Tag: nevin manimala

Phys Rev E. 2023 May;107(5-1):054801. doi: 10.1103/PhysRevE.107.054801.

ABSTRACT

A simple two-dimensional statistical mechanical water model, called the rose model, was used in this work. We studied how a homogeneous constant electric field affects the properties of water. The rose model is a very simple model that helps explain the anomalous properties of water. Rose water molecules are represented as two-dimensional Lennard-Jones disks with potentials for orientation-dependent pairwise interactions mimicking formations of hydrogen bonds. The original model is modified by addition of charges for interaction with the electric field. We studied what kind of influence the electric field strength has on the model’s properties. To determine the structure and thermodynamics of the rose model under the influence of the electric field we used Monte Carlo simulations. Under the influence of a weak electric field the anomalous properties and phase transitions of the water do not change. On the other hand, the strong fields shift the phase transition points as well as the position of the density maximum.

PMID:37329104 | DOI:10.1103/PhysRevE.107.054801

Phys Rev E. 2023 May;107(5-2):055302. doi: 10.1103/PhysRevE.107.055302.

ABSTRACT

Many experimentally accessible, finite-sized interacting quantum systems are most appropriately described by the canonical ensemble of statistical mechanics. Conventional numerical simulation methods either approximate them as being coupled to a particle bath or use projective algorithms which may suffer from nonoptimal scaling with system size or large algorithmic prefactors. In this paper, we introduce a highly stable, recursive auxiliary field quantum Monte Carlo approach that can directly simulate systems in the canonical ensemble. We apply the method to the fermion Hubbard model in one and two spatial dimensions in a regime known to exhibit a significant “sign” problem and find improved performance over existing approaches including rapid convergence to ground-state expectation values. The effects of excitations above the ground state are quantified using an estimator-agnostic approach including studying the temperature dependence of the purity and overlap fidelity of the canonical and grand canonical density matrices. As an important application, we show that thermometry approaches often exploited in ultracold atoms that employ an analysis of the velocity distribution in the grand canonical ensemble may be subject to errors leading to an underestimation of extracted temperatures with respect to the Fermi temperature.

PMID:37329093 | DOI:10.1103/PhysRevE.107.055302

Phys Rev E. 2023 May;107(5-1):054135. doi: 10.1103/PhysRevE.107.054135.

ABSTRACT

Chromosomes are crumpled polymer chains further folded into a sequence of stochastic loops via loop extrusion. While extrusion has been verified experimentally, the particular means by which the extruding complexes bind DNA polymer remains controversial. Here we analyze the behavior of the contact probability function for a crumpled polymer with loops for the two possible modes of cohesin binding, topological and nontopological mechanisms. As we show, in the nontopological model the chain with loops resembles a comb-like polymer that can be solved analytically using the quenched disorder approach. In contrast, in the topological binding case the loop constraints are statistically coupled due to long-range correlations present in a nonideal chain, which can be described by the perturbation theory in the limit of small loop densities. As we show, the quantitative effect of loops on a crumpled chain in the case of topological binding should be stronger, which is translated into a larger amplitude of the log-derivative of the contact probability. Our results highlight a physically different organization of a crumpled chain with loops by the two mechanisms of loop formation.

PMID:37329090 | DOI:10.1103/PhysRevE.107.054135

Phys Rev E. 2023 May;107(5-1):054402. doi: 10.1103/PhysRevE.107.054402.

ABSTRACT

Purkinje cells exhibit a reduction of the mean firing rate at intermediate-noise intensities, which is somewhat reminiscent of the response enhancement known as “stochastic resonance” (SR). Although the comparison with the stochastic resonance ends here, the current phenomenon has been given the name “inverse stochastic resonance” (ISR). Recent research has demonstrated that the ISR effect, like its close relative “nonstandard SR” [or, more correctly, noise-induced activity amplification (NIAA)], has been shown to stem from the weak-noise quenching of the initial distribution, in bistable regimes where the metastable state has a larger attraction basin than the global minimum. To understand the underlying mechanism of the ISR and NIAA phenomena, we study the probability distribution function of a one-dimensional system subjected to a bistable potential that has the property of symmetry, i.e., if we change the sign of one of its parameters, we can obtain both phenomena with the same properties in the depth of the wells and the width of their basins of attraction subjected to Gaussian white noise with variable intensity. Previous work has shown that one can theoretically determine the probability distribution function using the convex sum between the behavior at small and high noise intensities. To determine the probability distribution function more precisely, we resort to the “weighted ensemble Brownian dynamics simulation” model, which provides an accurate estimate of the probability distribution function for both low and high noise intensities and, most importantly, for the transition of both behaviors. In this way, on the one hand, we show that both phenomena emerge from a metastable system where, in the case of ISR, the global minimum of the system is in a state of lower activity, while in the case of NIAA, the global minimum is in a state of increased activity, the importance of which does not depend on the width of the basins of attraction. On the other hand, we see that quantifiers such as Fisher information, statistical complexity, and especially Shannon entropy fail to distinguish them, but they show the existence of the mentioned phenomena. Thus, noise management may well be a mechanism by which Purkinje cells find an efficient way to transmit information in the cerebral cortex.

PMID:37329070 | DOI:10.1103/PhysRevE.107.054402

Phys Rev E. 2023 May;107(5):L053001. doi: 10.1103/PhysRevE.107.L053001.

ABSTRACT

The Poynting effect is a paragon of nonlinear soft matter mechanics. It is the tendency (found in all incompressible, isotropic, hyperelastic solids) exhibited by a soft block to expand vertically when sheared horizontally. It can be observed whenever the length of the cuboid is at least four times its thickness. Here we show that the Poynting effect can be easily reversed and the cuboid can shrink vertically, simply by reducing this aspect ratio. In principle, this discovery means that for a given solid, say one used as a seismic wave absorber under a building, an optimal ratio exists where vertical displacements and vibrations can be completely eliminated. Here we first recall the classical theoretical treatment of the positive Poynting effect, and then show experimentally how it can be reversed. Using finite-element simulations, we then investigate how the effect can be suppressed. We find that cubes always provide a reverse Poynting effect, irrespective of their material properties (in the third-order theory of weakly nonlinear elasticity).

PMID:37329069 | DOI:10.1103/PhysRevE.107.L053001

Phys Rev E. 2023 May;107(5-1):054128. doi: 10.1103/PhysRevE.107.054128.

ABSTRACT

Embedded random matrix ensembles with k-body interactions are well established to be appropriate for many quantum systems. For these ensembles the two point correlation function is not yet derived, though these ensembles are introduced 50 years back. Two-point correlation function in eigenvalues of a random matrix ensemble is the ensemble average of the product of the density of eigenvalues at two eigenvalues, say E and E^{‘}. Fluctuation measures such as the number variance and Dyson-Mehta Δ_{3} statistic are defined by the two-point function and so also the variance of the level motion in the ensemble. Recently, it is recognized that for the embedded ensembles with k-body interactions the one-point function (ensemble averaged density of eigenvalues) follows the so called q-normal distribution. With this, the eigenvalue density can be expanded by starting with the q-normal form and using the associated q-Hermite polynomials He_{ζ}(x|q). Covariances S_{ζ}S_{ζ^{‘}}[over ¯] (overline representing ensemble average) of the expansion coefficients S_{ζ} with ζ≥1 here determine the two-point function as they are a linear combination of the bivariate moments Σ_{PQ} of the two-point function. Besides describing all these, in this paper formulas are derived for the bivariate moments Σ_{PQ} with P+Q≤8, of the two-point correlation function, for the embedded Gaussian unitary ensembles with k-body interactions [EGUE(k)] as appropriate for systems with m fermions in N single particle states. Used for obtaining the formulas is the SU(N) Wigner-Racah algebra. These formulas with finite N corrections are used to derive formulas for the covariances S_{ζ}S_{ζ^{‘}}[over ¯] in the asymptotic limit. These show that the present work extends to all k values, the results known in the past in the two extreme limits with k/m→0 (same as q→1) and k=m (same as q=0).

PMID:37329068 | DOI:10.1103/PhysRevE.107.054128

Phys Rev E. 2023 May;107(5-2):055304. doi: 10.1103/PhysRevE.107.055304.

ABSTRACT

We present a general and numerically efficient method for calculation of collision integrals for interacting quantum gases on a discrete momentum lattice. Here we employ the original analytical approach based on Fourier transform covering a wide spectrum of solid-state problems with various particle statistics and arbitrary interaction models, including the case of momentum-dependent interaction. The comprehensive set of the transformation principles is given in detail and realized as a computer Fortran 90 library FLBE (Fast Library for Boltzmann Equation).

PMID:37329067 | DOI:10.1103/PhysRevE.107.055304

Phys Rev E. 2023 May;107(5-2):055212. doi: 10.1103/PhysRevE.107.055212.

ABSTRACT

A recent numerical treatment of data obtained by the Parker Solar Probe spacecraft describes the electron concentration in solar wind as a function of the heliocentric distance based on a Kappa distribution with spectral index κ=5. In this work, we derive and, subsequently, solve an entirely different class of nonlinear partial differential equations describing the one-dimensional diffusion of a suprathermal gas. The theory is applied to describe the aforementioned data and we find a spectral index κ≳1.5 providing the widely acknowledged identification of Kappa electrons in solar wind. We also find that suprathermal effects increase the length scale of classical diffusion by one order of magnitude. Such a result does not depend on the microscopic details of the diffusion coefficient since our theory is based on a macroscopic formulation. Forthcoming extensions of our theory by including magnetic fields and relating our formulation to nonextensive statistics are briefly addressed.

PMID:37329056 | DOI:10.1103/PhysRevE.107.055212

Phys Rev E. 2023 May;107(5-1):054139. doi: 10.1103/PhysRevE.107.054139.

ABSTRACT

A variety of transport processes in natural and man-made systems are intrinsically random. To model their stochasticity, lattice random walks have been employed for a long time, mainly by considering Cartesian lattices. However, in many applications in bounded space the geometry of the domain may have profound effects on the dynamics and ought to be accounted for. We consider here the cases of the six-neighbor (hexagonal) and three-neighbor (honeycomb) lattices, which are utilized in models ranging from adatoms diffusing in metals and excitations diffusing on single-walled carbon nanotubes to animal foraging strategy and the formation of territories in scent-marking organisms. In these and other examples, the main theoretical tool to study the dynamics of lattice random walks in hexagonal geometries has been via simulations. Analytic representations have in most cases been inaccessible, in particular in bounded hexagons, given the complicated “zigzag” boundary conditions that a walker is subject to. Here we generalize the method of images to hexagonal geometries and obtain closed-form expressions for the occupation probability, the so-called propagator, for lattice random walks both on hexagonal and honeycomb lattices with periodic, reflective, and absorbing boundary conditions. In the periodic case, we identify two possible choices of image placement and their corresponding propagators. Using them, we construct the exact propagators for the other boundary conditions, and we derive transport-related statistical quantities such as first-passage probabilities to one or multiple targets and their means, elucidating the effect of the boundary condition on transport properties.

PMID:37329046 | DOI:10.1103/PhysRevE.107.054139

Phys Rev E. 2023 May;107(5-2):055309. doi: 10.1103/PhysRevE.107.055309.

ABSTRACT

Digital cores can characterize the true internal structure of rocks at the pore scale. This method has become one of the most effective ways to quantitatively analyze the pore structure and other properties of digital cores in rock physics and petroleum science. Deep learning can precisely extract features from training images for a rapid reconstruction of digital cores. Usually, the reconstruction of three-dimensional (3D) digital cores is performed by optimization using generative adversarial networks. The training data required for the 3D reconstruction are 3D training images. In practice, two-dimensional (2D) imaging devices are widely used because they can achieve faster imaging, higher resolution, and easier identification of different rock phases, so replacing 3D images with 2D ones avoids the difficulty of acquiring 3D images. In this paper, we propose a method, named EWGAN-GP, for the reconstruction of 3D structures from a 2D image. Our proposed method includes an encoder, a generator, and three discriminators. The main purpose of the encoder is to extract statistical features of a 2D image. The generator extends the extracted features into 3D data structures. Meanwhile, the three discriminators have been designed to gauge the similarity of morphological characteristics between cross sections of the reconstructed 3D structure and the real image. The porosity loss function is used to control the distribution of each phase in general. In the entire optimization process, a strategy using Wasserstein distance with gradient penalty makes the convergence of the training process faster and the reconstruction result more stable; it also avoids the problems of gradient disappearance and mode collapse. Finally, the reconstructed 3D structure and the target 3D structure are visualized to ascertain their similar morphologies. The morphological parameter indicators of the reconstructed 3D structure were consistent with those of the target 3D structure. The microstructure parameters of the 3D structure were also compared and analyzed. The proposed method can achieve accurate and stable 3D reconstruction compared with classical stochastic methods of image reconstruction.

PMID:37329045 | DOI:10.1103/PhysRevE.107.055309