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Planck space

Vitaly A Shneidman
The classical description of nucleation of cavities in a stretched fluid relies on a one-dimensional Fokker-Planck equation (FPE) in the space of their sizes r, with the diffusion coefficient D(r) constructed for all r from macroscopic hydrodynamics and thermodynamics, as shown by Zeldovich. When additional variables (e.g., vapor pressure) are required to describe the state of a bubble, a similar approach to construct a diffusion tensor D^ generally works only in the direct vicinity of the thermodynamic saddle point corresponding to the critical nucleus...
August 14, 2017: Journal of Chemical Physics
Gabriel G Carlo, Leonardo Ermann, Alejandro M F Rivas, María E Spina, Dario Poletti
In the context of dissipative systems, we show that for any quantum chaotic attractor a corresponding classical chaotic attractor can always be found. We provide a general way to locate them, rooted in the structure of the parameter space (which is typically bidimensional, accounting for the forcing strength and dissipation parameters). In cases where an approximate pointlike quantum distribution is found, it can be associated with exceptionally large regular structures. Moreover, supposedly anomalous quantum chaotic behavior can be very well reproduced by the classical dynamics plus Gaussian noise of the size of an effective Planck constant ℏ_{eff}...
June 2017: Physical Review. E
Tatsushi Ikeda, Yoshitaka Tanimura
Photoisomerization in a system with multiple electronic states and anharmonic potential surfaces in a dissipative environment is investigated using a rigorous numerical method employing quantum hierarchical Fokker-Planck equations (QHFPEs) for multi-state systems. We have developed a computer code incorporating QHFPE for general-purpose computing on graphics processing units that can treat multi-state systems in phase space with any strength of diabatic coupling of electronic states under non-perturbative and non-Markovian system-bath interactions...
July 7, 2017: Journal of Chemical Physics
Timur E Gureyev, Alexander Kozlov, Yakov I Nesterets, David M Paganin, Harry M Quiney
An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit is determined by the vacuum fluctuations within the volume corresponding to the width of the mode. This result also leads to a generalized form of the Heisenberg uncertainty principle for boson fields in which the lower limit for the product of uncertainties in the spatial and momentum localization of a mode is equal to the product of Planck's constant and a dimensionless functional which reflects the joint signal-to-noise ratio of the position and momentum of vacuum fluctuations in the region of the phase space occupied by the mode...
July 3, 2017: Scientific Reports
Moritz Augustin, Josef Ladenbauer, Fabian Baumann, Klaus Obermayer
The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated...
June 2017: PLoS Computational Biology
Christopher G R Wallis, Yves Wiaux, Jason D McEwen
We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems, and combinations thereof, are considered as examples. Inverse problems are solved in both the analysis and synthesis settings, with a number of different sampling schemes. The most effective approach is that with the most restricted solution-space, which depends on the interplay between the adopted sampling scheme, the selection of the analysis/synthesis problem, and any weighting of the ℓ1 norm appearing in the regularisation problem...
June 16, 2017: IEEE Transactions on Image Processing: a Publication of the IEEE Signal Processing Society
Jiaye Su, Yunzhen Zhao, Chang Fang, Yue Shi
Understanding the water permeation through a cell membrane is of primary importance for biological activities and a key step to capture its shape transformation in salt solution. In this work, we reveal the dynamical behaviors of osmotically driven transport of water molecules across a vesicle membrane by molecular dynamics simulations. Of particular interest is that the water transport in and out of vesicles is highly distinguishable given the osmotic force are the same, suggesting an asymmetric osmotic transportation...
May 28, 2017: Journal of Chemical Physics
B C Yang, Jesús Pérez-Ríos, F Robicheaux
We examine a dipolar-gas model to address fundamental issues regarding the correspondence between classical chaos and quantum observations in ultracold dipolar collisions. The theoretical model consists of a short-range Lennard-Jones potential well with an anisotropic, long-range dipole-dipole interaction between two atoms. Both the classical and quantum dynamics are explored for the same Hamiltonian of the system. The classical chaotic scattering is revealed by the fractals developed in the scattering function (defined as the final atom separation as a function of initial conditions), while the quantum chaotic features lead to the repulsion of the eigenphases from the corresponding quantum S matrix...
April 14, 2017: Physical Review Letters
Umberto Marini Bettolo Marconi, Andrea Puglisi, Claudio Maggi
Methods of stochastic thermodynamics and hydrodynamics are applied to a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system's Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show that a Clausius inequality holds, with the local (non-uniform) temperature of the active bath replacing the uniform temperature usually encountered in equilibrium systems...
April 21, 2017: Scientific Reports
Jérôme Hurst, Paul-Antoine Hervieux, Giovanni Manfredi
Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin-[Formula: see text] fermions (typically, electrons) including the Zeeman effect and the spin-orbit coupling. This Wigner equation is coupled to the appropriate Maxwell equations to form a self-consistent mean-field model. A set of semiclassical Vlasov equations with spin effects is obtained by expanding the full quantum model to first order in the Planck constant. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function...
April 28, 2017: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
Markus F Weber, Erwin Frey
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations...
April 2017: Reports on Progress in Physics
A V Artemyev, A I Neishtadt, A A Vasiliev, D Mourenas
In this paper we provide a theoretical model describing the evolution of the charged-particle distribution function in a system with nonlinear wave-particle interactions. Considering a system with strong electrostatic waves propagating in an inhomogeneous magnetic field, we demonstrate that individual particle motion can be characterized by the probability of trapping into the resonance with the wave and by the efficiency of scattering at resonance. These characteristics, being derived for a particular plasma system, can be used to construct a kinetic equation (or generalized Fokker-Planck equation) modeling the long-term evolution of the particle distribution...
February 2017: Physical Review. E
J M Nava-Sedeño, H Hatzikirou, F Peruani, A Deutsch
Cellular automata (CA) are discrete time, space, and state models which are extensively used for modeling biological phenomena. CA are "on-lattice" models with low computational demands. In particular, lattice-gas cellular automata (LGCA) have been introduced as models of single and collective cell migration. The interaction rule dictates the behavior of a cellular automaton model and is critical to the model's biological relevance. The LGCA model's interaction rule has been typically chosen phenomenologically...
February 27, 2017: Journal of Mathematical Biology
Paul C Bressloff
We generalize the Feynman-Kac formula to analyze the local and occupation times of a Brownian particle moving in a stochastically gated one-dimensional domain. (i) The gated local time is defined as the amount of time spent by the particle in the neighborhood of a point in space where there is some target that only receives resources from (or detects) the particle when the gate is open; the target does not interfere with the motion of the Brownian particle. (ii) The gated occupation time is defined as the amount of time spent by the particle in the positive half of the real line, given that it can only cross the origin when a gate placed at the origin is open; in the closed state the particle is reflected...
January 2017: Physical Review. E
Luca Di Luzio, Federico Mescia, Enrico Nardi
A major goal of axion searches is to reach inside the parameter space region of realistic axion models. Currently, the boundaries of this region depend on somewhat arbitrary criteria, and it would be desirable to specify them in terms of precise phenomenological requirements. We consider hadronic axion models and classify the representations R_{Q} of the new heavy quarks Q. By requiring that (i) the Q's are sufficiently short lived to avoid issues with long-lived strongly interacting relics, (ii) no Landau poles are induced below the Planck scale; 15 cases are selected which define a phenomenologically preferred axion window bounded by a maximum (minimum) value of the axion-photon coupling about 2 times (4 times) larger than is commonly assumed...
January 20, 2017: Physical Review Letters
Geir Halnes, Tuomo Mäki-Marttunen, Daniel Keller, Klas H Pettersen, Ole A Andreassen, Gaute T Einevoll
Recorded potentials in the extracellular space (ECS) of the brain is a standard measure of population activity in neural tissue. Computational models that simulate the relationship between the ECS potential and its underlying neurophysiological processes are commonly used in the interpretation of such measurements. Standard methods, such as volume-conductor theory and current-source density theory, assume that diffusion has a negligible effect on the ECS potential, at least in the range of frequencies picked up by most recording systems...
November 2016: PLoS Computational Biology
Ilya Kuprov
This paper presents an overview of the Fokker-Planck formalism for non-biological magnetic resonance simulations, describes its existing applications and proposes some novel ones. The most attractive feature of Fokker-Planck theory compared to the commonly used Liouville - von Neumann equation is that, for all relevant types of spatial dynamics (spinning, diffusion, stationary flow, etc.), the corresponding Fokker-Planck Hamiltonian is time-independent. Many difficult NMR, EPR and MRI simulation problems (multiple rotation NMR, ultrafast NMR, gradient-based zero-quantum filters, diffusion and flow NMR, off-resonance soft microwave pulses in EPR, spin-spin coupling effects in MRI, etc...
September 2016: Journal of Magnetic Resonance
Manoj Prasad, Filip Strubbe, Filip Beunis, Kristiaan Neyts
Charged inverse micelles (CIMs) generated during a continuous polarizing voltage between electrodes in the model system of polyisobutylene succinimide in dodecane do not populate a diffuse double layer like CIMs present in equilibrium (regular CIMs), but instead end up in interface layers. When the applied voltage is reversed abruptly after a continuous polarizing voltage step, two peaks are observed in the transient current. The first peak is due to the release of regular CIMs from the diffuse double layers formed during the polarizing voltage step, which is understood on the basis of the Poisson-Nernst-Planck equations...
July 28, 2016: Physical Chemistry Chemical Physics: PCCP
Suvodip Mukherjee, Tarun Souradeep
Recent measurements of the temperature field of the cosmic microwave background (CMB) provide tantalizing evidence for violation of statistical isotropy (SI) that constitutes a fundamental tenet of contemporary cosmology. CMB space based missions, WMAP, and Planck have observed a 7% departure in the SI temperature field at large angular scales. However, due to higher cosmic variance at low multipoles, the significance of this measurement is not expected to improve from any future CMB temperature measurements...
June 3, 2016: Physical Review Letters
Atsushi Sawada
The Poisson-Nernst-Planck (PNP) model has been widely used for analyzing impedance or dielectric spectra observed for dilute electrolytic cells. In the analysis, the behavior of mobile ions in the cell under an external electric field has been explained by a conductive nature regardless of ionic concentrations. However, if the cell has parallel-plate blocking electrodes, the mobile ions may also play a role as a dielectric medium in the cell by the effect of space-charge polarization when the ionic concentration is sufficiently low...
May 2016: Physical Review. E
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