We present a comprehensive set of measurements of optical, dielectric, diamagnetic, elastic, and viscous properties in the nematic (N) phase formed by a liquid crystalline dimer. The studied dimer, 1,7-bis-4-(4′-cyanobiphenyl) heptane (CB7CB), is composed of two rigid rodlike cyanobiphenyl segments connected by a flexible aliphatic link with seven methyl groups. CB7CB and other nematic dimers are of interest due to their tendency to adopt bent configurations and to form two states possessing a modulated nematic director structure, namely, the twist-bend nematic, ${\mathrm{N}}_{\mathrm{TB}}$, and the oblique helicoidal cholesteric, $\mathrm{C}{\mathrm{h}}_{\mathrm{OH}}$, which occurs when the achiral dimer is doped with a chiral additive and exposed to an external electric or magnetic field. We characterize the material parameters as functions of temperature in the entire temperature range of the N phase, including the pretransitional regions near the $\mathrm{N}\text{−}{\mathrm{N}}_{\mathrm{TB}}$ and N-to-isotropic (I) transitions. The splay constant $K_{11}$ is determined by two direct and independent techniques, namely, detection of the Frederiks transition and measurement of director fluctuation amplitudes by dynamic light scattering (DLS). The bend $K_{33}$ and twist $K_{22}$ constants are measured by DLS. $K_{33}$, being the smallest of the three constants, shows a strong nonmonotonous temperature dependence with a negative slope in both N-I and $\mathrm{N}\text{−}{\mathrm{N}}_{\mathrm{TB}}$ pretransitional regions. The measured ratio $K_{11}/K_{22}$ is larger than 2 in the entire nematic temperature range. The orientational viscosities associated with splay, twist, and bend fluctuations in the N phase are comparable to those of nematics formed by rodlike molecules. All three show strong temperature dependence, increasing sharply near the $\mathrm{N}\text{−}{\mathrm{N}}_{\mathrm{TB}}$ transition.

The two principal ingredients determining the failure modes of disordered solids are the strength of heterogeneity and the length scale of the region affected in the solid following a local failure. While the latter facilitates damage nucleation, the former leads to diffused damage—the two extreme natures of the failure modes. In this study, using the random fiber bundle model as a prototype for disordered solids, we classify all failure modes that are the results of interplay between these two effects. We obtain scaling criteria for the different modes and propose a general phase diagram that provides a framework for understanding previous theoretical and experimental attempts of interpolation between these modes. As the fiber bundle model is a long-standing model for interpreting various features of stressed disordered solids, the general phase diagram can serve as a guiding principle in anticipating the responses of disordered solids in general.

The macroscopic permeability of a natural shale is determined by using structural measurements on three different scales. Transmission electron microscopy yields two-dimensional (2D) images with pixels smaller than 1 nm; these images are used to reconstruct 3D nanostructures. Three-dimensional focused ion beam–scanning electron microscopy (5.95- to 8.48-nm voxel size) provides 3D mesoscale pores of limited relative volume (1.71–5.9%). Micro-computed tomography (700-nm voxel size) provides information on the mineralogy of the shale, including the pores on this scale which do not percolate; synthetic 3D media are derived on the macroscopic scale by a training image technique. Permeability of the nanoscale, of the mesoscale structures and of their superposition is determined by solving the Stokes equation and this enables us to estimate the permeabilities of the 700-nm voxels located within the clay matrix. Finally, the Darcy equation is solved on synthetic 3D macroscale media to obtain the macroscopic permeability which is found in good agreement with experimental results obtained on the centimetric scale.

The structure of the turbulence-driven power fluctuations in a wind farm is fundamentally described from basic concepts. A derived tuning-free model, supported with experiments, reveals the underlying spectral content of the power fluctuations of a wind farm. It contains two power-law trends and oscillations in the relatively low- and high-frequency ranges. The former is mostly due to the turbulent interaction between the flow and the turbine properties, whereas the latter is due to the advection between turbine pairs. The spectral wind-farm scale power fluctuations ${\mathrm{\Phi }}_P$ exhibit a power-law decay proportional to $f^{-5/3-2}$ in the region corresponding to the turbulence inertial subrange and at relatively large scales, ${\mathrm{\Phi }}_P\sim f^{-2}$. Due to the advection and turbulent diffusion of large-scale structures, a spectral oscillation exists with the product of a sinusoidal behavior and an exponential decay in the frequency domain.

For the purpose of checking material conservation of various numerical algorithms used in the self-consistent-field theory (SCFT) of polymeric systems, we develop an algebraic method using matrix and bra-ket notation, which traces the Hermiticity of the product of the volume and evolution matrices. Algebraic tests for material conservation reveal that the popular pseudospectral method in the Cartesian grid conserves material perfectly, while the finite-volume method (FVM) is the proper tool when real-space SCFT with the Crank-Nicolson method is adopted in orthogonal coordinate systems. We also find that alternating direction implicit methods combined with the FVM exhibit small mass errors in the SCFT calculation. By introducing fractional cells in the FVM formulation, accurate SCFT calculations are performed for systems with irregular geometries and the results are consistent with previous experimental and theoretical works.

We investigate generalized non-Markovian stochastic Schrödinger equations (SSEs), driven by a multidimensional counting process and multidimensional Brownian motion introduced by A. Barchielli and C. Pellegrini [J. Math. Phys. 51, 112104 (2010)]. We show that these SSEs can be translated in a nonlinear form, which can be efficiently simulated. The simulation is illustrated by the model of a two-level system in a structured bath, and the results of the simulations are compared with the exact solution of the generalized master equation.

We study the stochastic thermodynamics of resetting systems. Violation of microreversibility means that the well-known derivations of fluctuations theorems break down for dynamics with resetting. Despite that we show that stochastic resetting systems satisfy two integral fluctuation theorems. The first is the Hatano-Sasa relation describing the transition between two steady states. The second integral fluctuation theorem involves a functional that includes both dynamical and thermodynamic contributions. We find that the second law-like inequality found by Fuchs et al. for resetting systems [Europhys. Lett. 113, 60009 (2016)] can be recovered from this integral fluctuation theorem with the help of Jensen's inequality.

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

We address in detail the problem of true morphological phase separation (MPS) in three-dimensional or ($2+1$)-dimensional unstable thin liquid films $(>100\text{nm})$ under the influence of gravity. The free-energy functionals of these films are asymmetric and show two points of common tangency, which facilitates the formation of two equilibrium phases. Three distinct patterns formed by relative preponderance of these phases are clearly identified in “true MPS”. Asymmetricity induces two different pathways of pattern formation, viz., defect and direct pathway for true MPS. The pattern formation and phase-ordering dynamics have been studied using statistical measures such as structure factor, correlation function, and growth laws. In the late stage of coarsening, the system reaches into a scaling regime for both pathways, and the characteristic domain size follows the Lifshitz-Slyozov growth law $[L\left(t\right)\sim t^{1/3}]$. However, for the defect pathway, there is a crossover of domain growth behavior from $L\left(t\right)\sim t^{1/4}\to t^{1/3}$ in the dynamical scaling regime. We also underline the analogies and differences behind the mechanisms of MPS and true MPS in thin liquid films and generic spinodal phase separation in binary mixtures.

In this work maximum entropy distributions in the space of steady states of metabolic networks are considered upon constraining the first and second moments of the growth rate. Coexistence of fast and slow phenotypes, with bimodal flux distributions, emerges upon considering control on the average growth (optimization) and its fluctuations (heterogeneity). This is applied to the carbon catabolic core of Escherichia coli where it quantifies the metabolic activity of slow growing phenotypes and it provides a quantitative map with metabolic fluxes, opening the possibility to detect coexistence from flux data. A preliminary analysis on data for E. coli cultures in standard conditions shows degeneracy for the inferred parameters that extend in the coexistence region.

Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in $k$-space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in $k$-space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.

We consider the discrete Swift-Hohenberg equation with cubic and quintic nonlinearity, obtained from discretizing the spatial derivatives of the Swift-Hohenberg equation using central finite differences. We investigate the discretization effect on the bifurcation behavior, where we identify three regions of the coupling parameter, i.e., strong, weak, and intermediate coupling. Within the regions, the discrete Swift-Hohenberg equation behaves either similarly or differently from the continuum limit. In the intermediate coupling region, multiple Maxwell points can occur for the periodic solutions and may cause irregular snaking and isolas. Numerical continuation is used to obtain and analyze localized and periodic solutions for each case. Theoretical analysis for the snaking and stability of the corresponding solutions is provided in the weak coupling region.

We propose a neuronal network model which undergoes a saddle node on an invariant circle bifurcation as the mechanism of the transition from the interictal to the ictal (seizure) state. In the vicinity of this transition, the model captures important dynamical features of both interictal and ictal states. We study the nature of interictal spikes and early warnings of the transition predicted by this model. We further demonstrate that recurrent seizures emerge due to the interaction between two networks.

Using high-resolution confocal rheometry, we study the shear profiles of well-entangled DNA solutions under large-amplitude oscillatory shear in a rectilinear planar shear cell. With increasing Weissenberg number (Wi), we observe successive transitions from normal Newtonian linear shear profiles to wall-slip dominant shear profiles and, finally, to shear-banding profiles at high Wi. To investigate the microscopic origin of the observed shear banding, we study the dynamics of micron-sized tracers embedded in DNA solutions. Surprisingly, tracer particles in the shear frame exhibit transient superdiffusivity and strong dynamic heterogeneity. The probability distribution functions of particle displacements follow a power-law scaling at large displacements, indicating a Lévy-walk-type motion, reminiscent of tracer dynamics in entangled wormlike micelle solutions and sheared colloidal glasses. We further characterize the length and time scales associated with the abnormal dynamics of tracer particles. We hypothesize that the unusual particle dynamics arise from localized shear-induced chain disentanglement.

Interfacial instability is highly relevant to many important biological processes. A key example arises in wound healing experiments, which observe that an epithelial layer with an initially straight edge does not heal uniformly. We consider the phenomenon in the context of active fluids. Improving upon the approximation used by Zimmermann, Basan, and Levine [Eur. Phys. J.: Spec. Top. 223, 1259 (2014)], we perform a linear stability analysis on a two-dimensional incompressible hydrodynamic model of an active fluid with an open interface. We categorize the stability of the model and find that for experimentally relevant parameters, fingering instability is always absent in this minimal model. Our results point to the crucial role of density variation in the fingering instability in tissue regeneration.

We develop the linear theory for the asymptotic growth of the incompressible Rayleigh-Taylor instability of an accelerated solid slab of density ${\rho }_2$, shear modulus $G$, and thickness $h$, placed over a semi-infinite ideal fluid of density ${\rho }_1<{\rho }_2$. It extends previous results for Atwood number $A_T=1$ [B. J. Plohr and D. H. Sharp, Z. Angew. Math. Phys. 49, 786 (1998)] to arbitrary values of $A_T$ and unveil the singular feature of an instability threshold below which the slab is stable for any perturbation wavelength. As a consequence, an accelerated elastic-solid slab is stable if ${\rho }_{2}gh/G\le 2(1-A_T)/A_T$.

We have extended a recently developed multispecies, multitemperature Bhatnagar-Gross-Krook model [Haack et al., J. Stat. Phys. 168, 822 (2017)], to include multiphysics capabilities that enable modeling of a wider range of physical conditions. In terms of geometry, we have extended from the spatially homogeneous setting to one spatial dimension. In terms of the physics, we have included an atomic ionization model, accurate collision physics across coupling regimes, self-consistent electric fields, and degeneracy in the electronic screening. We apply the model to a warm dense matter scenario in which the ablator-fuel interface of an inertial confinement fusion target is heated, but for larger length and time scales and for much higher temperatures than can be simulated using molecular dynamics. Relative to molecular dynamics, the kinetic model greatly extends the temperature regime and the spatiotemporal scales over which we are able to model. In our numerical results we observe hydrogen from the ablator material jetting into the fuel during the early stages of the implosion and compare the relative size of various diffusion components (Fickean diffusion, electrodiffusion, and barodiffusion) that drive this process. We also examine kinetic effects, such as anisotropic distributions and velocity separation, in order to determine when this problem can be described with a hydrodynamic model.

An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.

The orientational phase transitions that occur in the deposition of longitudinal polymers of length $k$ (in terms of lattice units) are characterized by information theory techniques. We calculate the absolute value of an order parameter $\delta$, which weights the relative orientations of the deposited rods, which varies between 0.0 (random orientation) and 1.0 (fully oriented in either of the two equivalent directions in an $L\times L$ square lattice). A Monte Carlo (MC) algorithm is implemented to induce a dynamics allowing for accommodation of the rods for any given density or coverage $\theta$ (ratio of the occupied sites over all the sites in the lattice). The files storing $\delta \left(t\right)$ (with time $t$ measured in MC steps) are then treated by data recognizer wlzip based on data compressor techniques yielding the information content measured by a parameter $\eta \left(\theta \right)$. This allows us to recognize two maxima separated by a well-defined minimum for $\eta \left(\theta \right)$ provided $k\ge 7$. The first maximum is associated with an isotropic-nematic ($I\text{−}N$) phase transition occurring at intermediate density, while the second maximum is associated with some kind of nematic-isotropic transition at high coverage. In the cases of $k<7$, the curves for $\eta \left(\theta \right)$ are almost constant, presenting a very broad maximum which can hardly be associated with a phase transition. The study varies $L$ and $k$, allowing for a basic scaling of the found critical densities towards the thermodynamic limit. These calculations confirm the tendency obtained by different methods in the case of the intermediate-density $I\text{−}N$ phase transition, while this tendency is established here in the case of the high-density phase transition.