We investigate the thermodynamic uncertainty relations (TURs) in mesoscopic devices for all universal symmetry classes of Wigner-Dyson and Dirac (chiral). The observables of interest include the TUR (MS), which is defined in terms of the ratio between the mean noise and mean conductance, as well as a new TUR (R) proposed in this article, which is based on the ensemble mean of the noise-to-conductance ratio. A detailed study is made on the quantum interference corrections associated with the TURs. We also analyze the influence of orbital and sublattice/chiral degrees of freedom for the validity of the observables in these chaotic mesoscopic billiards. Our investigation is based on the concatenation between the Landauer-Büttiker theory, the Mahaux-Wendeinmüller theory, and the TURs. We simulate the universal mesoscopic chaotic quantum dots using the random-matrix theory and compare our numerical results with the pertinent experimental data. The results were obtained for a different number of channels and tunneling rates that vary from the opaque to the ideal regime and, in all cases, demonstrate a clear phenomenological distinction between the TURs. In particular, the opaque regime engenders remarkable differences between the observables, even in the semiclassical regime, which characterizes a clear violation of the central limit theorem. Furthermore, we show that the phenomenology of the quantum interference corrections is strikingly robust, surprisingly exhibiting an order of magnitude greater than the supposedly leading semiclassical term for the TUR (R).

Polymer networks formed by cross linking flexible polymer chains are ubiquitous in many natural and synthetic soft-matter systems. Current micromechanics models generally do not account for excluded volume interactions except, for instance, through imposing a phenomenological incompressibility constraint at the continuum scale. This work aims to examine the role of excluded volume interactions on the mechanical response. The approach is based on the framework of the self-consistent statistical field theory of polymers, which provides an efficient mesoscale approach that enables the accounting of excluded volume effects without the expense of large-scale molecular modeling. A mesoscale representative volume element is populated with multiple interacting chains, and the macroscale nonlinear elastic deformation is imposed by mapping the end-to-end vectors of the chains by this deformation. In the absence of excluded volume interactions, it recovers the closed-form results of the classical theory of rubber elasticity. With excluded volume interactions, the model is solved numerically in three dimensions using a finite element method to obtain the energy, stresses, and linearized moduli under imposed macroscale deformation. Highlights of the numerical study include: (i) the linearized Poisson's ratio is very close to the incompressible limit without a phenomenological imposition of incompressibility; (ii) despite the harmonic Gaussian chain as a starting point, there is an emergent strain-softening and strain-stiffening response that is characteristic of real polymer networks, driven by the interplay between the entropy and the excluded volume interactions; and (iii) the emergence of a deformation-sensitive localization instability at large excluded volumes.

The present work revisits and improves the Shannon entropy approach when applied to the estimation of an instability timescale for chaotic diffusion in multidimensional Hamiltonian systems. This formulation has already been proved efficient in deriving the diffusion timescale in 4D symplectic maps and planetary systems, when the diffusion proceeds along the chaotic layers of the resonance's web. Herein the technique is used to estimate the diffusion rate in the Arnold model, i.e., of the motion along the homoclinic tangle of the so-called guiding resonance for several values of the perturbation parameter such that the overlap of resonances is almost negligible. Thus differently from the previous studies, the focus is fixed on deriving a local timescale related to the speed of an Arnold diffusion-like process. The comparison of the current estimates with determinations of the diffusion time obtained by straightforward numerical integration of the equations of motion reveals a quite good agreement.

We provide a first-principles derivation of the Langevin equation with shear flow and its corresponding fluctuation-dissipation theorems. Shear flow of simple fluids has been widely investigated by numerical simulations. Most studies postulate a Markovian Langevin equation with a simple shear drag term in the manner of Stokes. However, this choice has never been justified from first principles. We start from a particle-bath system described by a classical Caldeira-Leggett Hamiltonian modified by adding a term proportional to the strain-rate tensor according to Hoover's DOLLS method, and we derive a generalized Langevin equation for the sheared system. We then compute, analytically, the noise time-correlation functions in different regimes. Based on the intensity of the shear rate, we can distinguish between close-to-equilibrium and far-from-equilibrium states. According to the results presented here, the standard, simple, and Markovian form of the Langevin equation with shear flow postulated in the literature is valid only in the limit of extremely weak shear rates compared to the effective vibrational temperature of the bath. For even marginally higher shear rates, the (generalized) Langevin equation is strongly non-Markovian, and nontrivial fluctuation-dissipation theorems are derived.

The response to an applied electric field in the $q_T=1/2$ subphase of the MC881-MC452 binary mixture system is studied by using thick homeotropically aligned cells. In the ordinary antiferroelectric $\mathrm{Sm}{C}_A^{*}$ and 1/2 (sub)phases, some nonplanar asymmetric distortions in the antiferroelectric unit cell structure produce induced polarization in the applied field direction, starts to unwind the helix from the beginning, and tends to align the averaged tilt plane direction parallel to the applied field. In the 1/2 subphase under consideration, however, the helix resists being deformed at the beginning and then the thresholdlike steep increase of birefringence $\mathrm{\Delta }n$ occurs in the transition from 1/2 to unwound $\mathrm{Sm}{C}^{*}$ at a field of less than $0.5 \mathrm{V}/\mu \mathrm{m}$; we conclude that the thermal fluctuations play an important role in promoting the director flip-flopping in a single layer under the applied field and bring about additional induced polarization, which counteracts the aforementioned ordinary induced one and prevents the helix from unwinding. This suggests that the Langevin-like director reorientation is the mechanism of the V-shaped switching which was actually observed in the thin films of Mitsui mixture [Phys. Rev. Lett. 87, 015701 (2001)] and must have been used in prototyped thresholdless antiferroelectric liquid-crystal displays.

We study the effect of disorder on the excitons in a semiconductor with screened Coulomb interaction. Examples are polymeric semiconductors and/or van der Waals structures. In the screened hydrogenic problem, we consider the disorder phenomenologically using the so-called fractional Scrödinger equation. Our main finding is that joint action of screening and disorder either destroys the exciton (strong screening) or enhances the bounding of electron and hole in an exciton, leading to its collapse in the extreme case. Latter effects may also be related to the quantum manifestations of chaotic exciton behavior in the above semiconductor structures. Hence, they should be considered in device applications, where the interplay between dielectric screening and disorder is important. Our theoretical results permit one to predict the various excitonic properties in semiconductor samples with different degrees of disorder and Coulomb interaction screenings.

Fluctuations in a vast range of physical systems can be described as a superposition of uncorrelated pulses with a fixed shape, a process commonly referred to as a (generalized) shot noise or a filtered Poisson process. In this paper, we present a systematic study of a deconvolution method to estimate the arrival times and amplitudes of the pulses from realizations of such processes. The method shows that a time series can be reconstructed for various pulse amplitude and waiting time distributions. Despite a constraint on positive-definite amplitudes, it is shown that negative amplitudes may also be reconstructed by flipping the sign of the time series. The method performs well under moderate amounts of additive noise, both white noise and colored noise having the same correlation function as the process itself. The estimation of pulse shapes from the power spectrum is accurate except for excessively broad waiting time distributions. Although the method assumes constant pulse durations, it performs well under narrowly distributed pulse durations. The most important constraint on the reconstruction is information loss, which limits the method to intermittent processes. The ratio between the sampling time and the average waiting time between pulses must be about 1/20 or smaller for a well-sampled signal. Finally, given the system forcing, the average pulse function may be recovered. This recovery is only weakly constrained by the intermittency of the process.

We utilize a model of Wilson-Cowan oscillators to investigate structure-function relationships in the human brain by means of simulations of the spontaneous dynamics of brain networks generated through human connectome data. This allows us to establish relationships between the global excitability of such networks and global structural network quantities for connectomes of two different sizes for a number of individual subjects. We compare the qualitative behavior of such correlations between biological networks and shuffled networks, the latter generated by shuffling the pairwise connectivities of the former while preserving their distribution. Our results point towards a remarkable propensity of the brain to achieve a trade-off between low network wiring cost and strong functionality, and highlight the unique capacity of brain network topologies to exhibit a strong transition from an inactive state to a globally excited one.

Active particles that self-propel by transforming energy into mechanical motion represent a growing area of research in mathematics, physics, and chemistry. Here we investigate the dynamics of nonspherical inertial active particles moving in a harmonic potential, introducing geometric parameters which take into account the role of eccentricity for nonspherical particles. A comparison between the overdamped and underdamped models for elliptical particles is performed. The model of overdamped active Brownian motion has been used to describe most of the basic aspects of micrometer-sized particles moving in a liquid (“microswimmers”). We consider active particles by extending the active Brownian motion model to incorporate translation and rotation inertia and account for the role of eccentricity. We show how the overdamped and the underdamped models behave in the same way for small values of activity (Brownian case) if eccentricity is equal to zero, but increasing eccentricity leads the two dynamics to substantially depart from each other—in particular, the action of a torque induced by external forces, induced a marked difference close to the walls of the domain if eccentricity is high. Effects induced by inertia include an inertial delay time of the self-propulsion direction from the particle velocity, and the differences between the overdamped and underdamped systems are particularly evident in the first and second moments of the particle velocities. Comparison with the experimental results of vibrated granular particles shows good agreement and corroborates the notion that self-propelling massive particles moving in gaseous media are dominated by inertial effects.

When applying an oscillatory electric potential to an electrolyte solution, it is commonly assumed that the choice of which electrode is grounded or powered does not matter because the time average of the electric potential is zero. Recent theoretical, numerical, and experimental work, however, has established that certain types of multimodal oscillatory potentials that are “nonantiperiodic” can induce a net steady field toward either the grounded or powered electrode [A. Hashemi et al., Phys. Rev. E 105, 065001 (2022)]. Here, we elaborate on the nature of these steady fields through numerical and theoretical analyses of the asymmetric rectified electric field (AREF). We demonstrate that AREFs induced by a nonantiperiodic electric potential, e.g., by a two-mode waveform with modes at 2 and $3\mathrm{Hz}$, invariably yields a steady field that is spatially dissymmetric between two parallel electrodes, such that swapping which electrode is powered changes the direction of the field. Furthermore, we show that, while the single-mode AREF occurs in asymmetric electrolytes, nonantiperiodic electric potentials create a steady field in electrolytes even if the cations and anions have the same mobilities. Additionally, using a perturbation expansion, we demonstrate that the dissymmetric AREF occurs due to odd nonlinear orders of the applied potential. We further generalize the theory by demonstrating that the dissymmetric field occurs for all classes of zero-time-average (no dc bias) periodic potentials, including triangular and rectangular pulses, and we discuss how these steady fields can tremendously change the interpretation, design, and applications of electrochemical and electrokinetic systems.

Transformation optics has been a powerful tool to manipulate physical fields if the governing equations in two spaces satisfy a certain form invariance. A recent interest has been applying this method to design hydrodynamic metamaterials described by the Navier-Stokes equations. However, transformation optics may not be applicable to such a general fluid model while especially the rigorous analysis is still absent. In this work, we give a definite criterion of the required form invariance, i.e., metric of one space and its affine connections that appear in curvilinear coordinates can be incorporated into material properties or interpreted by extra physical mechanisms introduced in another space. Based on this criterion, we prove that the Navier-Stokes equations, as well as its simplification in creeping flows (the Stokes equation), cannot be form invariant due to the redundant affine connections from their viscous terms. On the contrary, the creeping flows under the lubrication approximation, saying the classical Hele-Shaw model and its anisotropic counterpart, can retain the form of their governing equations for steady incompressible isothermal Newtonian fluids. Besides, we propose the design of multilayered structures with spatially varying cell depth to mimic the required anisotropic shear viscosity for modulating Hele-Shaw flows. Our results correct previous misunderstandings about the applicability of transformation optics under the Navier-Stokes equations, reveal the decisive role of lubrication approximation in maintaining form invariance (consistent with recent experiments featuring shallow configurations), and provide a feasible approach in experimental fabrication.

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.

Depinning of elastic systems advancing on disordered media can usually be described by the quenched Edwards-Wilkinson equation (qEW). However, additional ingredients such as anharmonicity and forces that cannot be derived from a potential energy may generate a different scaling behavior at depinning. The most experimentally relevant is the Kardar-Parisi-Zhang (KPZ) term, proportional to the square of the slope at each site, which drives the critical behavior into the so-called quenched KPZ (qKPZ) universality class. We study this universality class both numerically and analytically: by using exact mappings we show that at least for $d=1,2$ this class encompasses not only the qKPZ equation itself, but also anharmonic depinning and a well-known class of cellular automata introduced by Tang and Leschhorn. We develop scaling arguments for all critical exponents, including size and duration of avalanches. The scale is set by the confining potential strength $m^2$. This allows us to estimate numerically these exponents as well as the $m$-dependent effective force correlator $\mathrm{\Delta }\left(w\right)$, and its correlation length $\rho :=\mathrm{\Delta }\left(0\right)/|{\mathrm{\Delta }}^{\prime }\left(0\right)|$. Finally, we present an algorithm to numerically estimate the effective ($m$-dependent) elasticity $c$, and the effective KPZ nonlinearity $\lambda$. This allows us to define a dimensionless universal KPZ amplitude $\mathcal{A}:=\rho \lambda /c$, which takes the value $\mathcal{A}=1.10\left(2\right)$ in all systems considered in $d=1$. This proves that qKPZ is the effective field theory for all these models. Our work paves the way for a deeper understanding of depinning in the qKPZ class, and in particular, for the construction of a field theory that we describe in a companion paper.

There are two main universality classes for depinning of elastic interfaces in disordered media: quenched Edwards-Wilkinson (qEW) and quenched Kardar-Parisi-Zhang (qKPZ). The first class is relevant as long as the elastic force between two neighboring sites on the interface is purely harmonic and invariant under tilting. The second class applies when the elasticity is nonlinear or the surface grows preferentially in its normal direction. It encompasses fluid imbibition, the Tang-Leschorn cellular automaton of 1992 (TL92), depinning with anharmonic elasticity (aDep), and qKPZ. While the field theory is well developed for qEW, there is no consistent theory for qKPZ. The aim of this paper is to construct this field theory within the functional renormalization group (FRG) framework, based on large-scale numerical simulations in dimensions $d=1$, 2, and 3, presented in a companion paper [Mukerjee et al., Phys. Rev. E 107, 054136 (2023)]. In order to measure the effective force correlator and coupling constants, the driving force is derived from a confining potential with curvature $m^2$. We show, that contrary to common belief, this is allowed in the presence of a KPZ term. The ensuing field theory becomes massive and can no longer be Cole-Hopf transformed. In exchange, it possesses an IR attractive stable fixed point at a finite KPZ nonlinearity $\lambda$. Since there is neither elasticity nor a KPZ term in dimension $d=0$, qEW and qKPZ merge there. As a result, the two universality classes are distinguished by terms linear in $d$. This allows us to build a consistent field theory in dimension $d=1$, which loses some of its predictive powers in higher dimensions.

The capability for molecular dynamics simulations to treat relativistic dynamics is extended by the inclusion of relativistic kinetic energy. In particular, relativistic corrections to the diffusion coefficient are considered for an argon gas modeled with a Lennard-Jones interaction. Forces are transmitted instantaneously without being retarded, an approximation that is allowed due to the short-range nature of the Lennard-Jones interaction. At a mass density of $1.4\text{g}/{\text{cm}}^3$, significant deviations from classical results are observed at temperatures above $k_{\text{B}}T\approx 0.05m{c}^2$, corresponding to an average thermal velocity of 32% of the speed of light. For temperatures approaching $k_{\text{B}}T\approx m{c}^2$, the semirelativistic simulations agree with analytical results for hard spheres, which is seen to be a good approximation as far as diffusion effects are concerned.

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.

A previously developed agent model, based on bounded rational planning, is extended by introducing learning, with bounds on the memory of the agents. The exclusive impact of learning, especially in longer games, is investigated. Based on our results, we provide testable predictions for experiments on repeated public goods games (PGG) with synchronized actions. We observe that noise in player contributions can have a positive impact of group cooperation in PGG. We theoretically explain the experimental results on the impact of group size as well as mean per capita return (MPCR) on cooperation.

Combining experimental observations of Quincke roller clusters with computer simulations and a stability analysis, we explore the formation and stability of two interlocked self-propelled dumbbells. For large self-propulsion and significant geometric interlocking, there is a stable joint spinning motion of two dumbbells. The spinning frequency can be tuned by the self-propulsion speed of a single dumbbell, which is controlled by an external electric field for the experiments. For typical experimental parameters the rotating pair is stable with respect to thermal fluctuations but hydrodynamic interactions due to the rolling motion of neighboring dumbbells leads to a breakup of the pair. Our results provide a general insight into the stability of spinning active colloidal molecules, which are geometrically locked.

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.