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Artykuły w czasopismach na temat „Nonlocal Transport”

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Data publikacji: 26 października 2024

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1

Shin, Hyeyum Hailey, i Song-You Hong. "Representation of the Subgrid-Scale Turbulent Transport in Convective Boundary Layers at Gray-Zone Resolutions". Monthly Weather Review 143, nr 1 (1.01.2015): 250–71. http://dx.doi.org/10.1175/mwr-d-14-00116.1.

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Abstract Parameterization of the unresolved vertical transport in the planetary boundary layer (PBL) is one of the key physics algorithms in atmospheric models. This study attempts to represent the subgrid-scale (SGS) turbulent transport in convective boundary layers (CBLs) at gray-zone resolutions by investigating the effects of grid-size dependency in the vertical heat transport parameterization for CBL simulations. The SGS transport profile is parameterized based on the 2013 conceptual derivation by Shin and Hong. First, nonlocal transport via strong updrafts and local transport via the remaining small-scale eddies are separately calculated. Second, the SGS nonlocal transport is formulated by multiplying a grid-size dependency function with the total nonlocal transport profile fit to the large-eddy simulation (LES) output. Finally, the SGS local transport is formulated by multiplying a grid-size dependency function with the total local transport profile, which is calculated using an eddy-diffusivity formula. The new algorithm is evaluated against the LES output and compared with a conventional nonlocal PBL parameterization. For ideal CBL cases, by considering the scale dependency in the parameterized vertical heat transport, improvements over the conventional nonlocal K-profile model appear in mean profiles, resolved and SGS vertical transport profiles with their grid-size dependency, and the energy spectrum. Real-case simulations for convective rolls show that the simulated roll structures are more robust with stronger intensity when the new algorithm is used.

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2

Li, Zhipeng, Hongwu Tang, Saiyu Yuan, Huiming Zhang, Lingzhong Kong i HongGuang Sun. "Modeling Long-Distance Forward and Backward Diffusion Processes in Tracer Transport Using the Fractional Laplacian on Bounded Domains". Fractal and Fractional 7, nr 11 (15.11.2023): 823. http://dx.doi.org/10.3390/fractalfract7110823.

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Recent studies have emphasized the importance of the long-distance diffusion model in characterizing tracer transport occurring within both subsurface and surface environments, particularly in heterogeneous systems. Long-distance diffusion, often referred to as nonlocal diffusion, signifies that tracer particles may experience a considerably long distance in either the forward or backward direction along preferential channels during the transport. The classical advection–diffusion (ADE) model has been widely used to describe tracer transport; however, they often fall short in capturing the intricacies of nonlocal diffusion processes. The fractional operator has gained recognition among hydrologists due to its potential to capture distinct mechanisms of transport and storage for tracer particles exhibiting nonlocal dynamics. However, the hypersingularity of the fractional Laplacian operator presents considerable difficulties in its numerical approximation in bounded domains. This study focuses on the development and application of the fractional Laplacian-based model to characterize nonlocal tracer transport behavior, specifically considering both forward and backward diffusion processes on bounded domains. The Riesz fractional Laplacian provides a mathematical framework for describing tracer diffusion processes on a bounded domain, and a novel finite difference method (FDM) is introduced as an effective numerical solver for addressing the fractional Laplacian-based model. Applications reveal that the fractional Laplacian-based model can effectively capture the observed nonlocal tracer transport behavior in a heterogeneous system, and nonlocal tracer transport exhibits dynamic characteristics, influenced by the evolving heterogeneity of the media at various temporal scales.

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3

Tzou, D. Y. "Nonlocal behavior in phonon transport". International Journal of Heat and Mass Transfer 54, nr 1-3 (styczeń 2011): 475–81. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.09.022.

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4

Li, Dong, i Jose Rodrigo. "Remarks on a nonlocal transport". Advances in Mathematics 374 (listopad 2020): 107345. http://dx.doi.org/10.1016/j.aim.2020.107345.

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5

Del Sorbo, D., J. L. Feugeas, Ph Nicolaï, M. Olazabal-Loumé, B. Dubroca i V. Tikhonchuk. "Extension of a reduced entropic model of electron transport to magnetized nonlocal regimes of high-energy-density plasmas". Laser and Particle Beams 34, nr 3 (20.06.2016): 412–25. http://dx.doi.org/10.1017/s0263034616000252.

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AbstractLaser-produced high-energy-density plasmas may contain strong magnetic fields that affect the energy transport, which can be nonlocal. Models which describe the magnetized nonlocal transport are formally complicated and based on many approximations. This paper presents a more straightforward approach to the description of the electron transport in this regime, based on the extension of a reduced entropic model. The calculated magnetized heat fluxes are compared with the known asymptotic limits and applied for studying of a magnetized nonlocal plasma thermalization.

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6

Shin, Hyeyum Hailey, i Song-You Hong. "Analysis of Resolved and Parameterized Vertical Transports in Convective Boundary Layers at Gray-Zone Resolutions". Journal of the Atmospheric Sciences 70, nr 10 (1.10.2013): 3248–61. http://dx.doi.org/10.1175/jas-d-12-0290.1.

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Abstract The gray zone of a physical process in numerical models is defined as the range of model resolution in which the process is partly resolved by model dynamics and partly parameterized. In this study, the authors examine the grid-size dependencies of resolved and parameterized vertical transports in convective boundary layers (CBLs) for horizontal grid scales including the gray zone. To assess how stability alters the dependencies on grid size, four CBLs with different surface heating and geostrophic winds are considered. For this purpose, reference data for grid-scale (GS) and subgrid-scale (SGS) fields are constructed for 50–4000-m mesh sizes by filtering 25-m large-eddy simulation (LES) data. As relative importance of shear increases, the ratio of resolved turbulent kinetic energy increases for a given grid spacing. Vertical transports of potential temperature, momentum, and a bottom-up diffusion passive scalar behave in a similar fashion. The effects of stability are related to the horizontal scale of coherent large-eddy structures that change in the different stability. The subgrid-scale vertical transport of heat and the bottom-up scalar are divided into a nonlocal mixing owing to the coherent structures and remaining local mixing. The separate treatment of the nonlocal and local transports shows that the grid-size dependency of the SGS nonlocal flux and its sensitivity to stability predominantly determine the dependency of total (nonlocal plus local) SGS transport.

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7

Silva, S. S. A., J. C. Santos, J. Büchner i M. V. Alves. "Nonlocal heat flux effects on temperature evolution of the solar atmosphere". Astronomy & Astrophysics 615 (lipiec 2018): A32. http://dx.doi.org/10.1051/0004-6361/201730580.

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Context. Heat flux is one of the main energy transport mechanisms in the weakly collisional plasma of the solar corona. There, rare binary collisions let hot electrons travel over long distances and influence other regions along magnetic field lines. Thus, the fully collisional heat flux models might not describe transport well enough since they consider only the local contribution of electrons. The heat flux in weakly collisional plasmas at high temperatures with large mean free paths has to consider the nonlocality of the energy transport in the frame of nonlocal models in order to treat energy balance in the solar atmosphere properly. Aims. We investigate the impact of nonlocal heat flux on the thermal evolution and dynamics of the solar atmosphere by implementing a nonlocal heat flux model in a 3D magnetohydrodynamic simulation of the solar corona. Methods. We simulate the evolution of solar coronal plasma and magnetic fields considering both a local collision dominated and a nonlocal heat flux model. The initial magnetic field is obtained by a potential extrapolation of the observed line-of-sight magnetic field of AR11226. The system is perturbed by moving the plasma at the photosphere. We compared the simulated evolution of the solar atmosphere in its dependence on the heat flux model. Results. The main differences for the average temperature profiles were found in the upper chromosphere/transition region. In the nonlocal heat transport model case, thermal energy is transported more efficiently to the upper chromosphere and lower transition region and leads to an earlier heating of the lower atmosphere. As a consequence, the structure of the solar atmosphere is affected with the nonlocal simulations producing on average a smoother temperature profile and the transition region placed about 500 km higher. Using a nonlocal heat flux also leads to two times higher temperatures in some of the regions in the lower corona. Conclusions. The results of our 3D MHD simulations considering nonlocal heat transport supports the previous results of simpler 1D two-fluid simulations. They demonstrated that it is important to consider a nonlocal formulation for the heat flux when there is a strong energy deposit, like the one observed during flares, in the solar corona.

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8

Ghannam, Khaled, Tomer Duman, Gabriel Katul i Marcelo Chamecki. "GRADIENT-DIFFUSION CLOSURE AND THE EJECTION-SWEEP CYCLE IN CONVECTIVE BOUNDARY LAYERS". Ciência e Natura 38 (20.07.2016): 552. http://dx.doi.org/10.5902/2179460x21576.

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The inadequacy of conventional gradient-diffusion closure in modeling turbulent heat flux within the convective atmospheric boundary-layer is often alleviated by accounting for nonlocal transport. Such nonlocal effects are a manifestation of the inherent asymmetry in vertical transport in the convective boundary layer, which is in turn associated with third-order moments (skewness and fluxes of fluxes). In this work, the role of these third-order moments in second-order turbulence closure of the sensible heat flux is examined with the goal of reconciling the models to various closure assumptions. Surface layer similarity theory and mixed-layer parametrizations are used here, complemented by LES results when needed. The turbulent heat flux with various closure assumptions of the flux transport term is solved, including both local and nonlocal approaches. We connect to ejection-sweep cycles in the flow field using the GramCharlier cumulant expansion of the joint probability distribution of vertical velocity and potential temperature. In this nonlocal closure, the transport asymmetry models that include the vertical velocity skewness as a correction term to H originate from ejection-sweep events. Vertical inhomogeneity results in a modified-skewness correction to the nonlocal contribution to the heat flux associated with the relative intensity of ejections and sweeps.

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9

del-Castillo-Negrete, D. "Fractional diffusion models of nonlocal transport". Physics of Plasmas 13, nr 8 (sierpień 2006): 082308. http://dx.doi.org/10.1063/1.2336114.

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10

Bychenkov, V. Yu, J. P. Matte i T. W. Johnston. "Nonlocal electron transport in spherical plasmas". Physics of Plasmas 3, nr 4 (kwiecień 1996): 1280–83. http://dx.doi.org/10.1063/1.871752.

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11

Ohtsu, S., S. Tanaka i M. Yamawaki. "Divertor simulation with nonlocal transport effect". Journal of Nuclear Materials 220-222 (kwiecień 1995): 1005–9. http://dx.doi.org/10.1016/0022-3115(94)00462-5.

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12

Spizzo, Gianluca, Roscoe White, Marc Maraschek, Valentin Igochine i Gustavo Granucci. "Nonlocal transport in toroidal plasma devices". Nuclear Fusion 59, nr 1 (13.12.2018): 016019. http://dx.doi.org/10.1088/1741-4326/aaf07c.

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13

Cushman, J. H., i B. X. Hu. "A resumé of nonlocal transport theories". Stochastic Hydrology and Hydraulics 9, nr 2 (czerwiec 1995): 105–16. http://dx.doi.org/10.1007/bf01585601.

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14

Shaing, K. C. "Potato, banana, local, and nonlocal transport". Physics of Plasmas 7, nr 12 (grudzień 2000): 5081–86. http://dx.doi.org/10.1063/1.1322560.

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15

Ferry, D. K., i R. Akis. "Nonlocal effects in semiconductor nanostructure transport". Journal of Physics: Condensed Matter 20, nr 45 (23.10.2008): 454201. http://dx.doi.org/10.1088/0953-8984/20/45/454201.

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16

Karpen, Judith T., i C. Richard Devore. "Nonlocal thermal transport in solar flares". Astrophysical Journal 320 (wrzesień 1987): 904. http://dx.doi.org/10.1086/165608.

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17

Bychenkov, V. Yu, W. Rozmus, V. T. Tikhonchuk i A. V. Brantov. "Nonlocal Electron Transport in a Plasma". Physical Review Letters 75, nr 24 (11.12.1995): 4405–8. http://dx.doi.org/10.1103/physrevlett.75.4405.

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18

Pogodaev, Nikolay, i Maxim Staritsyn. "Impulsive control of nonlocal transport equations". Journal of Differential Equations 269, nr 4 (sierpień 2020): 3585–623. http://dx.doi.org/10.1016/j.jde.2020.03.007.

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19

Li, Kai, i Wen Yi Huo. "The nonlocal electron heat transport under the non-Maxwellian distribution in laser plasmas and its influence on laser ablation". Physics of Plasmas 30, nr 4 (kwiecień 2023): 042702. http://dx.doi.org/10.1063/5.0130888.

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The electron heat transport plays an important role in laser driven inertial confinement fusion. For the plasmas created by intense laser, the traditional Spitzer–Härm theory cannot accurately describe the electron heat transport process mainly due to two physical effects. First, the electron distribution function would significantly differ from the Maxwellian distribution because of the inverse bremsstrahlung heating. Second, the long mean free paths of heat carrying electrons relative to the temperature scale length indicate that the electron heat flux has the nonlocal feature. In 2020, we have developed a nonlocal electron heat transport model based on the non-Maxwellian electron distribution function (NM-NL model) to describe the electron heat flux in laser plasmas. Recently, this model is successfully incorporated into our radiation hydrodynamical code RDMG. In this article, we numerically investigated the electron heat flux in laser plasmas, especially the nonlocal feature of heat flux and the influence of the non-Maxwellian distribution. The influence of electron heat transport on laser ablation is also discussed. The simulated plasma conditions based on different electron heat transport models are presented and compared with experiments. Our results show that the nonlocal feature of heat flux and the influence of non-Maxwellian distribution function are considerable in plasmas heated by intense lasers.

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20

Zhao, Hanzhi, Zhengming Sheng i Suming Weng. "Nonlocal thermal transport in magnetized plasma along different directions". Matter and Radiation at Extremes 7, nr 4 (1.07.2022): 045901. http://dx.doi.org/10.1063/5.0086783.

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Nonlocal thermal transport in magnetized plasmas is studied theoretically and numerically with the Vlasov–Fokker–Planck (VFP) model, in which the magnetic field has nonzero components both perpendicular to and along the temperature gradient. Nonlocal heat transport is found in both the longitudinal and transverse directions, provided the temperature gradients are sufficiently large. The magnetic field tends to reduce the nonlocality of the thermal transport in the direction perpendicular to the magnetic field, i.e., the difference between the heat fluxes predicted by the Braginskii theory and the VFP simulation decreases with increasing magnetic field strength. When the initial temperature gradient is steep, the nonlocal heat flux depends not only on the present temperature profile, but also on its time history. Moreover, the contribution of high-order terms in the spherical harmonic expansion of the electron distribution function becomes important for a magnetized plasma, in particular for thermal transport in the direction perpendicular to the temperature gradient.

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21

TAKABE, Hideaki, i Shoichi YAMADA. "Nonlocal Transport Phenomena and Various Structure Formations in Plasmas. Nonlocal Transport in Laser Implosion and Supernova Explosion." Journal of Plasma and Fusion Research 78, nr 9 (2002): 861–70. http://dx.doi.org/10.1585/jspf.78.861.

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22

Ma, K. H., M. V. Patel, M. Sherlock, W. A. Farmer i E. Johnsen. "Thermal transport modeling of laser-irradiated spheres". Physics of Plasmas 29, nr 11 (listopad 2022): 112307. http://dx.doi.org/10.1063/5.0005552.

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Thermal transport of uniformly laser-irradiated spheres of various materials is investigated computationally. One-dimensional simulations of low- to mid-Z materials (Be, Al, and Cu) are performed to evaluate the impact of nonlocal electron transport on experimental observables under laser intensities of relevance to direct-drive inertial confinement fusion. We compare thermal transport models of different levels of fidelity: flux-limited Spitzer–Harm diffusion, the Schurtz–Nicolai–Busquet (SNB) reduced-order nonlocal model, and a Fokker–Planck description. Spitzer–Harm diffusion with different flux-limiter factors are compared with different implementations of the SNB model in the HYDRA radiation hydrodynamics code. Under the conditions of interest, the peak heat flux in the thermal front with the SNB model shows good agreement with Fokker–Planck calculations, with the largest errors below 10% at 1015 W/cm2 laser intensity. From HYDRA-SNB simulations, two experimentally relevant effects are observed from nonlocal heat transport when compared to flux-limited Spitzer–Harm modeling: coronal temperatures are cooler due to reduced heat fluxes in the expanding plasma and (for mid-Z materials) x-ray emissions are enhanced due to preheating in the dense plasma.

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23

Wu, Elynn, Handa Yang, Jan Kleissl, Kay Suselj, Marcin J. Kurowski i João Teixeira. "On the Parameterization of Convective Downdrafts for Marine Stratocumulus Clouds". Monthly Weather Review 148, nr 5 (14.04.2020): 1931–50. http://dx.doi.org/10.1175/mwr-d-19-0292.1.

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Abstract The role of nonlocal transport on the development and maintenance of marine stratocumulus (Sc) clouds in coarse-resolution models is investigated, with a special emphasis on the downdraft contribution. A new parameterization of cloud-top-triggered downdrafts is proposed and validated against large-eddy simulation (LES) for two Sc cases. The applied nonlocal mass-flux scheme is part of the stochastic multiplume eddy-diffusivity/mass-flux (EDMF) framework decomposing the turbulent transport into local and nonlocal contributions. The complementary local turbulent transport is represented with the Mellor–Yamada–Nakanishi–Niino (MYNN) scheme. This EDMF version has been implemented in the Weather Research and Forecasting (WRF) single-column model (SCM) and tested for three model versions: without mass flux, with updrafts only, and with both updrafts and downdrafts. In the LES, the downdraft and updraft contributions to the total heat and moisture transport are comparable and significant. The WRF SCM results show a good agreement between the parameterized downdraft turbulent transport and LES. While including updrafts greatly improves the modeling of Sc clouds over the simulation without mass flux, the addition of downdrafts is less significant, although it helps improve the moisture profile in the planetary boundary layer.

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24

Brantov, A. V., i V. Yu Bychenkov. "Nonlocal transport in hot plasma. Part I". Plasma Physics Reports 39, nr 9 (wrzesień 2013): 698–744. http://dx.doi.org/10.1134/s1063780x13090018.

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25

Brantov, A. V., i V. Yu Bychenkov. "Nonlocal transport in hot plasma. Part II". Plasma Physics Reports 40, nr 7 (lipiec 2014): 505–63. http://dx.doi.org/10.1134/s1063780x14060026.

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26

Jacchia, A., P. Mantica, F. De Luca, P. Galli i G. Gorini. "Nonlocal diffusivity: Impact on transient transport studies". Physics of Plasmas 2, nr 12 (grudzień 1995): 4589–95. http://dx.doi.org/10.1063/1.871444.

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27

Spizzo, G., R. B. White, S. Cappello i L. Marrelli. "Nonlocal transport in the reversed field pinch". Plasma Physics and Controlled Fusion 51, nr 12 (11.11.2009): 124026. http://dx.doi.org/10.1088/0741-3335/51/12/124026.

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28

Mirza, Arshad M., G. Murtaza i M. S. Qaisar. "Nonlocal electron transport in laser-produced plasmas". Physica Scripta 42, nr 1 (1.07.1990): 85–88. http://dx.doi.org/10.1088/0031-8949/42/1/014.

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29

Shifren, L., i D. K. Ferry. "Inclusion of nonlocal scattering in quantum transport". Physics Letters A 306, nr 5-6 (styczeń 2003): 332–36. http://dx.doi.org/10.1016/s0375-9601(02)01603-1.

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30

Mora, P., i J. F. Luciani. "Nonlocal electron transport in laser created plasmas". Laser and Particle Beams 12, nr 3 (wrzesień 1994): 387–400. http://dx.doi.org/10.1017/s0263034600008247.

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The classical linear Spitzer-Härm formula has been shown to lead to an overestimation of the electron heat flux in laser-plasma interaction experiments. We briefly review the classical theory of heat transport in a plasma, and give a simplified demonstration of the Spitzer-Härm formula. The electron heat conductivity is calculated for a large value of the ion charge Z. Correction due to a finite value of Z is evaluated with a simplified electron-electron collision operator. We then show that in a steep temperature gradient, the collisional mean free path of the electrons that transport the energy may be larger than the scale length of the temperature gradient. In this case the Spitzer-Härm formula overestimates the actual heat flux in the main part of the temperature gradient, and predicts a too small heat flux slightly away from the location of the large temperature gradient.A nonlocal macroscopic formula, which is a sort of convolution of the Spitzer-Härm heat flux by a delocalization function, is shown to accurately describe the electron heat flow in both smooth and steep temperature gradients. This nonlocal formula for the heat flow is analytically justified. A selection of slightly different delocalization functions proposed in the literature is compared to the original one and to the results of Fokker-Planck calculations of the heat flow.

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31

Silvestre, Luis, i Vlad Vicol. "On a transport equation with nonlocal drift". Transactions of the American Mathematical Society 368, nr 9 (6.11.2015): 6159–88. http://dx.doi.org/10.1090/tran6651.

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32

Canullo, M. V., A. Costa i C. Ferro-Fontan. "Nonlocal Heat Transport in the Solar Wind". Astrophysical Journal 462 (maj 1996): 1005. http://dx.doi.org/10.1086/177214.

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33

Brantov, A. V., V. Yu Bychenkov, V. T. Tikhonchuk i W. Rozmus. "Nonlocal electron transport in laser heated plasmas". Physics of Plasmas 5, nr 7 (lipiec 1998): 2742–53. http://dx.doi.org/10.1063/1.872962.

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34

Wolf, M. J., F. Hübler, S. Kolenda i D. Beckmann. "Charge and spin transport in mesoscopic superconductors". Beilstein Journal of Nanotechnology 5 (17.02.2014): 180–85. http://dx.doi.org/10.3762/bjnano.5.18.

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Background: Non-equilibrium charge transport in superconductors has been investigated intensely in the 1970s and 1980s, mostly in the vicinity of the critical temperature. Much less attention has been paid to low temperatures and the role of the quasiparticle spin. Results: We report here on nonlocal transport in superconductor hybrid structures at very low temperatures. By comparing the nonlocal conductance obtained by using ferromagnetic and normal-metal detectors, we discriminate charge and spin degrees of freedom. We observe spin injection and long-range transport of pure, chargeless spin currents in the regime of large Zeeman splitting. We elucidate charge and spin transport by comparison to theoretical models. Conclusion: The observed long-range chargeless spin transport opens a new path to manipulate and utilize the quasiparticle spin in superconductor nanostructures.

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35

Fagioli, Simone, Alic Kaufmann i Emanuela Radici. "Optimal control problems of nonlocal interaction equations". ESAIM: Control, Optimisation and Calculus of Variations 29 (2023): 40. http://dx.doi.org/10.1051/cocv/2023029.

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In the present work we deal with the existence of solutions for optimal control problems associated to transport equations. The behaviour of a population of individuals will be influenced by the presence of a population of control agents whose role is to lead the dynamics of the individuals towards a specific goal. The dynamics of the population of individuals is described by a suitable nonlocal transport equation, while the role of the population of agents is designed by the optimal control problem. This model has been first studied in [12] for a class of continuous nonlocal potentials, while in the present project we consider the case of mildly singular potentials in a gradient flow formulation of the target transport equation.

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36

TAKIZUKA, Tomonori, Hitoshi HOJO i Tadatsugu HATORI. "Nonlocal Transport Phenomena and Various Structure Formations in Plasmas. Classical Nonlocal Phenomena in Magnetic Confinement Plasmas Nonlocal Transport Related to Dynamics along the Magnetic Field." Journal of Plasma and Fusion Research 78, nr 9 (2002): 878–84. http://dx.doi.org/10.1585/jspf.78.878.

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37

Das, Shankar P. "Lattice Gas Model with Nonlocal Interactions". International Journal of Modern Physics B 11, nr 30 (10.12.1997): 3581–94. http://dx.doi.org/10.1142/s0217979297001799.

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We analyze the nature of the hydrodynamic modes in a Lattice Gas Automata (LGA) model defined on a hexagonal lattice and having nonlocal interactions of attractive and repulsive type simultaneously. The model is similar in spirit to the liquid gas model of Appert and Zaleski [Phys. Rev. Lett.64, 1 (1990)]. The phase diagram for the model is computed using the kinetic pressure. The dynamics is studied with a mean field type approach in the Boltzmann approximation ignoring effects of correlated collisions. We compute the transport coefficients and the speed of sound propagation. The presence of attractive interactions show increase in the transport coefficients at intermediate densities.

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38

Lazar, Omar. "On a 1D nonlocal transport equation with nonlocal velocity and subcritical or supercritical diffusion". Journal of Differential Equations 261, nr 9 (listopad 2016): 4974–96. http://dx.doi.org/10.1016/j.jde.2016.07.009.

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NISHIGUCHI, Akio. "Nonlocal Electron Heat Transport in Magnetized Dense Plasmas". Plasma and Fusion Research 9 (2014): 1404096. http://dx.doi.org/10.1585/pfr.9.1404096.

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40

Zheng, Zhen, W. Rozmus, V. Yu Bychenkov, A. V. Brantov i C. E. Capjack. "Nonlocal transport model in equilibrium two-component plasmas". Physics of Plasmas 16, nr 10 (październik 2009): 102301. http://dx.doi.org/10.1063/1.3234240.

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