Appealing to the 1902 Gibbs formalism for classical statistical mechanics (SM)—the first SM axiomatic theory ever that successfully explained equilibrium thermodynamics—we show that already at the classical level there is a strong correlation between Renyi's exponent $\alpha$ and the number of particles for very simple systems. No reference to heat baths is needed for such a purpose.

We investigate the impact of noise on a two-dimensional simple paradigmatic piecewise-smooth dynamical system. For that purpose, we consider the motion of a particle subjected to dry friction and colored noise. The finite correlation time of the noise provides an additional dimension in phase space, causes a nontrivial probability current, and establishes a proper nonequilibrium regime. Furthermore, the setup allows for the study of stick-slip phenomena, which show up as a singular component in the stationary probability density. Analytic insight can be provided by application of the unified colored noise approximation, developed by Jung and Hänggi [Phys. Rev. A 35, 4464(R) (1987)]. The analysis of probability currents and of power spectral densities underpins the observed stick-slip transition, which is related with a critical value of the noise correlation time.

Fluctuation-induced (“Casimir”) forces caused by thermal and quantum fluctuations are investigated for ideal and imperfect Bose gases confined to $d$-dimensional films of size ${\infty }^{d-1}\times D$ under periodic (P), antiperiodic (A), Dirichlet-Dirichlet (DD), Neumann-Neumann (NN), and Robin (R) boundary conditions (BCs). The full scaling functions ${\mathrm{{\rm Y}}}_d^{\text{BC}}(x_{\lambda }=D/{\lambda }_{\text{th}},x_{\xi }=D/\xi )$ of the residual reduced grand potential per area ${\phi }_{\text{res},d}^{\text{BC}}(T,\mu ,D)=D^{-(d-1)}{\mathrm{{\rm Y}}}_d^{\text{BC}}(x_{\lambda },x_{\xi })$ are determined for the ideal gas case with these BCs, where ${\lambda }_{\text{th}}$ and $\xi$ are the thermal de Broglie wavelength and the bulk correlation length, respectively. The associated limiting scaling functions ${\mathrm{\Theta }}_d^{\text{BC}}\left(x_{\xi }\right)\equiv {\mathrm{{\rm Y}}}_d^{\text{BC}}(\infty ,x_{\xi })$ describing the critical behavior at the bulk condensation transition are shown to agree with those previously determined from a massive free $O\left(2\right)$ theory for $\text{BC}=\text{P},\text{A},\text{DD},\text{DN},\text{NN}$. For $d=3$, they are expressed in closed analytical form in terms of polylogarithms. The analogous scaling functions ${\mathrm{{\rm Y}}}_d^{\text{BC}}(x_{\lambda },x_{\xi },c_{1}D,c_{2}D)$ and ${\mathrm{\Theta }}_d^{\text{R}}(x_{\xi },c_{1}D,c_{2}D)$ under the RBCs $({\partial }_z-c_1)\varphi {{|}_{z=0}=({\partial }_z+c_2)\varphi |}_{z=D}=0$ with $c_1\ge 0$ and $c_2\ge 0$ are also determined. The corresponding scaling functions ${\mathrm{{\rm Y}}}_{\infty ,d}^{\text{P}}(x_{\lambda },x_{\xi })$ and ${\mathrm{\Theta }}_{\infty ,d}^{\text{P}}\left(x_{\xi }\right)$ for the imperfect Bose gas are shown to agree with those of the interacting Bose gas with $n$ internal degrees of freedom in the limit $n\to \infty$. Hence, for $d=3, {\mathrm{\Theta }}_{\infty ,d}^{\text{P}}\left(x_{\xi }\right)$ is known exactly in closed analytic form. To account for the breakdown of translation invariance in the direction perpendicular to the boundary planes implied by free BCs such as DDBCs, a modified imperfect Bose gas model is introduced that corresponds to the limit $n\to \infty$ of this interacting Bose gas. Numerically and analytically exact results for the scaling function ${\mathrm{\Theta }}_{\infty ,3}^{\mathbb{DD}}\left(x_{\xi }\right)$ therefore follow from those of the $O\left(2n\right){\varphi }^4$ model for $n\to \infty$.

The fluctuations of unwound helical structure have been observed in deformed helix ferroelectric liquid crystal (DHFLC) and conventional FLC sample cells. The helix is partially unwound by strong anchoring on the substrates. In such sample cells, the helical decarlization lines are not observed in the texture under crossed polarized microscope. The dielectric spectroscopy is employed to observe the behavior of dielectric relaxation processes in these sample cells. A dielectric relaxation process is observed at a lower frequency than the Goldstone mode processes in DHFLC and FLC, which we call partially unwound helical mode (p-UHM). However, the p-UHM process is not observed in the sample cell in which the helical lines appear. The application of various amplitudes of probing ac voltages on this mode has shown the higher frequency shift, i.e., the larger the amplitude of ac voltage, the higher is the relaxation frequency of p-UHM. At sufficient amplitude of applied probing ac voltage, the p-UHM merges with the Goldstone mode process and is difficult to detect. However, the Goldstone mode relaxation frequency is almost independent of the cell geometry and sample configuration. The electro-optical behavior of the p-UHM has also been confirmed by electro-optical technique. The dielectric relaxation of UHM at a frequency lower than the Goldstone mode is interpreted as the fluctuation of partially unwound helix.

We report on the size dependence of the surface tension of a free surface of an isotropic fluid. The size dependence of the surface tension is evaluated based on the Gibbs-Tolman-Koenig-Buff equation for positive and negative values of curvatures and the Tolman lengths. For all combinations of positive and negative signs of curvature and the Tolman length, we succeed to have a continuous function, avoiding the existing discontinuity at zero curvature (flat interfaces). As an example, a water droplet in the thermodynamical equilibrium with the vapor is analyzed in detail. The size dependence of the surface tension and the Tolman length are evaluated with the use of experimental data of the International Association for the Properties of Water and Steam. The evaluated Tolman length of our approach is in good agreement with molecular dynamics and experimental data.

We develop asymptotic modeling for two- or three-dimensional viscous fluid flow and convective transfer at the interface between a fluid and a porous layer. The asymptotic model is based on the fact that the thickness $d$ of the interfacial transition region ${\mathrm{\Omega }}_{\text{fp}}$ of the one-domain representation is very small compared to the macroscopic length scale $L$. The analysis leads to an equivalent two-domain representation where transport phenomena in the transition layer of the one-domain approach are represented by algebraic jump boundary conditions at a fictive dividing interface $\mathrm{\Sigma }$ between the homogeneous fluid and porous regions. These jump conditions are thus stated up to first-order in $O(d/L)$ with $d/L\ll 1$. The originality and relevance of this asymptotic model lies in its general and multidimensional character. Indeed, it is shown that all the jump interface conditions derived for the commonly used 1D-shear flow are recovered by taking the tangential component of the asymptotic model. In that case, the comparison between the present model and the different models available in the literature gives explicit expressions of the effective jump coefficients and their associated scaling. In addition for multi-dimensional flows, the general asymptotic model yields the different components of the jump conditions including a new specific equation for the cross-flow pressure jump on $\mathrm{\Sigma }$.

Cells can adjust to their growth environments and regulate their behavior accordingly. To study how cells accomplish this growth-dependent adjustment from the molecular to the behavioral level, we used bacterial chemotaxis as a model system to explore the behavioral difference for bacteria grown in nutrient-rich and nutrient-poor media. We found that bacteria grown in a nutrient-poor medium exhibit faster chemotaxis adaptation, and this enables them to respond more rapidly to a changing environment and increases their ability to localize to a nutrient concentration peak. We identified the molecular mechanisms behind this behavioral difference through coarse-grained modeling, and demonstrated its physiological consequences by simulating bacterial chemotactic motion in spatiotemporally varying environments and in a static environment with a nutrient concentration peak.

The correlation function of the director fluctuations in a free-standing smectic ferroelectric film is calculated theoretically. In the functional of free energy, the anisotropy of the Coulomb interaction of polarization charges is taken into account. The results of calculations were used to obtain the angular dependences of scattered light intensity. It has been shown that for relatively thick films, the anisotropy of the Coulomb interaction of polarization charges can change significantly the scattered light intensity.

A fundamental issue in analyzing diffusion in heterogeneous media is interpreting the space dependence of the associated diffusion coefficient. This reflects the well-known Ito-Stratonovich dilemma for continuous stochastic processes with multiplicative noise. In order to resolve this dilemma it is necessary to introduce additional constraints regarding the underlying physical system. Here we introduce a mechanism for generating nonlinear Brownian motion based on a form of temporal disorder. Motivated by switching processes in molecular biology, we consider a Brownian particle that randomly switches between two distinct conformational states with different diffusivities. In each state the particle undergoes normal diffusion (additive noise) so there is no ambiguity in the interpretation of the noise. However, if the switching rates depend on position, then in the fast-switching limit one obtains Brownian motion with a space-dependent diffusivity. We show that the resulting multiplicative noise process is of the Ito form. In particular, we solve a first-passage time problem for finite switching rates and show that the mean first-passage time reduces to the Ito version in the fast-switching limit.

We propose a toy model for a cyclic order-disorder transition and introduce a geometric methodology to understand stochastic processes involved in transitions. Specifically, our model consists of a pair of forward and backward processes (FPs and BPs) for the emergence and disappearance of a structure in a stochastic environment. We calculate time-dependent probability density functions (PDFs) and the information length $\mathcal{L}$, which is the total number of different states that a system undergoes during the transition. Time-dependent PDFs during transient relaxation exhibit strikingly different behavior in FPs and BPs. In particular, FPs driven by instability undergo the broadening of the PDF with a large increase in fluctuations before the transition to the ordered state accompanied by narrowing the PDF width. During this stage, we identify an interesting geodesic solution accompanied by the self-regulation between the growth and nonlinear damping where the time scale $\tau$ of information change is constant in time, independent of the strength of the stochastic noise. In comparison, BPs are mainly driven by the macroscopic motion due to the movement of the PDF peak. The total information length $\mathcal{L}$ between initial and final states is much larger in BPs than in FPs, increasing linearly with the deviation $\gamma$ of a control parameter from the critical state in BPs while increasing logarithmically with $\gamma$ in FPs. $\mathcal{L}$ scales as $|lnD|$ and $D^{-1/2}$ in FPs and BPs, respectively, where $D$ measures the strength of the stochastic forcing. These differing scalings with $\gamma$ and $D$ suggest a great utility of $\mathcal{L}$ in capturing different underlying processes, specifically, diffusion vs advection in phase transition by geometry. We discuss physical origins of these scalings and comment on implications of our results for bistable systems undergoing repeated order-disorder transitions (e.g., fitness).

We present a Landau theory for large-$l$ orientational phase transitions and apply it to the assembly of icosahedral viral capsids. The theory predicts two distinct types of ordering transitions. Transitions dominated by the $l=6,10,12$, and 18 icosahedral spherical harmonics resemble robust first-order phase transitions that are not significantly affected by chirality. The remaining transitions depend essentially on including mixed $l$ states denoted as $l=15+16$ corresponding to a mixture of $l=15$ and $l=16$ spherical harmonics. The $l=15+16$ transition is either continuous or weakly first-order and it is strongly influenced by chirality, which suppresses spontaneous chiral symmetry breaking. The icosahedral state is in close competition with states that have tetrahedral, $D_5$, and octahedral symmetries. We present a group-theoretic method to analyze the competition between the different symmetries. The theory is applied to a variety of viral shells.

Subdiffusion in conformational dynamics of proteins is observed both experimentally and in simulations. Although its origin has been attributed to multiple mechanisms, including trapping on a rugged energy landscape, fractional Brownian noise, or a fractal topology of the energy landscape, it is unclear which of these, if any, is most relevant. To obtain insights into the actual mechanism, we introduce an analytically tractable hierarchical trapping model and apply it to molecular dynamics simulation trajectories of three proteins in solution. The analysis of the simulations introduces a subdiffusive exponent that varies with time and associates plateaus in the mean-squared displacement with traps on the energy landscape. This analysis permits us to separate the component of subdiffusion due to a trapping mechanism from that due to an underlying fluctuating process, such as fractional Brownian motion. The present results thus provide insights concerning the physical origin of subdiffusion in the dynamics of proteins.

The enthalpic response of amorphous polymers depends strongly on their thermal and deformation history. Annealing just below the glass transition temperature ($T_{\text{g}}$) causes a large endothermic overshoot of the isobaric heat capacity at $T_{\text{g}}$ as measured by differential scanning calorimetry, while plastic deformation (cold work) can erase this overshoot and create an exothermic undershoot. This indicates that a strong coupling exists between the polymer structure, thermal response, and mechanical deformation. In this work, we apply a recently developed thermomechanical model for glassy polymers that couples structural evolution and viscoplastic deformation to investigate the effect of annealing and plastic deformation on the accumulation of stored energy during cold work and calorimetry measurements of heat flow. The thermomechanical model introduces the effective temperature as an additional state variable in a nonequilibrium thermodynamics setting to describe the structural evolution of the material. The results show that the model accurately describes the stress and enthalpy response of quenched and annealed polymers with different plastic predeformations. The model also shows that at 30% strain in uniaxial compression, 45% of the applied work is converted into stored energy, which is consistent with experimental data from literature.

A discretization of the wave-number space is proposed, using nested polyhedra, in the form of alternating dodecahedra and icosahedra that are self-similarly scaled. This particular choice allows the possibility of forming triangles using only discretized wave vectors when the scaling between two consecutive dodecahedra is equal to the golden ratio and the icosahedron between the two dodecahedra is the dual of the inner dodecahedron. Alternatively, the same discretization can be described as a logarithmically spaced (with a scaling equal to the golden ratio), nested dodecahedron-icosahedron compounds. A wave vector which points from the origin to a vertex of such a mesh, can always find two other discretized wave vectors that are also on the vertices of the mesh (which is not true for an arbitrary mesh). Thus, the nested polyhedra grid can be thought of as a reduction (or decimation) of the Fourier space using a particular set of self-similar triads arranged approximately in a spherical form. For each vertex (i.e., discretized wave vector) in this space, there are either 9 or 15 pairs of vertices (i.e., wave vectors) with which the initial vertex can interact to form a triangle. This allows the reduction of the convolution integral in the Navier-Stokes equation to a sum over 9 or 15 interaction pairs, transforming the equation in Fourier space to a network of “interacting” nodes that can be constructed as a numerical model, which evolves each component of the velocity vector on each node of the network. This model gives the usual Kolmogorov spectrum of $k^{-5/3}$. Since the scaling is logarithmic, and the number of nodes for each scale is constant, a very large inertial range (i.e., a very high Reynolds number) with a much lower number of degrees of freedom can be considered. Incidentally, by assuming isotropy and a certain relation between the phases, the model can be used to systematically derive shell models.

A theory is presented for the transition between the coflowing and the drop-generation regimes observed in microfluidic channels with a rectangular cross section. This transition is characterized by a critical ratio of the dispersed- to continuous-phase volume flow rates. At flow-rate ratios higher than this critical value, drop generation is suppressed. The critical ratio corresponds to the fluid cross section where the dispersed-phase fluid is just tangent to the channel walls. The transition criterion is a function of the ratio of the fluid viscosities, the three-phase contact angle formed between the fluid phases and the channel walls, and the aspect ratio of the channel cross section; the transition is independent of interfacial tension. Hysteretic behavior of drop generation with respect to the flow-rate ratio is predicted for partially wetting dispersed-phase fluids. Experimental data are consistent with this theory.

Solid-density plasmas driven by intense x-ray free-electron laser (XFEL) radiation are seeded by sources of nonthermal photoelectrons and Auger electrons that ionize and heat the target via collisions. Simulation codes that are commonly used to model such plasmas, such as collisional-radiative (CR) codes, typically assume a Maxwellian distribution and thus instantaneous thermalization of the source electrons. In this study, we present a detailed description and initial applications of a collisional particle-in-cell code, picls, that has been extended with a self-consistent radiation transport model and Monte Carlo models for photoionization and $KLL$ Auger ionization, enabling the fully kinetic simulation of XFEL-driven plasmas. The code is used to simulate two experiments previously performed at the Linac Coherent Light Source investigating XFEL-driven solid-density Al plasmas. It is shown that picls-simulated pulse transmissions using the Ecker-Kröll continuum-lowering model agree much better with measurements than do simulations using the Stewart-Pyatt model. Good quantitative agreement is also found between the time-dependent picls results and those of analogous simulations by the CR code scfly, which was used in the analysis of the experiments to accurately reproduce the observed $K\alpha$ emissions and pulse transmissions. Finally, it is shown that the effects of the nonthermal electrons are negligible for the conditions of the particular experiments under investigation.

In this paper, a variant of the acoustic multipole source (AMS) method is proposed within the framework of the lattice Boltzmann method. A quadrupole term is directly included in the stress system (equilibrium momentum flux), and the dependency of the quadrupole source in the inviscid limit upon the fortuitous discretization error reported in the works of E. M. Viggen [Phys. Rev. E 87, 023306 (2013)] is removed. The regularized lattice Boltzmann (RLB) method with this variant AMS method is presented for the 2D and 3D acoustic problems in the inviscid limit, and without loss of generality, the D3Q19 model is considered in this work. To assess the accuracy and the advantage of the RLB scheme with this AMS for acoustic point sources, the numerical investigations and comparisons with the multiple-relaxation-time (MRT) models and the analytical solutions are performed on the 2D and 3D acoustic multipole point sources in the inviscid limit, including monopoles, $x$ dipoles, and $xx$ quadrupoles. From the present results, the good precision of this AMS method is validated, and the RLB scheme exhibits some superconvergence properties for the monopole sources compared with the MRT models, and both the RLB and MRT models have the same accuracy for the simulations of acoustic dipole and quadrupole sources. To further validate the capability of the RLB scheme with AMS, another basic acoustic problem, the acoustic scattering from a solid cylinder presented at the Second Computational Aeroacoustics Workshop on Benchmark Problems, is numerically considered. The directivity pattern of the acoustic field is computed at $r=7.5$; the present results agree well with the exact solutions. Also, the effects of slip and no-slip wall treatments within the regularized boundary condition on this pure acoustic scattering problem are tested, and compared with the exact solution, the slip wall treatment can present a better result. All simulations demonstrate that the RLB scheme with the AMS method is capable of accurately simulating 2D and 3D acoustic generation, propagation, and scattering at zero viscosity.

Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension $d$ at the band bottom and the exponent $\alpha$ that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality $d>4$.