the generalized Boussinesq equations and the forced Korteweg-de Vries (fKdV) equation, both of which admit two types of forcing agencies in the form of an external surface pressure and a bottom topography. Numerical results are obtained using both theoretical models for the two types of forcings. These results illustrate that within a transcritical speed range, a succession of solitary waves are generated, periodically and indefinitely, to form a procession advancing upstream of the disturbance, while a train of weakly nonlinear and weakly dispersive waves develops downstream of an ever elongating stretch of a uniformly depressed water surface immediately behind the disturbance. This is a beautiful example showing that the response of a dynamic system to steady forcing need not asymptotically tend to a steady state, but can be conspicuously periodic, after an impulsive start, when the system is being forced at resonance.A series of laboratory experiments was conducted with a cambered bottom topography impulsively started from rest to a constant transcritical velocity U, the corresponding depth Froude number F = U/(gh0)½ (g being the gravitational constant and h0 the original uniform water depth) being nearly the critical value of unity. For the two types of forcing, the generalized Boussinesq model indicates that the surface pressure can be more effective in generating the precursor solitary waves than the submerged topography of the same normalized spatial distribution. However, according to the fKdV model, these two types of forcing are entirely equivalent. Besides these and some other rather refined differences, a broad agreement is found between theory and experiment, both in respect of the amplitudes and phases of the waves generated, when the speed is nearly critical (0.9 < F < 1.1) and when the forcing is sufficiently weak (the topography-height to water-depth ratio less than 0.15) to avoid breaking. Experimentally, wave breaking was observed to occur in the precursor solitary waves at low supercritical speeds (about 1.1 < F < 1.2) and in the first few trailing waves at high subcritical speeds (about 0.8 < F < 0.9), when sufficiently forced. For still lower subcritical speeds, the trailing waves behaved more like sinusoidal waves as found in the classical case and the forward-running solitary waves, while still experimentally discernible and numerically predicted for 0.6 > F > 0.2, finally disappear at F ≈ 0.2. In the other direction, as the Froude number is increased beyond F ≈ 1.2, the precursor soliton phenomenon was found also to evanesce as no finite-amplitude solitary waves can outrun, nor can any two-dimensional waves continue to follow, the rapidly moving disturbance. In this supercritical range and for asymptotically large times, all the effects remain only local to the disturbance. Thus, the criterion of the fascinating phenomenon of the generation of precursor solitons is ascertained.

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Krone, Stephen M., and Claudia Neuhauser. "A spatial model of range-dependent succession." Journal of Applied Probability 37, no. 04 (December 2000): 1044–60. http://dx.doi.org/10.1017/s0021900200018210.

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We consider an interacting particle system in which each site of the d-dimensional integer lattice can be in state 0, 1, or 2. Our aim is to model the spread of disease in plant populations, so think of 0 = vacant, 1 = healthy plant, 2 = infected plant. A vacant site becomes occupied by a plant at a rate which increases linearly with the number of plants within range R, up to some saturation level, F 1, above which the rate is constant. Similarly, a plant becomes infected at a rate which increases linearly with the number of infected plants within range M, up to some saturation level, F 2. An infected plant dies (and the site becomes vacant) at constant rate δ. We discuss coexistence results in one and two dimensions. These results depend on the relative dispersal ranges for plants and disease.

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Krone, Stephen M., and Claudia Neuhauser. "A spatial model of range-dependent succession." Journal of Applied Probability 37, no. 4 (December 2000): 1044–60. http://dx.doi.org/10.1239/jap/1014843082.

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We consider an interacting particle system in which each site of the d-dimensional integer lattice can be in state 0, 1, or 2. Our aim is to model the spread of disease in plant populations, so think of 0 = vacant, 1 = healthy plant, 2 = infected plant. A vacant site becomes occupied by a plant at a rate which increases linearly with the number of plants within range R, up to some saturation level, F1, above which the rate is constant. Similarly, a plant becomes infected at a rate which increases linearly with the number of infected plants within range M, up to some saturation level, F2. An infected plant dies (and the site becomes vacant) at constant rate δ. We discuss coexistence results in one and two dimensions. These results depend on the relative dispersal ranges for plants and disease.

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5

Brown, David R., Lisa A. Cassis, Dennis L. Silcox, Laura V. Brown, and David C. Randall. "Empirical and theoretical analysis of the extremely low frequency arterial blood pressure power spectrum in unanesthetized rat." American Journal of Physiology-Heart and Circulatory Physiology 291, no. 6 (December 2006): H2816—H2824. http://dx.doi.org/10.1152/ajpheart.00135.2006.

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The slope of the log of power versus the log of frequency in the arterial blood pressure (BP) power spectrum is classically considered constant over the low-frequency range (i.e., “fractal” behavior), and is quantified by β in the relationship “1/ fβ.” In practice, the fractal range cannot extend to indefinitely low frequencies, but factor(s) that terminate this behavior, and determine β, are unclear. We present 1) data in rats ( n = 8) that reveal an extremely low frequency spectral region (0.083–1 cycle/h), where β approaches 0 (i.e., the “shoulder”); and 2) a model that 1) predicts realistic values of β within that range of the spectrum that conforms to fractal dynamics (∼1–60 cycles/h), 2) offers an explanation for the shoulder, and 3) predicts that the “successive difference” in mean BP (mBP) is an important parameter of circulatory function. We recorded BP for up to 16 days. The absolute difference between successive mBP samples at 0.1 Hz (the successive difference, or Δ) was 1.87 ± 0.21 mmHg (means ± SD). We calculated β for three frequency ranges: 1) 0.083–1; 2) 1–6; and 3) 6–60 cycles/h. The β for all three regions differed ( P < 0.01). For the two higher frequency ranges, β indicated a fractal relationship (β6–60/h = 1.27 ± 0.01; β1–6/h = 1.80 ± 0.16). Conversely, the slope of the lowest frequency region (i.e., the shoulder) was nearly flat (β0.083–1 /h = 0.32 ± 0.28). We simulated the BP time series as a random walk about 100 mmHg with ranges above and below of 10, 30, and 50 mmHg and with Δ from 0.5 to 2.5. The spectrum for the conditions mimicking actual BP time series (i.e., range, 85–115 mmHg; Δ, 2.00) resembled the observed spectra, with β in the lowest frequency range = 0.207 and fractal-like behavior in the two higher frequency ranges (β = 1.707 and 2.057). We suggest that the combined actions of mechanisms limiting the excursion of arterial BP produce the shoulder in the spectrum and that Δ contributes to determining β.

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Schneider, Linda, Christian Barthlott, Corinna Hoose, and Andrew I. Barrett. "Relative impact of aerosol, soil moisture, and orography perturbations on deep convection." Atmospheric Chemistry and Physics 19, no. 19 (October 7, 2019): 12343–59. http://dx.doi.org/10.5194/acp-19-12343-2019.

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Abstract. The predictability of deep moist convection depends on many factors, such as the synoptic-scale flow, the geographical region (i.e., the presence of mountains), and land surface–atmosphere as well as aerosol–cloud interactions. This study addresses all these factors by investigating the relative impact of orography, soil moisture, and aerosols on precipitation over Germany in different weather regimes. To this end, we conduct numerical sensitivity studies with the COnsortium for Small-sale MOdelling (COSMO) model at high spatial resolution (500 m grid spacing) for 6 days with weak and strong synoptic forcing. The numerical experiments consist of (i) successive smoothing of topographical features, (ii) systematic changes in the initial soil moisture fields (spatially homogeneous increase/decrease, horizontal uniform soil moisture, different realizations of dry/wet patches), and (iii) different assumptions about the ambient aerosol concentration (spatially homogeneous and heterogeneous fields). Our results show that the impact of these perturbations on precipitation is on average higher for weak than for strong synoptic forcing. Soil moisture and aerosols are each responsible for the maximum precipitation response for three of the cases, while the sensitivity to terrain forcing always shows the smallest spread. For the majority of the analyzed cases, the model produces a positive soil moisture–precipitation feedback when averaged over the entire model domain. Furthermore, the amount of soil moisture affects precipitation more strongly than its spatial distribution. The precipitation response to changes in the CCN concentration is more complex and case dependent. The smoothing of terrain shows weaker impacts on days with strong synoptic forcing because surface fluxes are less important and orographic ascent is still simulated reasonably well, despite missing fine-scale orographic features. We apply an object-based characterization to identify whether and how the perturbations affect the structure, location, timing, and intensity of precipitation. These diagnostics reveal that the structure component, comparing the size and shape of precipitating objects to the reference simulation, is on average highest in the soil moisture and aerosol simulations, often due to changes in the maximum precipitation amounts. This indicates that the dominant mechanisms for convection initiation remain but that precipitation amounts depend on the strength of the trigger mechanisms. Location and amplitude parameters both vary over a much smaller range. Still, the temporal evolution of the amplitude component correlates well with the rain rate. Our results suggest that for quantitative precipitation forecasting, both aerosols and soil moisture are of similar importance and that their inclusion in convective-scale ensemble forecasting containing classical sources of uncertainty should be assessed in the future.

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7

Da Silva, F. W. O., and A. S. T. Pires. "Short-Range Order in the Quasi-One-Dimensional Classical Heisenberg Model." physica status solidi (b) 130, no. 2 (August 1, 1985): K117—K120. http://dx.doi.org/10.1002/pssb.2221300255.

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8

Gupta, Shamik, and David Mukamel. "Quasistationarity in a model of classical spins with long-range interactions." Journal of Statistical Mechanics: Theory and Experiment 2011, no. 03 (March 14, 2011): P03015. http://dx.doi.org/10.1088/1742-5468/2011/03/p03015.

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9

Sarkanych, P., Yu Holovatch, and R. Kenna. "Classical phase transitions in a one-dimensional short-range spin model." Journal of Physics A: Mathematical and Theoretical 51, no. 50 (November 15, 2018): 505001. http://dx.doi.org/10.1088/1751-8121/aaea02.

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10

Bell, Graham, and Étienne Fortier-Dubois. "Trophic dynamics of a simple model ecosystem." Proceedings of the Royal Society B: Biological Sciences 284, no. 1862 (September 13, 2017): 20171463. http://dx.doi.org/10.1098/rspb.2017.1463.

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We have constructed a model of community dynamics that is simple enough to enumerate all possible food webs, yet complex enough to represent a wide range of ecological processes. We use the transition matrix to predict the outcome of succession and then investigate how the transition probabilities are governed by resource supply and immigration. Low-input regimes lead to simple communities whereas trophically complex communities develop when there is an adequate supply of both resources and immigrants. Our interpretation of trophic dynamics in complex communities hinges on a new principle of mutual replenishment, defined as the reciprocal alternation of state in a pair of communities linked by the invasion and extinction of a shared species. Such neutral couples are the outcome of succession under local dispersal and imply that food webs will often be made up of suites of trophically equivalent species. When immigrants arrive from an external pool of fixed composition a similar principle predicts a dynamic core of webs constituting a neutral interchange network, although communities may express an extensive range of other webs whose membership is only in part predictable. The food web is not in general predictable from whole-community properties such as productivity or stability, although it may profoundly influence these properties.

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11

Jenkins, Kurt J., and R. Gerald Wright. "Simulating Succession of Riparian Spruce Forests and White-Tailed Deer Carrying Capacity in Northwestern Montana." Western Journal of Applied Forestry 2, no. 3 (July 1, 1987): 80–83. http://dx.doi.org/10.1093/wjaf/2.3.80.

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Abstract Rates of succession were determined during the period 1945-80 in six floodplain plant communities along the North Fork of the Flathead River, Montana. A succession model was developed to forecast the long-range effects of land-use change on the carrying capacity of white-tailed deer winter range. The areas occupied by mature spruce (Picea englemannii x glauca hybrid) and spruce-black cottonwood (Populus trichocarpa) forests on the floodplain were relatively constant between 1945-1980. Early seral types were more variable due to short-term variations in river flow. Successional modelling demonstrated the effects of two timber harvesting strategies on white-tailed deer populations. Simulated populations declined following two timber harvesting schedules, but recovered after cessation of harvest. An additional application of the model showed the potential effects of increased erosion rates on deer populations and demonstrated the versatility of land succession models for resource monitoring. West. J. Appl. For. 2(3):80-83, July 1987

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Kapikranian, O., B. Berche, and Yu Holovatch. "Quasi-long-range ordering in a finite-size 2D classical Heisenberg model." Journal of Physics A: Mathematical and Theoretical 40, no. 14 (March 20, 2007): 3741–48. http://dx.doi.org/10.1088/1751-8113/40/14/001.

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13

Rosenberger, A. T., C. C. Sung, S. D. Pethel, and C. M. Bowden. "Classical model for high-field ionization suppression in a short-range potential." Physical Review A 56, no. 3 (September 1, 1997): 2459–62. http://dx.doi.org/10.1103/physreva.56.2459.

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Oh, Suhk Kun, Chang No Yoon, and Jean S. Chung. "Dynamic finite-size effect in an infinite-range classical antiferromagnetic spin model." Physical Review B 55, no. 1 (January 1, 1997): 44–47. http://dx.doi.org/10.1103/physrevb.55.44.

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Jamet, J. L., N. Jean, G. Bogé, S. Richard, and D. Jamet. "Plankton succession and assemblage structure in two neighbouring littoral ecosystems in the north-west Mediterranean Sea." Marine and Freshwater Research 56, no. 1 (2005): 69. http://dx.doi.org/10.1071/mf04102.

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We studied seasonal variations in bacterial abundance and succession in phyto- and zooplankton assemblages (particularly small taxa) in two neighbouring shallow bays (near Toulon, Mediterranean Sea, France): Little Bay (polluted, eutrophic), and Niel Bay (less polluted, oligotrophic). In Little Bay, bacteria developed in northern spring and phytoplankton (Dinophyceae > 20 µm) in late northern winter–early spring. Zooplankton levels peaked at the end of northern spring and in autumn; this community was dominated by Oithona nana. In Niel Bay, bacterial levels peaked during northern spring and autumn. Phytoplankton (Dinophyceae, Bacillariophyceae) abundance was low and only peaked in June. Zooplankton levels peaked in northern mid-summer. Little Bay was influenced more by the land and by human activities than by the sea. Seasonal factors (e.g. water temperature) and sudden influences (e.g. rain and, indirectly, Mistral wind) may have modified the succession of the plankton communities in this bay. Successions did not follow Margalef’s model and the classical scheme for zooplankton. Conversely, Niel Bay functioning and plankton assemblages were most influenced by the physical environment of the sea than by the land or by human activities. Successions were closely related to the classical scheme of the Mediterranean Sea.

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Stolarski, Adam, Waldemar Cichorski, and Anna Szcześniak. "Non-Classical Model of Dynamic Behavior of Concrete." Applied Sciences 9, no. 13 (June 26, 2019): 2590. http://dx.doi.org/10.3390/app9132590.

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Modeling of dynamic properties of concrete is presented in the paper. The non-classical model of dynamic deformation was proposed. The essence of this model is the method of determination of the initial dynamic yield surface. For this purpose, the dynamic strength criterion was used. The model describes the elastic properties until attaining the dynamic strength of concrete, perfectly plastic properties in the limited range of deformation, material softening, material dilatation, and cracking or crushing of material as the residual stress processes during tension or compression. Degradation of elastic material constants was taken into consideration. Comparative analysis with previously published experimental results and theoretical models demonstrated that the proposed model is well approximates the basic dynamic properties of concrete and can be used in numerical analysis to evaluate the dynamic load capacity of reinforced concrete structures.

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OKUYUCU, CENGİZ, TATYANA K. DIMITROVA, MEHMET CEMAL GÖNCÜOĞLU, and İBRAHİM GEDİK. "Late Permian (Tatarian) fluvio-lacustrine successions in NW Anatolia (Zonguldak Terrane, Turkey): palaeogeographic implications." Geological Magazine 154, no. 5 (July 25, 2016): 1073–87. http://dx.doi.org/10.1017/s0016756816000674.

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AbstractLate Permian fluvio-lacustrine successions of the Çakraz Formation in the Zonguldak Terrane between the regions of Akçakoca and Ereğli were investigated in order to describe the litho- and biostratigraphic properties and explain the depositional environment. The studied succession with black, dark-grey to greenish-grey shales, siltstones and limestones is named the Alaplı Member to distinguish it from the classical red clastic successions, which are tentatively named the Ereğli Member of the Çakraz Formation. The organic-rich black shales, mudstones and limestones of the Alaplı Member yielded palynological assemblages suggesting a Lopingian (Tatarian) age. The lack of any marine macro- or microfossils, the fine-grained character of the lithofacies with abundant plant material and the association of poorly sorted conglomerates in the middle part of the succession indicate possible deposition in a broad range of fluvial and lacustrine environments. Successions of similar age and depositional environment are known from the East European Variscan Belt in Bulgaria and Romania. Common successions were also developed in actively extending shallow-marine platforms on the NW Palaeotethyan margin at the end of the Permian Period.

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Priyanka, Sayani Chatterjee, and Kavita Jain. "Slow quench dynamics in classical systems: kinetic Ising model and zero-range process." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 3 (March 1, 2021): 033208. http://dx.doi.org/10.1088/1742-5468/abe2a2.

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19

Yang, Zhiqiang, Warren B. Cohen, and Mark E. Harmon. "Modeling early forest succession following clear-cutting in western Oregon." Canadian Journal of Forest Research 35, no. 8 (August 1, 2005): 1889–900. http://dx.doi.org/10.1139/x05-132.

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In the Pacific Northwest, the process of conifer development after stand-replacing disturbance has important implications for many forest processes (e.g., carbon storage, nutrient cycling, and biodiversity). This paper examines conifer development in the Coast Range Province and Western Cascades Province of Oregon using repeat interpretation of historic aerial photographs from 1959 to 1997 to examine the canopy cover change of different life forms: shrubs, hardwood trees, and conifer trees. Ninety-four stands from the Western Cascades Province and 59 stands from the Coast Range Province were photointerpreted in roughly 5-year intervals. A ChapmanRichards growth function was used to model conifer cover development for all sample stands. Based on the photo data and the ChapmanRichards function, these stands were classified into one of seven early forest successional trajectories defined by the vegetation physiognomy. Succession in the Coast Range Province and Western Cascades Province were compared using parameters derived from the ChapmanRichards growth function. Our results echo previous studies in that rates and densities of conifer regeneration varied markedly among sites; however, our results also indicate that early forest succession differs in the two study regions in terms of both trajectories and rates. Conifer regeneration in the Western Cascades Province tends to have longer delays in establishing and slower rates compared with the Coast Range Province.

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Negrete, Oscar A., Patricio Vargas, Francisco J. Peña, Gonzalo Saravia, and Eugenio E. Vogel. "Short-Range Berezinskii-Kosterlitz-Thouless Phase Characterization for the q-State Clock Model." Entropy 23, no. 8 (August 7, 2021): 1019. http://dx.doi.org/10.3390/e23081019.

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Beyond the usual ferromagnetic and paramagnetic phases present in spin systems, the usual q-state clock model presents an intermediate vortex state when the number of possible orientations q for the system is greater than or equal to 5. Such vortex states give rise to the Berezinskii-Kosterlitz-Thouless (BKT) phase present up to the XY model in the limit q→∞. Based on information theory, we present here an analysis of the classical order parameters plus new short-range parameters defined here. Thus, we show that even using the first nearest neighbors spin-spin correlations only, it is possible to distinguish the two transitions presented by this system for q greater than or equal to 5. Moreover, the appearance at relatively low temperature and disappearance of the BKT phase at a rather fix higher temperature is univocally determined by the short-range interactions recognized by the information content of classical and new parameters.

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Romano, S. "Monte Carlo simulation of a one dimensional classical Heisenberg model with long range interactions." Liquid Crystals 4, no. 5 (January 1989): 483–95. http://dx.doi.org/10.1080/02678298908033183.

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Campelo, M. W. V., J. P. de Lima, and L. L. Gonçalves. "Entanglement and quantum-classical crossover in the extended XX model with long-range interactions." Journal of Magnetism and Magnetic Materials 327 (February 2013): 110–20. http://dx.doi.org/10.1016/j.jmmm.2012.09.046.

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23

Breña Naranjo, J. A., M. Weiler, and K. Stahl. "Sensitivity of a data-driven soil water balance model to estimate summer evapotranspiration along a forest chronosequence." Hydrology and Earth System Sciences 15, no. 11 (November 17, 2011): 3461–73. http://dx.doi.org/10.5194/hess-15-3461-2011.

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Abstract. The hydrology of ecosystem succession gives rise to new challenges for the analysis and modelling of water balance components. Recent large-scale alterations of forest cover across the globe suggest that a significant portion of new biophysical environments will influence the long-term dynamics and limits of water fluxes compared to pre-succession conditions. This study assesses the estimation of summer evapotranspiration along three FLUXNET sites at Campbell River, British Columbia, Canada using a data-driven soil water balance model validated by Eddy Covariance measurements. It explores the sensitivity of the model to different forest succession states, a wide range of computational time steps, rooting depths, and canopy interception capacity values. Uncertainty in the measured EC fluxes resulting in an energy imbalance was consistent with previous studies and does not affect the validation of the model. The agreement between observations and model estimates proves that the usefulness of the method to predict summer AET over mid- and long-term periods is independent of stand age. However, an optimal combination of the parameters rooting depth, time step and interception capacity threshold is needed to avoid an underestimation of AET as seen in past studies. The study suggests that summer AET could be estimated and monitored in many more places than those equipped with Eddy Covariance or sap-flow measurements to advance the understanding of water balance changes in different successional ecosystems.

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MONETTE, L. "SPINODAL NUCLEATION." International Journal of Modern Physics B 08, no. 11n12 (May 30, 1994): 1417–527. http://dx.doi.org/10.1142/s0217979294000646.

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The aim of this paper is to present the theoretical foundations of spinodal nucleation, by reviewing key theoretical and numerical work. The basic ideas of classical nucleation theory are first presented: the classical droplet model, and the Becker-Döring theory, as these concepts are important to the development of the field theoretical formulation of nucleation. The field theoretical framework for classical nucleation is exposed in some detail, followed by the presentation of a similar framework, extended to nucleation in the proximity of a spinodal (non-classical nucleation), in the presence of long-range Ising interactions. The non-classical nucleating droplet is found to be diffuse, hence to strongly depart from the classical prediction of a compact object with a well-defined surface. The fact that the non-classical nucleating droplet is identified with a ramified object prompts the development of an appropriate cluster description. The basic principles of percolation theory are outlined, and some lattice percolation models introduced. The Kastaleyn-Fortuin mapping, which establishes a connection between a particular percolation model and a limit of the Potts model, is briefly described. This mapping is crucial to the development of a second mapping (Coniglio-Klein) of the Ising spinodal point into a percolation model, where the long-range Ising interactions are translated into a long-range connectivity in the appropriate percolation model. The final result consists of the most powerful tool available to identify precisely the non-classical nucleating droplet in numerical simulations of nucleation in proximity of a spinodal. Numerical simulation results are presented, which support the field theoretical formulation of non-classical nucleation. As the numerical results seem to support the fact that the non-classical nucleating droplet is also a percolation cluster, its fractal structure is investigated by considering the mean-field regime of the percolation model, i.e. a percolation model with long-range connectivity. This leads to an apparent contradiction between the field theory and the mean-field percolation model predictions concerning the mass (or density) scaling of the nucleating droplet. This inconsistency is resolved by postulating that the mean-field percolation clusters cannot be non-classical nucleating droplets, and proposing that the non-classical nucleating droplet is in fact the result of a coalescence of many such clusters. Finally, the calculation of the static prefactor in the nucleation rate by assuming a Becker-Döring dynamics for the coalescence mechanism is outlined. The result is found to be consistent with the predictions of the field theory for the static prefactor. Numerical results are also presented in support of the hypothesized coalescence mechanism.

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Padoan, Alberto, Fulvio Forni, and Rodolphe Sepulchre. "Balanced truncation for model reduction of biological oscillators." Biological Cybernetics 115, no. 4 (August 2021): 383–95. http://dx.doi.org/10.1007/s00422-021-00888-4.

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AbstractModel reduction is a central problem in mathematical biology. Reduced order models enable modeling of a biological system at different levels of complexity and the quantitative analysis of its properties, like sensitivity to parameter variations and resilience to exogenous perturbations. However, available model reduction methods often fail to capture a diverse range of nonlinear behaviors observed in biology, such as multistability and limit cycle oscillations. The paper addresses this need using differential analysis. This approach leads to a nonlinear enhancement of classical balanced truncation for biological systems whose behavior is not restricted to the stability of a single equilibrium. Numerical results suggest that the proposed framework may be relevant to the approximation of classical models of biological systems.

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Eisenberg, E., and R. Berkovits. "The addition spectrum of a classical short-range interaction model for a disordered quantum dot." Journal of Physics: Condensed Matter 10, no. 29 (July 27, 1998): 6515–22. http://dx.doi.org/10.1088/0953-8984/10/29/011.

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27

Romano, S. "One dimensional classical spin models with long range anisotropic interaction. An extreme nematogenic lattice model." Liquid Crystals 10, no. 1 (July 1991): 73–83. http://dx.doi.org/10.1080/02678299108028230.

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Ichimaru, Setsuo, Shuji Ogata, and Kenji Tsuruta. "Short-range screening potentials for classical Coulomb fluids: Monte Carlo sampling and cluster model studies." Physical Review E 50, no. 4 (October 1, 1994): 2977–85. http://dx.doi.org/10.1103/physreve.50.2977.

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Zakharov, Anatoly Yu. "Manifestations of Short-Range and Long-Range Parts of Interatomic Potentials In Rearrangement Processes of Multicomponent Condensed Systems." Solid State Phenomena 138 (March 2008): 347–54. http://dx.doi.org/10.4028/www.scientific.net/ssp.138.347.

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Helmholtz free energy functional for generalized lattice model is reduced to Ginzburg- Landau-like form. Connections between interatomic potentials characteristics and parameters of Ginzburg-Landau-like functional are established. Equations for equilibrium distributions of species in multicomponent systems are derived. Equations of rearrangement kinetics of multicomponent systems are obtained. Description of the rearrangement processes via non-classical partial differential equations is proposed.

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Shigaev, A. S., T. B. Feldman, V. A. Nadtochenko, M. A. Ostrovsky, and V. D. Lakhno. "Investigation of Rhodopsin Chromophore Photoisomerization Based on the Quantum-Classical Model." Mathematical Biology and Bioinformatics 13, no. 1 (May 25, 2018): 169–86. http://dx.doi.org/10.17537/2018.13.169.

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A quantum-classical model of cis-trans photoisomerization of the visual pigment rhodopsin chromophore was investigated in wide ranges of parameters. The quantum subsystem of the model includes three electronic states for rhodopsin: the ground state, the excited state, and the ground state of primary photoproduct. The local temperature of the mass points of the classical subsystem was used as a main reference quantity. The best agreement with experimental data was shown to be in the range of moderate temperatures in agreement with the Raman spectroscopy data. The essential role of a quick transfer of the photoexcitation excess energy into apoprotein part in photoproduct stabilization process was illustrated. Also, the fundamental nature and the local character of the photoreaction were shown in the numerical investigations.

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Mariñoso Guiu, Joan, Antoni Macià, and Stefan T. Bromley. "How to accurately model IR spectra of nanosized silicate grains." Proceedings of the International Astronomical Union 15, S350 (April 2019): 431–33. http://dx.doi.org/10.1017/s174392132000006x.

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AbstractWe assess the accuracy of various computational methods for obtaining infrared (IR) spectra of nanosized silicate dust grains directly from their atomistic structure and atomic motions. First, IR spectra for a selection of small nanosilicate clusters with a range of sizes and chemical compositions are obtained within the harmonic oscillator approximation employing density functional theory (DFT) based quantum chemical calculations. To check if anharmonic effects play a significant role in the IR spectra of these nanoclusters, we further obtain their IR spectra from finite temperature DFT-based ab initio molecular dynamics (AIMD). Finally, we also study the effect of temperature on the broadening of the obtained IR spectra peaks in larger nanosilicate grains with a range of crystallinities. In this case, less computationally costly classical molecular dynamics simulations are necessary due to the large number of atoms involved. Generally, we find that although DFT-based methods are more accurate, surprisingly good IR spectra can also be obtained from classical molecular dynamics calculations.

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Li, Hao. "Non-Classical Probability Seismic Reliability Based on Pushover Analysis." Applied Mechanics and Materials 638-640 (September 2014): 1822–27. http://dx.doi.org/10.4028/www.scientific.net/amm.638-640.1822.

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In this paper, the probabilistic model is used to quantify the uncertainty of structural resistance, and the convex model is used to quantify the seismic uncertainty. The distribution parameters for the probabilistic model, together with the interval range for the convex model, are obtained through pushover analysis. Two-level function equation method is employed to calculate the seismic reliability of the structure. Case study shows that compared with the classical probability method, the proposed method is more simple and reasonable for seismic reliability analysis.

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Carevic, Ivana, Darivojka Ljubovic-Obradovic, Monika Bozinovic, and Velimir Jovanovic. "Upper Barremian-Lower Aptian Urgonian limestone's in the Rakova bara section (Carpatho-balkanides, NE Serbia): Analysis and comparison with adjacent areas." Glasnik Srpskog geografskog drustva 90, no. 1 (2010): 1–16. http://dx.doi.org/10.2298/gsgd1001001c.

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The Upper Barremian-Lower Aptian succession is recorded from a limestone sequence that crops out in the surrounding of Rakova Bara in the Carpatho-Balkanides range in northeastern Serbia. The micropalaeontological and sedimentological studies lead to recognition of the two types of microfacies. The benthic foraminiferal association consists of Vercorsella laurentii, Rumanoloculina robusta, Praechrysalidina infracretaceae, Dictyoconus gr. arabicus, Debarina hahounerensis, Charentia cuvilieri and Pseudocyclammina lituus that confirm the stratigraphical and palaeoenvironmental connection of the microfossil assemblages with the classical Urgonian-type, shallow-water carbonate sedimentation. The association documented for the first time in the study area is considered typical of the Tethyan Realm. The stratigraphical position of the benthic foraminifera species within the Upper Barremian-Lower Aptian interval is discussed. The Urgonian Limestone's of the studied section are comparable with adjacent areas of eastern Serbia and Romanian South Carpathians. .

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Didion, Markus, Andrea D. Kupferschmid, Andreas Zingg, Lorenz Fahse, and Harald Bugmann. "Gaining local accuracy while not losing generality — extending the range of gap model applications." Canadian Journal of Forest Research 39, no. 6 (June 2009): 1092–107. http://dx.doi.org/10.1139/x09-041.

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For the study of long-term processes in forests, gap models generally sacrifice accuracy (i.e., simulating system behavior in a quantitatively accurate manner) for generality (i.e., representing a broad range of systems’ behaviors with the same model). We selected the gap model ForClim to evaluate whether the local accuracy of forest succession models can be increased based on a parsimonious modeling approach that avoids the additional complexity of a 3D crown model, thus keeping parameter requirements low. We improved the representation of tree crowns by introducing feedbacks between (i) light availability and leaf area per tree and (ii) leaf area per tree and diameter growth rate to account for the self-pruning in real stands. The local accuracy of the new model, ForClim v2.9.5, was considerably improved in simulations at three long-term forest research sites in the Swiss Alps, while its generality was maintained as shown in simulations of potential natural vegetation along a broad environmental gradient in Central Europe. We conclude that the predictive ability of a model does not depend on its complexity, but on the reproduction of patterns. Most importantly, model complexity should be consistent with the objectives of the study and the level of system understanding.

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Ramírez, J., and J. R. Sanmartín. "Self-similar expansion of laser plasmas with nonlocal heat flux." Laser and Particle Beams 12, no. 1 (March 1994): 55–64. http://dx.doi.org/10.1017/s0263034600007229.

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A previous hydrodynamic model of the expansion of a laser-produced plasma, using classical (Spitzer) heat flux, is reconsidered with a nonlocal heat flux model. The nonlocal law is shown to be valid beyond the range of validity of the classical law, breaking down ultimately, however, in agreement with recent predictions.

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Pagano, Guido, Aniruddha Bapat, Patrick Becker, Katherine S. Collins, Arinjoy De, Paul W. Hess, Harvey B. Kaplan, et al. "Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator." Proceedings of the National Academy of Sciences 117, no. 41 (October 6, 2020): 25396–401. http://dx.doi.org/10.1073/pnas.2006373117.

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Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.

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MASSANÉS, S. RIPOLL, and C. J. PÉREZ VICENTE. "CLASSICAL-LIKE RESONANCE INDUCED BY NOISE IN A FITZHUGH–NAGUMO NEURON MODEL." International Journal of Bifurcation and Chaos 09, no. 12 (December 1999): 2295–303. http://dx.doi.org/10.1142/s0218127499001784.

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We have studied the stochastic behavior of Fitzhugh–Nagumo neuron-like model (FN) induced by subthreshold external stimuli. Our analysis based on three standard measures: the power spectrum, interspike interval distribution (ISI) and autocorrelation function shows that it is possible to define a characteristic time scale which can be identified in the response of the system for a wide range of frequencies. In contrast to previous studies we have focused our attention on high frequency signals which could be of interest for real systems such as nervous fibers in the auditory system. We report behaviors which resemble those of classical deterministic oscillators but never the stochastic resonance phenomenon typical of low frequency signals.

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GOLDSTEIN, ROBERT S. "CLASSICAL XY SYSTEMS UNDER TIME DEPENDENT MAGNETIC FIELDS." Modern Physics Letters B 07, no. 01 (January 10, 1993): 47–55. http://dx.doi.org/10.1142/s0217984993000084.

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The phase diagram of the hard-spin XY model with infinite-range coupling under time dependent magnetic fields is investigated. Phases are distinguished by measuring time-average magnetization (TAM). For the case of an oscillating (AC) magnetic field, three phases with non-zero TAM are found in addition to a zero TAM phase. All phases are found to be synchronous with the driving frequency. The non-zero TAM-zero TAM transition line diverges to infinite magnetic field amplitude for low temperatures. An unusual type of hysteresis due to the infinite range coupling appears. Some strategic points in the phase diagram are analytically explained. Also, we interpolate between the AC and rotating magnetic field cases (investigated previously by Kuramoto's group) by studying an 'elliptical' magnetic field case.

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Cirto, Leonardo J. L., Leonardo S. Lima, and Fernando D. Nobre. "Controlling the range of interactions in the classical inertial ferromagnetic Heisenberg model: analysis of metastable states." Journal of Statistical Mechanics: Theory and Experiment 2015, no. 4 (April 29, 2015): P04012. http://dx.doi.org/10.1088/1742-5468/2015/04/p04012.

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40

Ichimaru, Setsuo, Shuji Ogata, and Kenji Tsuruta. "Erratum: Short-range screening potentials for classical Coulomb fluids: Monte Carlo sampling and cluster model studies." Physical Review E 51, no. 4 (April 1, 1995): 3788. http://dx.doi.org/10.1103/physreve.51.3788.

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41

Kang, Lakhwinder Singh, and Harpreet Sidhu. "Leadership Development and Succession Planning at ICICI Bank." Asian Case Research Journal 15, no. 02 (December 2011): 253–77. http://dx.doi.org/10.1142/s0218927511001551.

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On 19 December 2008, ICICI bank named joint managing director Chanda Kochhar as its new CEO from May 2009 to lead India's second-largest lender at a time of declining market share, soaring bad debts and a tough global environment. She would be the successor of the 61-year-old visionary banker K. V. Kamath, MD and CEO of ICICI Bank who was to retire on 30 April 2009 after completing his successful tenure of 11 years. ICICI bank with a network of 1,456 branches and 4,721 ATMs in India and presence in 18 countries, is India's second-largest bank with total assets of Rs. 3,793.01 billion (US$75 billion) and profit after tax of Rs. 37.58 billion for the year ending March 31, 2009. It offers a wide range of banking products and financial services to corporate and retail customers. The need for succession planning arose at ICICI as the term of one top level executive ended, one other retired and two left the company. This case has been developed to provide understanding on how leaders are identified, nurtured and developed at ICICI bank, the strengths and weaknesses of CEO centric model of leadership development being followed by Kamath and the new institutionalized process of leadership development. It also provides the scope for discussion about the strengths and weaknesses of hiring an insider or outsider for the position of a CEO and the role of outgoing CEO in the development and selection of his/her successor.

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Ryzhkova, Vera, Irina Danilova, and Mikhail Korets. "A Gis-Based Mapping and Estimation the Current Forest Landscape State and Dynamics." Journal of Landscape Ecology 4, no. 1 (January 1, 2011): 42–54. http://dx.doi.org/10.2478/v10285-012-0033-0.

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A Gis-Based Mapping and Estimation the Current Forest Landscape State and DynamicsClassification and inventory of the current diversity of forest communities and their environments (i.e. site conditions) were developed based on Kolesnikov's topogenetic classification approach in Angara region (Central Siberia). This classification considers characteristics of forest regeneration dynamics, such as trends and rates of forest regeneration succession in a range of site conditions; therefore, it is used as a basis of a key for a forest regeneration dynamics map. An algorithm of forest regeneration dynamics mapping based on a spatial analysis of multi-band satellite data, a digital elevation model (DEM), and ground data combined with expert estimates of the resulting land cover classes was applied using geographic information system (GIS) "Forests of Central Siberia". Based on this algorithm, Landsat 7 ETM+ satellite imagery, SRTM-3- DEM, and field data were processed for the Angara test site. The resulting maps include two polygonal vector layers: one is forest regeneration stages (stand types) and the other is forest succession series (forest types) in a range of site conditions.

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Papini, Giorgio. "Some Classical and Quantum Aspects of Gravitoelectromagnetism." Entropy 22, no. 10 (September 27, 2020): 1089. http://dx.doi.org/10.3390/e22101089.

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It has been shown that, even in linear gravitation, the curvature of space-time can induce ground state degeneracy in quantum systems, break the continuum symmetry of the vacuum and give rise to condensation in a system of identical particles. Condensation takes the form of a temperature-dependent correlation over distances, of momenta oscillations about an average momentum, of vortical structures and of a positive gravitational susceptibility. In the interaction with quantum matter and below a certain range, gravity is carried by an antisymmetric, second order tensor that satisfies Maxwell-type equations. Some classical and quantum aspects of this type of “gravitoelectromagnetism” were investigated. Gravitational analogues of the laws of Curie and Bloch were found for a one-dimensional model. A critical temperature for a change in phase from unbound to isolated vortices can be calculated using an XY-model.

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LIANG, YINGJIE, and WEN CHEN. "TWO-SCALE DISTRIBUTION OF PRIME NUMBER AND ITS DIFFUSION EQUATION MODEL." Fractals 25, no. 02 (April 2017): 1750022. http://dx.doi.org/10.1142/s0218348x17500220.

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This study reveals the two-scale characteristics in prime number distribution. It is observed a sub-diffusion process of power law decay at the small scale of the natural number [Formula: see text], but is found to obey the classical Brownian motion of an exponential decay at the large scale [Formula: see text]. Such two-scale mechanism gives rise to the multi-fractal scaling from the power law to the exponential law distributions in a transition region of the natural number [Formula: see text]. In the small range, the sub-diffusion of prime number distribution is well depicted by the fractional derivative equation model, and in the large scale, exponential decay distribution can accurately be described by a classical diffusion equation model. The Riemann diffusion equation proposed recently by the present authors can accurately model the prime distribution from small to moderate to large scales and is reduced to the fractional derivative sub-diffusion equation at small scale and the classical Brownian motion diffusion equation at large scale, respectively.

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LE VAN QUYEN, MICHEL, HEINZ G. SCHUSTER, and FRANCISCO J. VARELA. "FAST DYNAMIC COUPLING FROM SLOW NEURONAL OSCILLATORS." International Journal of Bifurcation and Chaos 06, no. 10 (October 1996): 1807–16. http://dx.doi.org/10.1142/s0218127496001144.

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We focus here on the possible role of the widely distributed slow (4–10 Hz) intrinsic bursting neurons in the establishment of long range spacetime coherent subgroups of neurons at multiple locations. We show that a dynamic coupling of these relaxation oscillators provides a simple mechanism whereby an excitatory interconnected network can give rise to coexisting synchronous assemblies of slow neurons in a phase ordered relationship. In the model, this sequential phase locking is dependent on fast inhibitory feedbacks. As a consequence, global rhythms of a broad frequency range spontaneously arise from the regular succession of synchronous assemblies.

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Sabi Takou, D., M. Karimou, F. Hontinfinde, and E. Albayrak. "Anisotropic Heisenberg model for the mixed spin-3/2 and spin-1/2 under random crystal field." Condensed Matter Physics 24, no. 1 (March 2021): 13704. http://dx.doi.org/10.5488/cmp.24.13704.

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Thermodynamic properties of the mixed spin-3/2 and spin-1/2 Heisenberg model are examined within the Oguchi approximation in the presence of a random crystal-field (RCF). The RCF is either introduced with probability p or turned off with probability 1-p randomly. The thermal variations of the global magnetization and free energy of the system are investigated to construct the phase diagrams for the classical, quantum and anisotropic cases. Different results revealed that no qualitative changes exist between them. Quantum effects are found to be present and abundant in the quantum model in the negative D -range. This phenomenon has a strong decreasing effect on the critical temperature which becomes much lower than in the classical case. In the presence of an external field, it was observed that coercivity and remanence decrease in a wide range of the absolute temperature.

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Tan, Zhenhua, Liangliang He, Danke Wu, Qiuyun Chang, and Bin Zhang. "Personalized Standard Deviations Improve the Baseline Estimation of Collaborative Filtering Recommendation." Applied Sciences 10, no. 14 (July 10, 2020): 4756. http://dx.doi.org/10.3390/app10144756.

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Baseline estimation is a critical component for latent factor-based collaborative filtering (CF) recommendations to obtain baseline predictions by evaluating global deviations for both users and items from personalized ratings. Classical baseline estimation presupposes that the user’s factual rating range is the same as the system’s given rating range. However, from observations on real datasets of movie recommender systems, we found that different users have different actual rating ranges, and users can be classified into four kinds according to their personalized rating criterion, including normal, strict, lenient, and middle. We analyzed ratings’ distributions and found that the proportion of user ratings’ local standard deviation to the system’s global standard deviation is equal to that of the user’s actual rating range to the system’s rating range. We propose an improved and unified baseline estimation model based on the standard deviation’s proportion to alleviate the influence of classical baseline estimation’s limitation. We also apply the proposed baseline estimation model in existing latent factor-based CF recommendations and propose two instances. We performed experiments on full ratings of datasets by cross evaluations, including Flixster, Movielens (10 M), Movielens (latest small), FilmTrust, and MiniFilm. The results prove that the proposed baseline estimation model has better predictive accuracy than the classical model and is efficient in improving prediction performance for existing latent factor-based CF recommendations.

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Jelby, Mads Engholm, Nicolas Thibault, Finn Surlyk, Clemens V. Ullmann, Rikke Harlou, and Christoph Korte. "The lower Maastrichtian Hvidskud succession, Møns Klint, Denmark: calcareous nannofossil biostratigraphy, carbon isotope stratigraphy, and bulk and brachiopod oxygen isotopes." Bulletin of the Geological Society of Denmark 62 (November 28, 2014): 89–104. http://dx.doi.org/10.37570/bgsd-2014-62-05.

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A new calcareous nannofossil and δ13C stratigraphy is established for the chalk exposed in the lower Maastrichtian Hvidskud succession, Møns Klint, Denmark. It is based on 21 nannofossil samples and analysis of 82 stable isotope samples, allowing correlation with a previously established brachiopod zonation. The succession, which belongs to the brachiopod spinosa-subtilis to pulchellus-pulchellus zones, extends upwards from calcareous nannofossil subzone UC16ii to UC19ii and encompasses δ13C events M1+ to M2+. A new chronostratigraphic and geochronological age model is proposed based on correlation with the cored boreholes Stevns-1 (Denmark) and ODP Site 762C (Indian Ocean). Hvidskud encompasses the 405 kyr eccentricity cycles Ma40513 – Ma40511 within magnetochron C31r. A sedimentation rate of 5.0 cm kyr-1 can be inferred from correlation to geochronological tie-points in ODP 762C, suggesting an age of ~70.9 Ma for the base of the succession and a duration of >680 kyr for the investigated interval. The Hvidskud succession is well-exposed, easily accessible, and the new stratigraphic framework and precise age model suggest that it can be used as a key locality for stratigraphic correlation of the lower Maastrichtian in north-western Europe. Information on palaeo-seawater temperatures can be drawn from oxygen isotope records obtained from bulk rock samples and 24 micromorphic brachiopod specimens (Terebratulina faujasii). The brachiopod data show a clear diagenetic trend but point to an upper range of unaltered values between –0.4 and –0.6‰. Assuming a δ18O value of –1‰ for seawater in a Cretaceous ice-free world, this would indicate bottom water temperatures of 13.6 to 14.3°C of the Danish Chalk Sea (45°N) during the early Maastrichtian cooling.

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WANG, CHUN-YANG, and XIANG-MU KONG. "AN ATTEMPT TO INTRODUCE LONG-RANGE INTERACTIONS INTO SMALL-WORLD NETWORKS." Modern Physics Letters B 24, no. 07 (March 20, 2010): 671–79. http://dx.doi.org/10.1142/s0217984910022743.

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Distinguishing the long-range bonds with the regular ones, the critical temperature of the spin-lattice Gaussian model built on two typical small-world networks is studied. The results show much difference from the classical case, and thus may induce some more accurate discussion on the critical properties of the spin-lattice systems combined with the small-world networks.

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Uezu, Tatsuya, Tomoyuki Kimoto, Shuji Kiyokawa, and Masato Okada. "Correspondence between Phase Oscillator Network and Classical XY Model with the Same Infinite-Range Interaction in Statics." Journal of the Physical Society of Japan 84, no. 3 (March 15, 2015): 033001. http://dx.doi.org/10.7566/jpsj.84.033001.

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Journal articles on the topic 'Classical range succession model'

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