Journal articles on the topic 'Time reversal of diffusion'
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1
Hutzenthaler, Martin, and Jesse Earl Taylor. "Time reversal of some stationary jump diffusion processes from population genetics." Advances in Applied Probability 42, no. 4 (December 2010): 1147–71. http://dx.doi.org/10.1239/aap/1293113155.
Abstract:
We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.
2
Hutzenthaler, Martin, and Jesse Earl Taylor. "Time reversal of some stationary jump diffusion processes from population genetics." Advances in Applied Probability 42, no. 04 (December 2010): 1147–71. http://dx.doi.org/10.1017/s0001867800004560.
Abstract:
We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.
3
Zang Rui, Wang Bing-Zhong, Ding Shuai, and Gong Zhi-Shuang. "Time reversal multi-target imaging technique based on eliminating the diffusion of the time reversal field." Acta Physica Sinica 65, no. 20 (2016): 204102. http://dx.doi.org/10.7498/aps.65.204102.
4
Haussmann, U. G., and E. Pardoux. "Time Reversal of Diffusions." Annals of Probability 14, no. 4 (October 1986): 1188–205. http://dx.doi.org/10.1214/aop/1176992362.
5
Millet, A., D. Nualart, and M. Sanz. "Integration by Parts and Time Reversal for Diffusion Processes." Annals of Probability 17, no. 1 (January 1989): 208–38. http://dx.doi.org/10.1214/aop/1176991505.
6
Cattiaux, Patrick. "Time reversal of diffusion processes with a boundary condition." Stochastic Processes and their Applications 28, no. 2 (June 1988): 275–92. http://dx.doi.org/10.1016/0304-4149(88)90101-9.
7
Petit, Frédérique. "Time reversal and reflected diffusions." Stochastic Processes and their Applications 69, no. 1 (July 1997): 25–53. http://dx.doi.org/10.1016/s0304-4149(97)00035-5.
8
Kardaras, Constantinos, and Scott Robertson. "Continuous-time perpetuities and time reversal of diffusions." Finance and Stochastics 21, no. 1 (August 10, 2016): 65–110. http://dx.doi.org/10.1007/s00780-016-0308-0.
9
Millet, Annie, David Nualart, and Marta Sanz. "Time reversal for infinite-dimensional diffusions." Probability Theory and Related Fields 82, no. 3 (August 1989): 315–47. http://dx.doi.org/10.1007/bf00339991.
10
Föllmer, H., and A. Wakolbinger. "Time reversal of infinite-dimensional diffusions." Stochastic Processes and their Applications 22, no. 1 (May 1986): 59–77. http://dx.doi.org/10.1016/0304-4149(86)90114-6.
11
Kidwell, Chelsea S., Jeffrey L. Saver, James Mattiello, Sidney Starkman, Y. Pierre Gobin, Gary Duckwiler, Paul M. Vespa, et al. "Late Secondary Injury in Patients Undergoing Vessel Recanalization with Intra-arterial Thrombolysis: Visualization with MRI, Frequency, and Clinical Correlates." Stroke 32, suppl_1 (January 2001): 317. http://dx.doi.org/10.1161/str.32.suppl_1.317-d.
Abstract:
8 Background: Late secondary injury following vessel recanalization, recently observed in animal stroke models, may limit the benefit of reperfusion therapy. The frequency and clinical correlates of secondary injury in humans have not been previously characterized. Methods: Diffusion-perfusion MRIs were performed prior to treatment, early after recanalization (median 4 hrs), and at day 7 in patients undergoing vessel recanalization with intra-arterial (IA) thrombolytics. Post-treatment MRIs were co-registered to the pretreatment scan to allow a voxel-by-voxel analysis of tissue fate over time. Results: Eighteen patients (13 females, 5 males) were studied. Mean age was 71 and median entry NIHSS score 13. Early after recanalization, partial or complete normalization of DWI abnormalities occurred in 8/18 (44%) patients, and of apparent diffusion coefficient (ADC) abnormalities in 13/18 (72%). Among the 8 patients with early DWI reversal, late secondary injury on day 7 (on DWI or T2W sequences) occurred in 5 (63%), and sustained normalization of all reversed tissue in 3 (38%). Across all patients, of tissues showing pretreatment DWI abnormality, 41% of voxels showed no early reversal, 33% early reversal with sustained normalization at day 7, and 18% early reversal but late secondary injury. Pretreatment ADC values were lowest in regions experiencing no reversal (mean ADC 624 um2/sec), intermediate in regions with reversal and secondary decline (641), and highest in regions with sustained reversal (677). Evolution of neurologic deficit (NIHSS) did not differ in patients with secondary injury vs. those with sustained reversal, nor did age, time to recanalization, degree of recanalization, or presence of post-ischemic hyperperfusion. Conclusions: Following vessel recanalization with IA thrombolysis, partial or complete reversal of initial DWI abnormality occurs in ∼40% of patients. A late, secondary signature of injury compromising some or all of the initially normalized tissue occurs in over 50% of these patients, but is not associated with clinical worsening.
12
MAJID, S. "QUANTUM RANDOM WALKS AND TIME REVERSAL." International Journal of Modern Physics A 08, no. 25 (October 10, 1993): 4521–45. http://dx.doi.org/10.1142/s0217751x93001818.
Abstract:
Classical random walks and Markov processes are easily described by Hopf algebras. It is also known that groups and Hopf algebras (quantum groups) lead to classical and quantum diffusions. We study here the more primitive notion of a quantum random walk associated with a general Hopf algebra and show that it has a simple physical interpretation in quantum mechanics. This is by means of a representation theorem motivated from the theory of Kac algebras: If H is any Hopf algebra, it may be realized in Lin(H) in such a way that Δh=W(h⊗1)W−1 for an operator W. This W is interpreted as the time evolution operator for the system at time t coupled quantum-mechanically to the system at time t+δ. Finally, for every Hopf algebra there is a dual one, leading us to a duality operation for quantum random walks and quantum diffusions and a notion of the coentropy of an observable. The dual system has its time reversed with respect to the original system, leading us to a novel kind of CTP theorem.
13
Padmanabhan, Hari, Jason M. Munro, Ismaila Dabo, and Venkatraman Gopalan. "Antisymmetry: Fundamentals and Applications." Annual Review of Materials Research 50, no. 1 (July 1, 2020): 255–81. http://dx.doi.org/10.1146/annurev-matsci-100219-101404.
Abstract:
Symmetry is fundamental to understanding our physical world. An antisymmetry operation switches between two different states of a trait, such as two time states, position states, charge states, spin states, or chemical species. This review covers the fundamental concepts of antisymmetry and focuses on four antisymmetries, namely, spatial inversion in point groups, time reversal, distortion reversal, and wedge reversion. The distinction between classical and quantum mechanical descriptions of time reversal is presented. Applications of these antisymmetries—in crystallography, diffraction, determining the form of property tensors, classifying distortion pathways in transition state theory, finding minimum energy pathways, diffusion, magnetic structures and properties, ferroelectric and multiferroic switching, classifying physical properties in arbitrary dimensions, and antisymmetry-protected topological phenomena—are described.
14
Zhang, Wei. "Some new results on relative entropy production, time reversal, and optimal control of time-inhomogeneous diffusion processes." Journal of Mathematical Physics 62, no. 4 (April 1, 2021): 043302. http://dx.doi.org/10.1063/5.0038740.
15
Sheng, Xia, Chunyu Ru, Honghui Zhao, Shouyi Jin, Bowen Wang, Yupeng Wang, Linghai Han, and Kui Jiao. "Study on Anode Catalyst Layer Configuration for Proton Exchange Membrane Fuel Cell with Enhanced Reversal Tolerance and Polarization Performance." Energies 15, no. 8 (April 8, 2022): 2732. http://dx.doi.org/10.3390/en15082732.
Abstract:
Hydrogen starvation leads to the extreme deterioration of fuel cell performance due to the induced voltage reversal and carbon corrosion in the anode catalyst layer (ACL) and gas diffusion layer. In this paper, reversal-tolerant anodes (RTAs) with different ACL configurations are proposed, where IrOx/C is used as a water electrolysis catalyst. Experimental results show that the separate IrOx/C catalyst layer of MEA samples, layered reversal-tolerant catalyst-coated membrane (layered-RTA), and reversal-tolerant gas diffusion electrode (GDE-RTA) significantly enhance the reversal tolerance and cell performance compared to conventional anode and common RTA consisting of a homogeneous catalyst layer mixed with IrOx/C and Pt/C (hybrid-RTA). Of these, GDE-RTA possessed a reversal tolerance time of 86 min, a power density of 1.42 W cm−2, and a minimum degradation rate of 2.4 mV min−1, suggesting it to be the best RTA structure. Cyclic voltammetry and electrochemical impedance spectrum were used to detect the properties of each sample. Additionally, the degradation mechanisms of the three RTAs are thoroughly investigated and discussed by means of microstructural characterization through scanning electron microscopy and transmission electron microscopy. This work provides novel ideas for the fabrication of a robust RTA by tuning the ACL configuration, which is practical for the commercialization of fuel cells.
16
Lu, Xi-Cheng, Yang Qiu, Jin Tian, Hai-Bo Wang, Ling Jiang, and Xin Chen. "Analysis of time reversal cavity characteristics based on multipath channel model." Acta Physica Sinica 71, no. 2 (2022): 024101. http://dx.doi.org/10.7498/aps.71.20210701.
Abstract:
The electromagnetic wave time reversal technology using time reversal cavity (TRC) has potential applications in many areas, such as pulse compression, power synthesis, perturbation detection, beamforming, etc. Microwave chaotic cavity with multi-path transmission characteristics is usually used in TRC. Based on diffraction theory, it can prove that this kind of cavity has spatiotemporal focusing characteristics and can be used for compressing pulses, but it cannot be used to analyze the reversal performance of the cavity. In order to obtain a suitable analysis method and guide the design of TRC, in this work, the scattering, diffusion and attenuation characteristics of electromagnetic wave propagation are analyzed and a multipath channel model of TRC is built by the channel theory. Moreover, the crosstalk characteristics between paths are studied, and the generation mechanism of time sidelobe, time sidelobe shift and interference are also investigated. In addition, under the assumption of random plane wave, the distribution characteristics of spatial focal spot are analyzed, which is consistent with the diffraction theory. Moreover, the actual focal spot size is not only limited by the diffraction limit, but also related to the initial focal spot size. The theoretical analysis results are basically consistent with the experimental and numerical simulation results.
17
Zhang, Zijian, Zhou Zhao, Jun Yu, and Qi Tian. "ShiftDDPMs: Exploring Conditional Diffusion Models by Shifting Diffusion Trajectories." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 3 (June 26, 2023): 3552–60. http://dx.doi.org/10.1609/aaai.v37i3.25465.
Abstract:
Diffusion models have recently exhibited remarkable abilities to synthesize striking image samples since the introduction of denoising diffusion probabilistic models (DDPMs). Their key idea is to disrupt images into noise through a fixed forward process and learn its reverse process to generate samples from noise in a denoising way. For conditional DDPMs, most existing practices relate conditions only to the reverse process and fit it to the reversal of unconditional forward process. We find this will limit the condition modeling and generation in a small time window. In this paper, we propose a novel and flexible conditional diffusion model by introducing conditions into the forward process. We utilize extra latent space to allocate an exclusive diffusion trajectory for each condition based on some shifting rules, which will disperse condition modeling to all timesteps and improve the learning capacity of model. We formulate our method, which we call ShiftDDPMs, and provide a unified point of view on existing related methods. Extensive qualitative and quantitative experiments on image synthesis demonstrate the feasibility and effectiveness of ShiftDDPMs.
18
Weber, Matthias. "Time Reversal for Gap Diffusions with Nonlocal Boundary Conditions." Mathematische Nachrichten 170, no. 1 (November 11, 2006): 299–306. http://dx.doi.org/10.1002/mana.19941700121.
19
Denzler, Jochen, and Robert J. McCann. "Nonlinear diffusion from a delocalized source: affine self-similarity, time reversal, & nonradial focusing geometries." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 25, no. 5 (September 2008): 865–88. http://dx.doi.org/10.1016/j.anihpc.2007.05.002.
20
DERODE, ARNAUD, MICKAËL TANTER, ARNAUD TOURIN, LAURENT SANDRIN, and MATHIAS FINK. "NUMERICAL AND EXPERIMENTAL TIME-REVERSAL OF ACOUSTIC WAVES IN RANDOM MEDIA." Journal of Computational Acoustics 09, no. 03 (September 2001): 993–1003. http://dx.doi.org/10.1142/s0218396x01001017.
Abstract:
In classical mechanics, a time-reversal experiment with a large number of particles is impossible. Because of the high sensitivity to initial conditions, one would need to resolve the positions and velocities of each particle with infinite accuracy. Thus, it would require an infinite amount of information, which is of course out of reach. In wave physics however, the amount of information required to describe a wave field is limited and depends on the shortest wavelength of the field. Thus we can propose an acoustic equivalent of the experiment we mentioned above. We start with a coherent transient pulse, let it propagate through a disordered highly scattering medium, then record the scattered field and time-reverse it: surprisingly, it travels back to its initial source, which is not predictable by usual theories for random media. Indeed, to study waves propagation in disordered media theoreticians, who find it difficult to deal with one realization of disorder, use concepts defined as an average over the realizations, which naturally leads to the diffusion approximation. But the corresponding equation is not time-reversal invariant and thus fails in describing our experiment. Then, to understand our experimental results and try to predict new ones, we have developed a finite elements simulation based on the real microscopic time-invariant equation of propagation. The experimental and numerical results are found to be in very good agreement.
21
Narita, Yasuhito, and Uwe Motschmann. "Can an interplanetary magnetic field reach the surface of Venus?" Annales Geophysicae 36, no. 6 (November 15, 2018): 1537–43. http://dx.doi.org/10.5194/angeo-36-1537-2018.
Abstract:
Abstract. We address the question of whether there is a possibility of an interplanetary magnetic field reaching Venus' surface by magnetic diffusion across the ionosphere. We present a model calculation, estimate the magnetic diffusion time at Venus, and find out that the typical diffusion timescale is in a range between 12 and 54 h, depending on the solar activity and the ionospheric magnetic field condition. The magnetic field can thus permeate Venus' surface and even its interior when the solar wind is stationary (i.e., no magnetic field reversal) on the timescale of half a day to several days.
22
Van Steenhoven, A. A., and F. J. H. M. Van De Beucken. "Dynamical analysis of electrochemical wall shear rate measurements." Journal of Fluid Mechanics 231 (October 1991): 599–614. http://dx.doi.org/10.1017/s0022112091003531.
Abstract:
The performance of a circular electrochemical wall shear rate probe under unsteady flow conditions is analysed through a combined experimental, numerical and analytical approach. The experiments arc performed with a ferri- and ferrocyanide redox couple and compared to finite element analyses of the two-dimensional time-dependent convection—diffusion equation. The results are related to the analytical Lévêque solution for steady flow and for some cases to Pedley's model for heat transfer in reversing shear flow (Pedley 1976).The steady flow analyses showed that in our experiments axial diffusion is only of minor importance but that for the lower Péclet numbers (< 104) three-dimensional effects, like tangential diffusion, may not be neglected. A similar result is found for the oscillating case. A fair agreement is found between experimental and numerical data during flow acceleration, but during flow reversal remarkable (about 15%) deviations are found. The observed insensitivity of the transducer during flow reversal is quite well predicted by Pedley's model. Finally, the performance of the probe may be improved somewhat by a decrease in cathode length and cathode—anode distance.
23
Bonilla-Licea, Moise, Dieter Schuch, and Moises Bonilla Estrada. "Diffusion Effect in Quantum Hydrodynamics." Axioms 11, no. 10 (October 13, 2022): 552. http://dx.doi.org/10.3390/axioms11100552.
Abstract:
In this paper, we introduce (at least formally) a diffusion effect that is based on an axiom postulated by Werner Heisenberg in the early days of quantum mechanics. His statement was that—in quantum mechanics—kinematical quantities such as velocity must be treated as complex matrices. In the hydrodynamic formulation of quantum mechanics according to Madelung, the complex Schrödinger equation is rewritten in terms of two real equations—a continuity equation and a modified Hamilton–Jacobi equation. Considering seriously Heisenberg’s axiom, the velocity occurring in the continuity equation should be replaced by a complex one, thus introducing a diffusion term with an imaginary diffusion coefficient. Therefore, in quantum mechanics, there should be a diffusion effect showing up in the dynamics. This is the case in the time evolution of the free-motion wave packet under time reversal. The maximum returns to the initial position; however, the width of the wave packet does not shrink to its initial width. This effect is obvious but—as far as we know—it is not mentioned in any textbook. In our paper, we discuss this effect in detail and show the connection with a complex version of quantum hydrodynamics.
24
Egami, Masahiko, and Rusudan Kevkhishvili. "Time reversal and last passage time of diffusions with applications to credit risk management." Finance and Stochastics 24, no. 3 (May 18, 2020): 795–825. http://dx.doi.org/10.1007/s00780-020-00423-6.
25
Alpaslan, Alper, Max Wintermark, László Pintér, Sumaira Macdonald, Richard Ruedy, and Ralf Kolvenbach. "Transcarotid Artery Revascularization With Flow Reversal." Journal of Endovascular Therapy 24, no. 2 (February 17, 2017): 265–70. http://dx.doi.org/10.1177/1526602817693607.
Abstract:
Purpose: To report a study evaluating the safety and efficacy of stenting via direct carotid access with flow reversal using the ENROUTE Transcarotid Neuroprotection System. Methods: Between March 2009 and June 2012, 75 patients (mean age 72.6 years; 45 men) underwent carotid artery stenting with the ENROUTE System; the majority of patients (63, 84%) were asymptomatic. The primary safety endpoint was the composite of major stroke, myocardial infarction, or death at 30 days. Efficacy outcomes included acute device success, procedure success, and tolerance to flow reversal. Fifty-six (74.7%) patients underwent diffusion-weighted magnetic resonance imaging (DW-MRI) before and after the procedure to assess the development of new ischemic brain lesions. Results: Acute device and procedure success were achieved in 68 (90.6%) patients. The reverse flow circuit was established in 71 (94.6%) patients; only 5 patients demonstrated transient intolerance to flow reversal that did not interfere with completion of the procedure. The mean time on flow reversal was 19.1 minutes. In the DW-MRI substudy, 10 (17.9%) of 56 patients had ipsilateral new white lesions with a mean volume of 0.17 mL. At 30 days, no major stroke, myocardial infarction, or death occurred; 1 patient had experienced a minor stroke that was adjudicated as not related to either the device or procedure. Conclusion: Results of the PROOF study demonstrate the safety and efficacy of transcarotid revascularization with the ENROUTE Transcarotid Neuroprotection System.
26
Morris, S. J. S. "On the contact region of a diffusion-limited evaporating drop: a local analysis." Journal of Fluid Mechanics 739 (December 18, 2013): 308–37. http://dx.doi.org/10.1017/jfm.2013.577.
Abstract:
AbstractMotivated by experiments showing that a sessile drop of volatile perfectly wetting liquid initially advances over the substrate, but then reverses, we formulate the problem describing the contact region at reversal. Assuming a separation of scales, so that the radial extent of this region is small compared with the instantaneous radius$a$of the apparent contact line, we show that the time scale characterizing the contact region is small compared with that on which the bulk drop is evolving. As a result, the contact region is governed by a boundary-value problem, rather than an initial-value problem: the contact region has no memory, and all its properties are determined by conditions at the instant of reversal. We conclude that the apparent contact angle$\theta $is a function of the instantaneous drop radius$a$, as found in the experiments. We then non-dimensionalize the boundary-value problem, and find that its solution depends on one parameter$\mathscr{L}$, a dimensionless surface tension. According to this formulation, the apparent contact angle is well-defined: at the outer edge of the contact region, the film slope approaches a limit that is independent of the curvature of bulk drop. In this, it differs from the dynamic contact angle observed during spreading of non-volatile drops. Next, we analyse the boundary-value problem assuming$\mathscr{L}$to be small. Though, for arbitrary$\mathscr{L}$, determining$\theta $requires solving the steady diffusion equation for the vapour, there is, for small$\mathscr{L}$, a further separation of scales within the contact region. As a result,$\theta $is now determined by solving an ordinary differential equation. We predict that$\theta $varies as${a}^{- 1/ 6} $, as found experimentally for small drops ($a\lt 1~\mathrm{mm} $). For these drops, predicted and measured angles agree to within 10–30 %. Because the discrepancy increases with$a$, but$\mathscr{L}$is a decreasing function of$a$, we infer that some process occurring outside the contact region is required to explain the observed behaviour of larger drops having$a\gt 1~\mathrm{mm} $.
27
Zhao, Feng, Yang Li, and Xianbin Liu. "A Prehistorical Approach to Optimal Fluctuations for General Langevin Dynamics with Weak Gaussian White Noises." Applied Sciences 12, no. 17 (August 26, 2022): 8569. http://dx.doi.org/10.3390/app12178569.
Abstract:
The dynamics of a stochastic system that exhibits large fluctuations to a given state are almost deterministic due to weak random perturbations. Such large fluctuations occur with overwhelming probability in the vicinity of the so-called optimal path, which is a vital concept in physics, chemistry, and biology, as it uncovers the way in which a physical process escapes from the attractive domain of a metastable state and transitions between different metastable states. In this paper, we examine the prehistorical description of the optimal fluctuation with the unifying framework of Langevin dynamics by means of a quantity called prehistory probability density. We show that the optimal fluctuation has a strong connection with the time reversal of the associated diffusion process. Specifically, in the stationary or quasi-stationary cases, it is found that the prehistory probability density actually acts as the transition probability density of the reversed process. As noise intensity approaches zero, it focuses on the average dynamics of the reversed process due to the law of large numbers, which is then shown to coincide with the time reversal of the optimal path. The local dispersion of the prehistory probability density can thus be reformulated as a Gaussian distribution corresponding to the linearized part of the reversed process. In addition, as an analogue of the original definition in the stationary states, it is proven that the concept of prehistory probability density can also be extended to nonstationary cases where similar properties are still valid. Based on these theoretical results, an algorithm is designed and then successfully applied to a one-dimensional example at the end, showing its accuracy for pinpointing the location of the optimal path and its efficacy in cases where multiple optimal paths coexist.
28
Davis, William, and Bruce Buffett. "Inferring core processes using stochastic models of the geodynamo." Geophysical Journal International 228, no. 3 (October 8, 2021): 1478–93. http://dx.doi.org/10.1093/gji/ggab412.
Abstract:
SUMMARY Recent studies have represented time variations in the Earth’s axial magnetic dipole field as a stochastic process, which comprise both deterministic and random elements. To explore how these elements are affected by the style and vigour of convection in the core, as well as the core–mantle boundary conditions, we construct stochastic models from a set of numerical dynamo simulations at low Ekman numbers. The deterministic part of the stochastic model, the drift term, characterizes the slow relaxation of the dipole back to its time average. We find that these variations are predominantly accommodated by the slowest decay mode, enhanced by turbulent diffusion to enable a faster relaxation. The random part—the noise term—is set by the amplitude and timescale of variations in dipole field generation, including contributions from both velocity and internal magnetic field variations. Applying these interpretations to the palaeomagnetic field suggest that reversal rates are very sensitive to rms variations in the field generation. Less than a 50 per cent reduction in rms field generation variations is sufficient to prevent reversals for the recent magnetic field.
29
Metman, Maurits C., Philip W. Livermore, Jonathan E. Mound, and Ciarán D. Beggan. "Modelling decadal secular variation with only magnetic diffusion." Geophysical Journal International 219, Supplement_1 (February 17, 2019): S58—S82. http://dx.doi.org/10.1093/gji/ggz089.
Abstract:
SUMMARY Secular variation (SV) of Earth’s internal magnetic field is the sum of two contributions, one resulting from core fluid flow and the other from magnetic diffusion. Based on the millenial diffusive timescale of global-scale structures, magnetic diffusion is widely perceived to be too weak to significantly contribute to decadal SV, and indeed is entirely neglected in the commonly adopted end-member of frozen-flux. Such an argument however lacks consideration of radially fine-scaled magnetic structures in the outermost part of the liquid core, whose diffusive timescale is much shorter. Here we consider the opposite end-member model to frozen flux, that of purely diffusive evolution associated with the total absence of fluid flow. Our work is based on a variational formulation, where we seek an optimized full-sphere initial magnetic field structure whose diffusive evolution best fits, over various time windows, a time-dependent magnetic field model. We present models that are regularized based on their magnetic energy, and consider how well they can fit the COV-OBS.x1 ensemble mean using a global error bound based on the standard deviation of the ensemble. With these regularized models, over time periods of up to 30 yr, it is possible to fit COV-OBS.x1 within one standard deviation at all times. For time windows up to 102 yr we show that our models can fit COV-OBS.x1 when adopting a time-averaged global uncertainty. Our modelling is sensitive only to magnetic structures in approximately the top 10 per cent of the liquid core, and show an increased surface area of reversed flux at depth. The diffusive models recover fundamental characteristics of field evolution including the historical westward drift, the recent acceleration of the North Magnetic Pole and reversed-flux emergence. Based on a global time-averaged residual, our diffusive models fit the evolution of the geomagnetic field comparably, and sometimes better than, frozen-flux models within short time windows.
30
Wapenaar, Kees, Evert Slob, Roel Snieder, and Andrew Curtis. "Tutorial on seismic interferometry: Part 2 — Underlying theory and new advances." GEOPHYSICS 75, no. 5 (September 2010): 75A211–75A227. http://dx.doi.org/10.1190/1.3463440.
Abstract:
In the 1990s, the method of time-reversed acoustics was developed. This method exploits the fact that the acoustic wave equation for a lossless medium is invariant for time reversal. When ultrasonic responses recorded by piezoelectric transducers are reversed in time and fed simultaneously as source signals to the transducers, they focus at the position of the original source, even when the medium is very complex. In seismic interferometry the time-reversed responses are not physically sent into the earth, but they are convolved with other measured responses. The effect is essentially the same: The time-reversed signals focus and create a virtual source which radiates waves into the medium that are subsequently recorded by receivers. A mathematical derivation, based on reciprocity theory, formalizes this principle: The crosscorrelation of responses at two receivers, integrated over differ-ent sources, gives the Green’s function emitted by a virtual source at the position of one of the receivers and observed by the other receiver. This Green’s function representation for seismic interferometry is based on the assumption that the medium is lossless and nonmoving. Recent developments, circumventing these assumptions, include interferometric representations for attenuating and/or moving media, as well as unified representations for waves and diffusion phenomena, bending waves, quantum mechanical scattering, potential fields, elastodynamic, electromagnetic, poroelastic, and electroseismic waves. Significant improvements in the quality of the retrieved Green’s functions have been obtained with interferometry by deconvolution. A trace-by-trace deconvolution process compensates for complex source functions and the attenuation of the medium. Interferometry by multidimensional deconvolution also compensates for the effects of one-sided and/or irregular illumination.
31
Davidson, P. A. "The interaction between swirling and recirculating velocity components in unsteady, inviscid flow." Journal of Fluid Mechanics 209 (December 1989): 35–55. http://dx.doi.org/10.1017/s0022112089003022.
Abstract:
In this paper we consider the transient evolution of a swirling, recirculating flow in a truncated cylinder. In particular, we consider an initial time period during which the evolution of the flow is controlled by inertia. Such flows exhibit a mutual interaction between the swirl and the poloidal recirculation, whereby any axial gradient in swirl alters the recirculation, which, in turn, redistributes the swirl. This interaction may be visualized as a flexing of the poloidal vortex lines, the best known example of which is the inertial wave. Physical arguments and numerical experiments suggest that, typically, a strong, oscillatory recirculation will develop. We examine the exchange of energy between the swirl and recirculation, and show that the direction of transfer depends on the relative signs of ψ and ηuθ/ηz. In addition, there is a limit to the amount of energy that may be exchanged, since conservation of angular momentum imposes a lower bound on the kinetic energy of the swirl. The characteristic reversal time for the recirculation is estimated by considering the history of fluid particles on the endwalls. Its magnitude depends on the relative strengths of the swirl and recirculation. When the recirculation is large, the reversal time exceeds the turn-over time for a poloidal eddy and, consequently, the vortex lines accumulate at the stagnation points on the endwalls. This leads to accelerated local diffusion on the axis. An elementary one-parameter model is proposed for these nonlinear oscillations. In the limit of very weak recirculation, this model is consistent with the exact solution for inertial waves, while for strong recirculation, it confirms that the reversal time is greater than the turn-over time, and that the vortex lines accumulate on the axis.
32
Leclaire, K., D. Osmon, and I. Driscoll. "C-18 A Distributional and Theoretical Analysis of Reaction Time in the Reversal Task Across Adulthood." Archives of Clinical Neuropsychology 34, no. 6 (July 25, 2019): 1047. http://dx.doi.org/10.1093/arclin/acz034.180.
Abstract:
Abstract Objective Reversal learning (RL) tasks, known to be frontal-lobe dependent, are frequently used in experimental paradigms to assess components of executive function. Extant literature has historically focused on measures of accuracy as their primary outcome, but reaction time (RT) has not yet been well examined. The present study thoroughly examines RT in order to better characterize RL performance and how it changes with age. Method 182 healthy aging participants completed a RL task, including 43 young (ages 18-30) and 139 community dwelling middle-aged adults (ages 40-61). In order to identify the best predictors of age among RL performance, an adaptive elastic net generalized regression with Poisson distribution modeling and Akakie information criteria (AIC) penalty was utilized. Variables were included from the Diffusion model (a, v, t0), ex-Gaussian distribution (mu, sigma, tau), Normal-3 Mixture distribution (location1-3, dispersion1-3, probability1-3), and RL trials-to-criterion. Results A Generalized R2=.83 demonstrated good prediction of age with 7 of 17 variables being significant predictors, including, in order of significance: Mu, Sigma, Dispersion1, Location1, Dispersion2, t0, and Tau. Only two of those predictors had Independent Resampled Variable Importance values greater than .1 (Mu=.645, Dispersion1=.221), indicating older age is associated with slower and more variable efficient responding. Conclusions RT adds unique variance to explaining age differences in reversal learning performance which suggests it’s important to measure RT as a fractionated construct. Older adults showed slower efficient mean RT and increased intra-individual variability, which has been linked to poorer frontal lobe processes and age-related cognitive decline.
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Gao, T. F., L. F. Wang, R. Z. Huang, and Z. G. Zheng. "Transport performance of feedback-coupled Brownian ratchets with closed-loop control strategy." International Journal of Modern Physics B 29, no. 12 (May 10, 2015): 1550069. http://dx.doi.org/10.1142/s0217979215500691.
Abstract:
The transport performance of two feedback-coupled Brownian particles, which are subjected to the external force, the unbiased time-periodic force and thermal noise, is investigated in the double-well ratchet potential. The average velocity, the average diffusion coefficient and the Pe number are calculated, respectively. The results demonstrate that the transport characteristic of Brownian particles is different under the action of two factors of unbiased time-periodic force, amplitude and frequency. The former factor induces the increase of the average velocity and the average diffusion coefficient with the decrease of thermal noise intensity within certain limits, whereas the latter makes the average velocity decrease in the transport of coupled particles. Moreover, it is found there is an optimal value of the driving frequency at which the Pe number reaches its maximum. Remarkably, it is shown that the current reversal can be achieved by increasing the external force, and the directed transport can be enhanced by varying the structure of the ratchet potential and the intensity of noise.
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You, Zhihong, Aparna Baskaran, and M. Cristina Marchetti. "Nonreciprocity as a generic route to traveling states." Proceedings of the National Academy of Sciences 117, no. 33 (August 4, 2020): 19767–72. http://dx.doi.org/10.1073/pnas.2010318117.
Abstract:
We examine a nonreciprocally coupled dynamical model of a mixture of two diffusing species. We demonstrate that nonreciprocity, which is encoded in the model via antagonistic cross-diffusivities, provides a generic mechanism for the emergence of traveling patterns in purely diffusive systems with conservative dynamics. In the absence of nonreciprocity, the binary fluid mixture undergoes a phase transition from a homogeneous mixed state to a demixed state with spatially separated regions rich in one of the two components. Above a critical value of the parameter tuning nonreciprocity, the static demixed pattern acquires a finite velocity, resulting in a state that breaks both spatial and time-reversal symmetry, as well as the reflection parity of the static pattern. We elucidate the generic nature of the transition to traveling patterns using a minimal model that can be studied analytically. Our work has direct relevance to nonequilibrium assembly in mixtures of chemically interacting colloids that are known to exhibit nonreciprocal effective interactions, as well as to mixtures of active and passive agents where traveling states of the type predicted here have been observed in simulations. It also provides insight on transitions to traveling and oscillatory states seen in a broad range of nonreciprocal systems with nonconservative dynamics, from reaction–diffusion and prey–predators models to multispecies mixtures of microorganisms with antagonistic interactions.
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Xing, Xiu-San. "On the Fundamental Equation of Nonequilibrium Statistical Physics." International Journal of Modern Physics B 12, no. 20 (August 10, 1998): 2005–29. http://dx.doi.org/10.1142/s0217979298001174.
Abstract:
In this paper we proposed a new fundamental equation of statistical physics in place of the Liouville equation. That is the anomalous Langevin equation in Γ space or its equivalent Liouville diffusion equation of time-reversal asymmetry. This equation reflects that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality and the law of motion of statistical thermodynamics is stochastic in essence, but not completely deterministic. Starting from this equation the BBGKY diffusion equation hierarchy, the law of entropy increase, the theorem of minimum entropy production, the balance equations of Gibbs and Boltzmann nonequilibrium entropy are derived and presented here. Furthermore we have derived a nonlinear evolution equation of Gibbs and Boltzmann nonequilibrium entropy density. To our knowledge, this is the first treatise on them. The evolution equation shows that the change of nonequilibrium entropy density originates together from drift, typical diffusion and complicated inherent source production. Contrary to conventional viewpoint, the entropy production density σ≥0 everywhere for any systems cannot be proved universally. Conversely, σ may be negative in some local space of some inhomogeneous systems far from equilibrium. The hydrodynamic equations, such as the generalized Navier–Stokes equation, the mass drift-diffusion equation and the thermal conductivity equation have been derived succinctly from the BBGKY diffusion equation hierarchy. The Liouville diffusion equation has the same equilibrium solution as that of the Liouville equation. All these derivations and results are unified and rigorous from the new fundamental equation without adding any extra assumption.
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Sugiyama, Jun, Ola K. Forslund, Elisabetta Nocerino, Yasmine Sassa, Martin Månsson, Adrian Hillier, and Katsuhiko Ishida. "Negative muon spin rotation and relaxation on superconducting MgB2." Journal of Physics: Conference Series 2462, no. 1 (March 1, 2023): 012059. http://dx.doi.org/10.1088/1742-6596/2462/1/012059.
Abstract:
Abstract The internal nuclear magnetic field in a superconducting MgB2 powder sample was studied with a µ− SR technique. Although the past µ +SR study on MgB2 reported the appearance of a dynamic behavior even below Tc due to µ + diffusion, µ− SR shows a static behavior in the whole temperature range measured, as expected. The ZF-µ− SR spectra do not suggest any appearance of additional magnetic field below Tc within the experimental accuracy. Considering the small asymmetry of the µ− SR signal, it is a challenge to detect the appearance of an internal magnetic field below Tc caused by the time reversal symmetry breaking.
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Taniguchi, Nobuhiko. "Universal and Nonuniversal Dynamical Conductivity in Small Metallic Grains: An Ambivalent Role of T-Invariance at Finite Frequency." Journal of Probability and Statistics 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/751395.
Abstract:
The idea of random matrix theory is applicable not only to the level statistics but also to various physical observables. Taking the dynamical conductivity in isolated quantum dots with diffusive dynamics, we investigate analytically intertwining effects of the time-reversal invariance, level repulsion and quantum interference. We clarify an ambivalent role of the time-reversal invariance at finite frequency by a new invariant analysis respecting the symmetry of the effective field theory. A subtlety of the operator insertion, and the fast-slow mode separation within the effective field description is pointed out.
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Ruggiero, G. A., Y. Ourmières, E. Cosme, J. Blum, D. Auroux, and J. Verron. "Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model." Nonlinear Processes in Geophysics 22, no. 2 (April 29, 2015): 233–48. http://dx.doi.org/10.5194/npg-22-233-2015.
Abstract:
Abstract. The diffusive back-and-forth nudging (DBFN) is an easy-to-implement iterative data assimilation method based on the well-known nudging method. It consists of a sequence of forward and backward model integrations, within a given time window, both of them using a feedback term to the observations. Therefore, in the DBFN, the nudging asymptotic behaviour is translated into an infinite number of iterations within a bounded time domain. In this method, the backward integration is carried out thanks to what is called backward model, which is basically the forward model with reversed time step sign. To maintain numeral stability, the diffusion terms also have their sign reversed, giving a diffusive character to the algorithm. In this article the DBFN performance to control a primitive equation ocean model is investigated. In this kind of model non-resolved scales are modelled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article, the DBFN approximations and their consequences for the data assimilation system set-up are analysed. Our main result is that the DBFN may provide results which are comparable to those produced by a 4Dvar implementation with a much simpler implementation and a shorter CPU time for convergence. The conducted sensitivity tests show that the 4Dvar profits of long assimilation windows to propagate surface information downwards, and that for the DBFN, it is worth using short assimilation windows to reduce the impact of diffusion-induced errors. Moreover, the DBFN is less sensitive to the first guess than the 4Dvar.
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Ruggiero, G. A., Y. Ourmières, E. Cosme, J. Blum, D. Auroux, and J. Verron. "Data assimilation experiments using the diffusive back and forth nudging for the NEMO ocean model." Nonlinear Processes in Geophysics Discussions 1, no. 2 (July 16, 2014): 1073–131. http://dx.doi.org/10.5194/npgd-1-1073-2014.
Abstract:
Abstract. The Diffusive Back and Forth Nudging (DBFN) is an easy-to-implement iterative data assimilation method based on the well-known Nudging method. It consists in a sequence of forward and backward model integrations, within a given time window, both of them using a feedback term to the observations. Therefore in the DBFN, the Nudging asymptotic behavior is translated into an infinite number of iterations within a bounded time domain. In this method, the backward integration is carried out thanks to what is called backward model, which is basically the forward model with reversed time step sign. To maintain numeral stability the diffusion terms also have their sign reversed, giving a diffusive character to the algorithm. In this article the DBFN performance to control a primitive equation ocean model is investigated. In this kind of model non-resolved scales are modeled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article the DBFN approximations and their consequences on the data assimilation system set-up are analyzed. Our main result is that the DBFN may provide results which are comparable to those produced by a 4Dvar implementation with a much simpler implementation and a shorter CPU time for convergence.
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Hess, Siegfried. "Construction And Test Of Thermostats And Twirlers For Molecular Rotations." Zeitschrift für Naturforschung A 58, no. 7-8 (August 1, 2003): 377–91. http://dx.doi.org/10.1515/zna-2003-7-801.
Abstract:
The equations of motion are coupled with a dynamical variable, referred to as twirler, which randomizes the angular momentum. The equations are time-reversal invariant, just as those for the standard Gaussian, Nosé-Hoover and configurational thermostats. The derivation of the basic equations is outlined. Test calculations are performed for the two-dimensional isotropic harmonic oscillator and for a nonlinear elastic dumbbell, used as a simple model to study properties of polymer molecules. Graphs of characteristic quantities and orbits, some of which are rather intriguing, are displayed. As applications, the rotational diffusion and the influence of a shear flow on the angular velocity and the deformation of the model polymer are analyzed.
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Mahadevan, Jagannathan. "A Study of the Effect of Fracture Walls on Tracer Transport." SPE Journal 23, no. 01 (August 17, 2017): 157–71. http://dx.doi.org/10.2118/187941-pa.
Abstract:
Summary Subsurface permeable systems are heterogeneous at multiple scales and are often fractured. Flow and transport in the subsurface formations are impacted by the presence of fractures, both natural and induced. The effects of permeability heterogeneity and fractures on tracer tests are not well-understood. Echo-tracer (i.e., single-well-injection withdrawal) and transmission-tracer (i.e., dipole) tests can provide information on the flow and transport-system heterogeneity in layered formations. The reversal of flow paths in the echo tests tends to cancel out the non-Gaussian, high-permeability flow behavior in the tracer histories, as observed in laboratory experiments. A question arises whether similar Echo-tracer behavior may be observed in tracer responses for an extreme case of heterogeneity, such as a multiporosity fractured permeable system. A fractured rock consists of high-permeability contrast with high fracture permeability and low matrix permeability, often differing by orders of magnitude. The tracer response from an echo test as well as a transmission test in fractured systems, with high level of heterogeneity, is known to be controlled by the extent of molecular diffusion into the matrix. Dispersion may be dominant in the fracture volume, whereas the molecular diffusion is expected to occur across the fracture/wall interface. We discuss the 1D propagator of diffusion, with convection, and its behavior in the presence of a reflecting and absorbing fracture wall. A wave model is presented to understand the tracer transport in a fracture with differential-diffusion properties. The model predicts that diffusion and adsorption of tracer can produce a retardation of the tracer propagation in the fracture in a transmission-tracer test. The retardation leads to a difference in the arrival times of the tracer, which can then be used to calculate the length of a fracture. The model prediction is compared with published transmission-tracer test experimental data in a fractured till rock. Comparison of the model prediction of tracer-front-arrival times shows good agreement. The arrival time depends on the diffusion coefficient, average time of exposure of the solution to the fractured system, the length of the fracture, and the fracture spacing. Prediction of the echo-tracer test shows that for a fractured system, the retardation of the tracer produces a delayed arrival of the diffusing tracer as opposed to the nondiffusing tracer. The study adapts existing techniques for simple-wave description of tracer transport to a fractured system with absorbing walls. The model for prediction of front movement in the fractured system is novel.
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Trowbridge, J. H., C. N. Kanetkar, and N. T. Wu. "NUMERICAL SIMULATION OF TURBULENT WAVE BOUNDARY LAYERS." Coastal Engineering Proceedings 1, no. 20 (January 29, 1986): 119. http://dx.doi.org/10.9753/icce.v20.119.
Abstract:
This paper reports numerical computations of fully rough turbulent boundary layers produced by first and second order Stokes waves. The computations are based on a mixing length turbulence closure and on a slightly more sophisticated turbulent kinetic energy closure. The first order results compare well with existing laboratory results. Reversal of the second order steady streaming under relatively long waves, which has been predicted analytically, is also predicted in the numerical results, The steady second order velocity field is found to become fully established only after a development time on the order of a few hundred wave periods. Both the first and second order results indicate that advection and diffusion of turbulent kinetic energy play a minor role in determining the Reynolds averaged velocity field.
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Berge, Lars Inge. "Radial migration of a single particle in a pore by the resistive pulse and the pressure reversal technique." Journal of Fluid Mechanics 217 (August 1990): 349–66. http://dx.doi.org/10.1017/s0022112090000751.
Abstract:
Radial migration (particle motion transverse to streamlines) in a system which combines frequent entry, straight pore, and exit regions were investigated experimentally for small particle and pore sizes. Pore diameters were less than 30 μm and typical particle to pore diameter ratios were about 0.25. Our new modification of the resistive pulse technique based on pressure reversal, extends this experimental technique to also include single-particle flow dynamics. By pressure drive, a particle in an electrolyte enters a current-carrying pore and an increase in resistance proportional to the particle volume is detected. When the particle exits the pore, the pressure can be reversed such that the particle re-enters the pore. Detailed studies of particle flow properties in a size range relevant to flow in porous media is now possible. The emphasis in this investigation is on radial migration. The effect of particle sedimentation has been negligible, while particle diffusion becomes significant for submicron particles. The measured evolution of the transit time as the particle migrates compares well with an empirical relationship for the migration velocity first proposed by Segré & Silberberg (1962 a, b) and later verified by Ishii & Hasimoto (1980). Entrance and exit effects do not seem to be important for long pores, the results scale very nicely when the pore length is changed.
44
Ulrich, T. J., Alexander M. Sutin, Thomas Claytor, Pallas Papin, Pierre-Yves Le Bas, and James A. TenCate. "The time reversed elastic nonlinearity diagnostic applied to evaluation of diffusion bonds." Applied Physics Letters 93, no. 15 (October 13, 2008): 151914. http://dx.doi.org/10.1063/1.2998408.
45
Ortland, David A. "A Study of the Global Structure of the Migrating Diurnal Tide Using Generalized Hough Modes." Journal of the Atmospheric Sciences 62, no. 8 (August 1, 2005): 2684–702. http://dx.doi.org/10.1175/jas3501.1.
Abstract:
Abstract The theory of generalized Hough modes developed in a companion paper is applied here to investigate the structure of the migrating diurnal tide in the mesosphere and lower thermosphere. A series of simple examples illustrate how equatorial and midlatitude jets affect the horizontal structure and vertical wavelength of the tidal modes. Complex damping coefficients are used to model the effects of diffusion and gravity wave forcing acting on the tide. It is shown that the imaginary part of the damping coefficient can have significant effects that cannot be adequately represented by real damping coefficients alone. An exact solution of the linearized equations obtained with realistic mean flow and diffusion values representing solstice conditions is compared to the approximate generalized Hough mode solution. It is found that excellent agreement is obtained when expanding to first order, where the corrections at this order account for the observed hemispheric asymmetry in tidal winds during solstice. It is concluded that the asymmetry arises as the result of strong vertical shear in the mean winds that result from the reversal of the sign of the summer and winter jets in the upper mesosphere.
46
Lubatsch, Andreas, and Regine Frank. "A Self-Consistent Quantum Field Theory for Random Lasing." Applied Sciences 9, no. 12 (June 18, 2019): 2477. http://dx.doi.org/10.3390/app9122477.
Abstract:
The spatial formation of coherent random laser modes in strongly scattering disordered random media is a central feature in the understanding of the physics of random lasers. We derive a quantum field theoretical method for random lasing in disordered samples of complex amplifying Mie resonators which is able to provide self-consistently and free of any fit parameter the full set of transport characteristics at and above the laser phase transition. The coherence length and the correlation volume respectively is derived as an experimentally measurable scale of the phase transition at the laser threshold. We find that the process of stimulated emission in extended disordered arrangements of active Mie resonators is ultimately connected to time-reversal symmetric multiple scattering in the sense of photonic transport while the diffusion coefficient is finite. A power law is found for the random laser mode diameters in stationary state with increasing pump intensity.
47
Lopes, Emmanuel V. C., E. Vernek, and Tome M. Schmidt. "RKKY interactions mediated by topological states in transition metal doped bismuthene." Journal of Applied Physics 133, no. 11 (March 21, 2023): 115105. http://dx.doi.org/10.1063/5.0140027.
Abstract:
We have investigated magnetic interactions between transition metal ions in bismuthene topological insulators with protected edge states. We find that these topological states have a crucial role in the magnetic interactions in 2D topological insulators. Using first-principles and model Hamiltonian, we make a comparative study of transition metal doped bulk and nanoribbon bismuthene. While a direct overlap between the transition metal prevails in gapped bulk bismuthene, at the borders of nanoribbons, a long-range magnetism is present. The exchange interactions are well described by a Ruderman–Kittel–Kasuya–Yosida-like Hamiltonian mediated by massive and topological states. Our results show a dominance of antiferromagnetism promoted by the topological states, preserving the spin-locked Dirac crossing states due to a global time-reversal symmetry preservation. This extended magnetic interactions mediated mainly by massless electrons can increase the spin diffusion length being promising for fast dissipationless spintronic devices.
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Che, Yong-Suk, Takashi Sagawa, Yuichi Inoue, Hiroto Takahashi, Tatsuki Hamamoto, Akihiko Ishijima, and Hajime Fukuoka. "Fluctuations in Intracellular CheY-P Concentration Coordinate Reversals of Flagellar Motors in E. coli." Biomolecules 10, no. 11 (November 12, 2020): 1544. http://dx.doi.org/10.3390/biom10111544.
Abstract:
Signal transduction utilizing membrane-spanning receptors and cytoplasmic regulator proteins is a fundamental process for all living organisms, but quantitative studies of the behavior of signaling proteins, such as their diffusion within a cell, are limited. In this study, we show that fluctuations in the concentration of the signaling molecule, phosphorylated CheY, constitute the basis of chemotaxis signaling. To analyze the propagation of the CheY-P signal quantitatively, we measured the coordination of directional switching between flagellar motors on the same cell. We analyzed the time lags of the switching of two motors in both CCW-to-CW and CW-to-CCW switching (∆τCCW-CW and ∆τCW-CCW). In wild-type cells, both time lags increased as a function of the relative distance of two motors from the polar receptor array. The apparent diffusion coefficient estimated for ∆τ values was ~9 µm2/s. The distance-dependency of ∆τCW-CCW disappeared upon loss of polar localization of the CheY-P phosphatase, CheZ. The distance-dependency of the response time for an instantaneously applied serine attractant signal also disappeared with the loss of polar localization of CheZ. These results were modeled by calculating the diffusion of CheY and CheY-P in cells in which phosphorylation and dephosphorylation occur in different subcellular regions. We conclude that diffusion of signaling molecules and their production and destruction through spontaneous activity of the receptor array generates fluctuations in CheY-P concentration over timescales of several hundred milliseconds. Signal fluctuation coordinates rotation among flagella and regulates steady-state run-and-tumble swimming of cells to facilitate efficient responses to environmental chemical signals.
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Vogl, Christopher J., Michael J. Miksis, and Stephen H. Davis. "Moving boundary problems governed by anomalous diffusion." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2147 (June 20, 2012): 3348–69. http://dx.doi.org/10.1098/rspa.2012.0170.
Abstract:
Anomalous diffusion can be characterized by a mean-squared displacement 〈 x 2 ( t )〉 that is proportional to t α where α ≠1. A class of one-dimensional moving boundary problems is investigated that involves one or more regions governed by anomalous diffusion, specifically subdiffusion ( α <1). A novel numerical method is developed to handle the moving interface as well as the singular history kernel of subdiffusion. Two moving boundary problems are solved: the first involves a subdiffusion region to the one side of an interface and a classical diffusion region to the other. The interface will display non-monotone behaviour. The subdiffusion region will always initially advance until a given time, after which it will always recede. The second problem involves subdiffusion regions to both sides of an interface. The interface here also reverses direction after a given time, with the more subdiffusive region initially advancing and then receding.
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Michelitsch, Thomas M., Federico Polito, and Alejandro P. Riascos. "Semi-Markovian Discrete-Time Telegraph Process with Generalized Sibuya Waiting Times." Mathematics 11, no. 2 (January 16, 2023): 471. http://dx.doi.org/10.3390/math11020471.
Abstract:
In a recent work we introduced a semi-Markovian discrete-time generalization of the telegraph process. We referred to this random walk as the ‘squirrel random walk’ (SRW). The SRW is a discrete-time random walk on the one-dimensional infinite lattice where the step direction is reversed at arrival times of a discrete-time renewal process and remains unchanged at uneventful time instants. We first recall general notions of the SRW. The main subject of the paper is the study of the SRW where the step direction switches at the arrival times of a generalization of the Sibuya discrete-time renewal process (GSP) which only recently appeared in the literature. The waiting time density of the GSP, the ‘generalized Sibuya distribution’ (GSD), is such that the moments are finite up to a certain order r≤m−1 (m≥1) and diverging for orders r≥m capturing all behaviors from broad to narrow and containing the standard Sibuya distribution as a special case (m=1). We also derive some new representations for the generating functions related to the GSD. We show that the generalized Sibuya SRW exhibits several regimes of anomalous diffusion depending on the lowest order m of diverging GSD moment. The generalized Sibuya SRW opens various new directions in anomalous physics.