Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To that effect, we aim to quantify approximations of the relevant Hertzian FPU-type lattice through both the Korteweg–de Vries (KdV) equation and the Toda lattice. Using the availability in such settings of both one-soliton and two-soliton solutions in explicit analytical form, we initialize such coherent structures in the granular chain and observe the proximity of the resulting evolution to the underlying integrable (KdV or Toda) model. While the KdV offers the possibility to accurately capture collisions of solitary waves propagating in the same direction, the Toda lattice enables capturing both copropagating and counterpropagating soliton collisions. The error in the approximation is quantified numerically and connections to bounds established in the mathematical literature are also given.

The direct numerical simulations of forced two-dimensional turbulent flow are presented by using the lattice Boltzmann method. The development of an energy-enstrophy double cascade is investigated in the two cases of external force of two-dimensional turbulence, Gaussian force and Kolmogorov force. It is found that the friction force is a necessary condition of the occurrence of a double cascade. The energy spectrum $k^{-3}$ in the enstrophy inertial range is in accord with the classical Kraichnan theory for both external forces. The energy spectrum of the Gaussian force case in an inverse cascade is $k^{-2}$; however, the Kolmogorov force drives the $k^{-5/3}$ energy in a backscatter cascade. The result agrees with Scott's standpoint, which describes nonrobustness of the two-dimensional turbulent inverse cascade. Also, intermittency is found for the enstrophy cascade in two cases of the external force form. Intermittency refers to the nonuniform distribution of saddle points in the two-dimensional turbulent flow.

It is shown that the transverse Rayleigh-Taylor-like (RT) instability in the hole-boring radiation pressure acceleration can be suppressed by using an elliptically polarized (EP) laser. A moderate $\mathit{J}\times \mathit{B}$ heating of the EP laser will thermalize the local electrons, which leads to the transverse diffusion of ions, suppressing the short wavelength perturbations of RT instability. A proper condition of polarization ratio is obtained analytically for the given laser intensity and plasma density. The idea is confirmed by two-dimensional particle-in-cell simulations, showing that the ion beam driven by the EP laser is more concentrated and intense compared with that of the circularly polarized laser.

We compute linear and quadratic static density response functions of three-dimensional Yukawa liquids by applying an external perturbation potential in molecular dynamics simulations. The response functions are also obtained from the equilibrium fluctuations (static structure factors) in the system via the fluctuation-dissipation theorems. The good agreement of the quadratic response functions, obtained in the two different ways, confirms the quadratic fluctuation-dissipation theorem. We also find that the three-point structure function may be factorizable into two-point structure functions, leading to a cluster representation of the equilibrium triplet correlation function.

Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark model.

In the time-dependent simulation of pure states dealing with transport in open quantum systems, the initial state is located outside of the active region of interest. Using the superposition principle and the analytical knowledge of the free time evolution of such a state outside the active region, together with absorbing layers and remapping, a model for a very significant reduction of the computational burden associated with the numerical simulation of open time-dependent quantum systems is presented. The model is specially suited to study (many-particle and high-frequency effects) quantum transport, but it can also be applied to any other research field where the initial time-dependent pure state is located outside of the active region. From numerical simulations of open quantum systems described by the (effective mass) Schrödinger and (atomistic) tight-binding equations, a reduction of the computational burden of about two orders of magnitude for each spatial dimension of the domain with a negligible error is presented.

We derive fluctuation relations for a many-body quantum system prepared in a generalized Gibbs ensemble subject to a general nonequilibrium protocol. By considering isolated integrable systems, we find generalizations to the Tasaki-Crooks and Jarzynski relations. Our approach is illustrated by studying the one-dimensional quantum Ising model subject to a sudden change in the transverse field, where we find that the statistics of the work done and irreversible entropy show signatures of quantum criticality. We discuss these fluctuation relations in the context of thermalization.

We generate time series from scale-free networks based on a finite-memory random walk traversing the network. These time series reveal topological and functional properties of networks via their temporal correlations. Remarkably, networks with different node-degree mixing patterns exhibit distinct self-similar characteristics. In particular, assortative networks are transformed into time series with long-range correlation, while disassortative networks are transformed into time series exhibiting anticorrelation. These relationships are consistent across a diverse variety of real networks. Moreover, we show that multiscale analysis of these time series can describe and classify various physical networks ranging from social and technological to biological networks according to their functional origin. These results suggest that there is a unified dynamical mechanism that governs the structural organization of many seemingly different networks.

The entrainment of periodic patterns to spatially periodic parametric forcing is studied. Using a weak nonlinear analysis of a simple pattern formation model we study the resonant responses of one-dimensional systems that lack inversion symmetry. Focusing on the first three $n:1$ resonances, in which the system adjusts its wavenumber to one $n\mathrm{th}$ of the forcing wavenumber, we delineate commonalities and differences among the resonances. Surprisingly, we find that all resonances show multiplicity of stable phase states, including the $1:1$ resonance. The phase states in the $2:1$ and $3:1$ resonances, however, differ from those in the $1:1$ resonance in remaining symmetric even when the inversion symmetry is broken. This is because of the existence of a discrete translation symmetry in the forced system. As a consequence, the $2:1$ and $3:1$ resonances show stationary phase fronts and patterns, whereas phase fronts within the $1:1$ resonance are propagating and phase patterns are transients. In addition, we find substantial differences between the $2:1$ resonance and the other two resonances. While the pattern forming instability in the $2:1$ resonance is supercritical, in the $1:1$ and $3:1$ resonances it is subcritical, and while the inversion asymmetry extends the ranges of resonant solutions in the $1:1$ and $3:1$ resonances, it has no effect on the $2:1$ resonance range. We conclude by discussing a few open questions.

The instantaneous release of energy in a localized area of a gas results in the formation of a low-density region and a series of shock and expansion waves. If this process occurs near a boundary, the shock reflections can interact with the density inhomogeneity, leading to the baroclinic generation of vorticity and the subsequent organization of the flow into several structures, including a vortex ring. By means of numerical simulations we illustrate the qualitative changes that occur in the pressure wave patterns and vorticity distribution as the distance from the area of energy release to the boundary is varied. Those changes are shown to be related to the combined effect of the shock waves that, respectively, initially move away and towards the center of the low-density region. In particular, we describe how for small enough offset distances the shocks internal to the inhomogeneity can make a substantial contribution to the vorticity field, influencing the circulation and characteristics of the resulting flow structures.

It is shown in direct numerical simulations of homogeneous isotropic non-stationary turbulence that there is a systematic and significant imbalance between the non-linear energy cascade to fine scales and its dissipation. This imbalance stems from the power required to induce or annihilate fine-scale motions in order to change the level of dissipation. The imbalance is present regardless of transfer time-lags and is applicable to a wide range of Reynolds numbers.

We demonstrate that the morphological diversity in liquid-crystal hybrid systems is much richer than previously anticipated. More importantly, we reveal the existence of a dual mechanism for self-assembly of nanoparticles via morphological instabilities at phase boundaries. Using numerical simulations, we study the growth of isolated nematic droplets in an isotropic liquid crystal (LC) doped with nanoparticles (NPs) and provide insight into the nature of microstructure evolution in LC hybrids. Our work expands the numerically accessible time and length scales in these systems, capturing morphologies which develop under the competition of nonequilibrium elastic interactions, diffusive instabilities mediated by NP transport, and the anisotropy of the nematic field. By mapping nematic morphologies, we also propose a methodology for estimating various important LC material parameters that are difficult to obtain experimentally.

We predict theoretically the existence of a class of colloidal structures in nematic liquid crystal (NLC) cells, which are induced by surface patterns on the plates of the cell (like cells with UV-irradiated polyamide surfaces using micron sized masks in front of the cell). These bulk structures arise from nonuniform boundary conditions for the director distortions at the confining surfaces. In particular, we demonstrate that quadrupole spherical particles (like spheres with boojums or Saturn-ring director configurations) form a square lattice inside a planar NLC cell, which has checkerboard patterns on both its plates.

We perform numerical measurements of the moments of the position of a tracer particle in a two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is known to exhibit a weak form of superdiffusion, in the sense that there is a logarithmic correction to the linear growth in time of the mean-squared displacement. We show numerically that this expected asymptotic behavior is easily overwhelmed by the subleading linear growth throughout the time range accessible to numerical simulations. We compare our simulations to analytical results for the variance of the anomalously rescaled limiting normal distributions.

Random packing of unoriented regular polygons and star polygons on a two-dimensional flat continuous surface is studied numerically using random sequential adsorption algorithm. Obtained results are analyzed to determine the saturated random packing ratio as well as its density autocorrelation function. Additionally, the kinetics of packing growth and available surface function are measured. In general, stars give lower packing ratios than polygons, but when the number of vertexes is large enough, both shapes approach disks and, therefore, properties of their packing reproduce already known results for disks.

Ideally, self-assembly should rapidly and efficiently produce stable correctly assembled structures. We study the tradeoff between enthalpic and entropic cost in self-assembling systems using RecA-mediated homology search as an example. Earlier work suggested that RecA searches could produce stable final structures with high stringency using a slow testing process that follows an initial rapid search of $\sim 9–15$ bases. In this work, we will show that as a result of entropic and enthalpic barriers, simultaneously testing all $\sim 9–15$ bases as separate individual units results in a longer overall searching time than testing them in groups and stages.

We present a theoretical study of the electronic structure of four periodic B-DNA models labeled $(\mathrm{AT}{)}_{10}$, $(\mathrm{GC}{)}_{10}$, $\left(\mathrm{AT}{)}_5\right(\mathrm{GC}{)}_5$, and $(\mathrm{AT}-\mathrm{GC}{)}_5$ where A denotes adenine, T denotes thymine, G denotes guanine, and C denotes cytosine. Each model has ten base pairs with Na counterions to neutralize the negative phosphate group in the backbone. The $\left(\mathrm{AT}{)}_5\right(\mathrm{GC}{)}_5$ and $(\mathrm{AT}-\mathrm{GC}{)}_5$ models contain two and five AT-GC bilayers, respectively. When compared against the average of the two pure models, we estimate the AT-GC bilayer interaction energy to be 19.015 Kcal/mol, which is comparable to the hydrogen bonding energy between base pairs obtained from the literature. Our investigation shows that the stacking of base pairs plays a vital role in the electronic structure, relative stability, bonding, and distribution of partial charges in the DNA models. All four models show a highest occupied molecular orbital (HOMO) to lowest unoccupied molecular orbital (LUMO) gap ranging from 2.14 to 3.12 eV with HOMO states residing on the ${\mathrm{PO}}_4 + \mathrm{Na}$ functional group and LUMO states originating from the bases. Our calculation implies that the electrical conductance of a DNA molecule should increase with increased base-pair mixing. Interatomic bonding effects in these models are investigated in detail by analyzing the distributions of the calculated bond order values for every pair of atoms in the four models including hydrogen bonding. The counterions significantly affect the gap width, the conductivity, and the distribution of partial charge on the DNA backbone. We also evaluate quantitatively the surface partial charge density on each functional group of the DNA models.

Cohesive powders have widely different bulk behavior due to their peculiar interactions. We use discrete element simulations to investigate the effect of contact cohesion on the steady state flow of dense powders in a slowly sheared split-bottom Couette cell, which imposes a wide stable shear band. The intensity of cohesive forces can be quantified by the granular Bond number (Bo), namely the ratio between maximum attractive force and average force due to external compression. We find that the shear banding phenomenon is almost independent of cohesion for Bond numbers $\mathrm{Bo}<1$, however for $\mathrm{Bo}\ge 1$ cohesive forces start to play an important role, as both width and center position of the band increase. Inside the shear band, the mean normal contact force is independent of cohesion and depends only on the confining stress. In contrast, when the behavior is analyzed focusing on the eigendirections of the local strain rate tensor, a dependence on cohesion shows up. Forces carried by contacts along the compressive and tensile directions are symmetric about the mean force (larger and smaller respectively), while the force along the third, neutral direction follows the mean force. This anisotropy of the force network increases with cohesion, just like the heterogeneity in all (compressive, tensile and neutral) directions.

The dynamical properties and diffusive behavior of a collection of mutually interacting particles are numerically investigated for two types of long-range interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It is shown that when the particles are uniformly distributed throughout the accessible space, the self-diffusion coefficient is always lowered by the considered interparticle interactions, irrespective of their attractive or repulsive character. This fact is also confirmed by a simple model to compute the correction to the Brownian diffusion coefficient due to the interactions among the particles. These interactions are also responsible for the onset of dynamical chaos and an associated chaotic diffusion which still follows an Einstein-Fick-like law for the mean-square displacement as a function of time. Transitional phenomena are observed for Coulomb-electrostatic (repulsive) and dipole-electrodynamic (attractive) interactions considered both separately and in competition. The outcomes reported in this paper clearly indicate a feasible experimental method to probe the activation of resonant electrodynamic interactions among biomolecules.