The classical theory of rubber elasticity fails in the regime of large deformation. The underlying physical mechanism has been under debate for a long time. In this work, we test the recently proposed mechanism of thermal elastic fluctuations by Xing, Goldbart, and Radzihovsky (XGR) against the biaxial stress-strain data of three distinct polymer networks with very different network structures, synthesized by Urayama and Kawabata, respectively. We find that both the two-parameter version and the one-parameter version of the XGR theory provide a satisfactory description of the elasticity in whole deformation range. For comparison, we also fit the same sets of data using the slip-link model by Edwards and Vilgis with four parameters. The fitting qualities of two theories are found to be comparable.

Coherent x-ray diffraction microscopy is a novel technique in the structural analyses of particles that are difficult to crystallize, such as the biological particles composing living cells. As water is indispensable for maintaining particles in functional structures, sufficient hydration of targeted particles is required during sample preparation for diffraction microscopy experiments. However, the water enveloping particles also contributes significantly to the diffraction patterns and reduces the electron-density contrast of the sample particles. In this study, we propose a protocol for the structural analyses of particles in water by applying a three-dimensional reconstruction method in real space for the projection images phase-retrieved from diffraction patterns, together with a developed density modification technique. We examined the feasibility of the protocol through three simulations involving a protein molecule in a vacuum, and enveloped in either a droplet or a cube-shaped water. The simulations were carried out for the diffraction patterns in the reciprocal planes normal to the incident x-ray beam. This assumption and the simulation conditions corresponded to experiments using x-ray wavelengths of shorter than 0.03 Å. The analyses demonstrated that our protocol provided an interpretable electron-density map. Based on the results, we discuss the advantages and limitations of the proposed protocol and its practical application for experimental data. In particular, we examined the influence of Poisson noise in diffraction patterns on the reconstructed three-dimensional electron density in the proposed protocol.

Genomic DNA is constantly subjected to various mechanical stresses arising from its biological functions and cell packaging. If the local mechanical properties of DNA change under torsional and tensional stress, the activity of DNA-modifying proteins and transcription factors can be affected and regulated allosterically. To check this possibility, appropriate steady forces and torques were applied in the course of all-atom molecular dynamics simulations of DNA with AT- and GC-alternating sequences. It is found that the stretching rigidity grows with tension as well as twisting. The torsional rigidity is not affected by stretching, but it varies with twisting very strongly, and differently for the two sequences. Surprisingly, for AT-alternating DNA it passes through a minimum with the average twist close to the experimental value in solution. For this fragment, but not for the GC-alternating sequence, the bending rigidity noticeably changes with both twisting and stretching. The results have important biological implications and shed light on earlier experimental observations.

The acceleration and heating of electrons by an intense laser normally incident on a steep overdense plasma interface is investigated using the particle-in-cell code osiris. Energetic electrons are generated by the laser’s electric field in the vacuum region within $\lambda /4$ of the surface. Only those electrons which originate within the plasma with a sufficiently large transverse momentum can escape the plasma. This mechanism relies on the standing wave structure created by the incoming and reflected wave and is therefore very different for linear and circularly polarized light.

Functionalities of a variety of complex systems involve cooperations among multiple components; for example, a transportation system provides convenient transfers among airlines, railways, roads, and shipping lines. A layered model with interacting networks can facilitate the description and analysis of such systems. In this paper we propose a model of traffic dynamics and reveal a transition at the onset of cooperation between layered networks. The cooperation strength, treated as an order parameter, changes from zero to positive at the transition point. Numerical results on artificial networks as well as two real networks, Chinese and European railway-airline transportation networks, agree well with our analysis.

We study propagating mode-I fracture in two-dimensional amorphous materials using atomistic simulations. We use the continuous random network model of an amorphous material, creating samples using a two-dimensional analog of the Wooten-Winer-Weaire Monte Carlo algorithm. For modeling fracture, molecular-dynamics simulations were run on the resulting samples. The results of our simulations reproduce the main experimental features. In addition to achieving a steady-state crack under a constant driving displacement (which has not yet been achieved by other atomistic models for amorphous materials), the runs show microbranching, which increases with driving, transitioning to macrobranching for the largest drivings. In addition to the qualitative visual similarity of the simulated cracks to experiment, the simulation also succeeds in reproducing qualitatively the experimentally observed oscillations of the crack velocity.

We propose a Markov chain method to efficiently generate surrogate networks that are random under the constraint of given vertex strengths. With these strength-preserving surrogates and with edge-weight-preserving surrogates we investigate the clustering coefficient and the average shortest path length of functional networks of the human brain as well as of the International Trade Networks. We demonstrate that surrogate networks can provide additional information about network-specific characteristics and thus help interpreting empirical weighted networks.

The dynamics of fully developed hydrodynamic turbulence still is a basically unsolved theoretical problem, due to the strong-coupling long-range nonlinearities in the Navier-Stokes equations. The present analysis focuses on the small-scale fluctuations in a turbulent boundary layer with one external length scale $y_o$. After taking a $(2+1)$D spatiotemporal spectral transform of the fluctuating vorticity fields, care is taken of large-scale sweeping which arises as a collective zero mode from the nonlinear flow terms. The “unswept” small-scale nonlinearities are then shown to be asymptotically locally isotropic (i.e., for wave numbers $k\to \infty$) by internal consistency, which allows to close the nonlinear hierarchy. The Navier-Stokes equations (without external forcing) are integrated to give the spectral response of the fluctuating small-scale velocity fields on the presence of a locally isotropic blob of turbulence while it is being swept around over an arbitrary steady state mean velocity profile, using viscous boundary conditions at $y=0$. Averaging the response spectrum over all possible orientational configurations and sweep velocities results in a novel self-consistency integral for the 4D energy spectrum function. The distribution of turbulence sweep velocities is modeled by means of Lévy-type densities, having an algebraic tail with power $p>1$. The generic case (which includes Von Kármán’s logarithmic mean velocity profile) is found to correspond to $1<p<3$. Asymptotic analysis of the self-consistency integral leads to a differential equation which fixes the scaling exponent $\lambda$ of the unswept frequency $\Delta$ and admits a nonempty, integrable and positive definite Airy-type frequency spectrum ${\mathcal{E}}^{ı}(k,\Delta /k^{\lambda })\sim k^{\mu }$ with so-called “normal” Kolmogorov scaling, that is, $\mu =-7/3$ and $\lambda =2/3$. Anomalous scaling is possible for one special mean profile.

The generalized elastic model encompasses several physical systems such as polymers, membranes, single-file systems, fluctuating surfaces, and rough interfaces. We consider the case of an applied localized potential, namely, an external force acting only on a single (tagged) probe, leaving the rest of the system unaffected. We derive the fractional Langevin equation for the tagged probe, as well as for a generic (untagged) probe, where the force is not directly applied. Within the framework of the fluctuation-dissipation relations, we discuss the unexpected physical scenarios arising when the force is constant and time periodic, whether or not the hydrodynamic interactions are included in the model. For short times, in the case of the constant force, we show that the average drift is linear in time for long-range hydrodynamic interactions and behaves ballistically or exponentially for local hydrodynamic interactions. Moreover, it can be opposite to the direction of the external disturbance for some values of the model’s parameters. When the force is time periodic, the effects are macroscopic: the system splits into two distinct spatial regions whose size is proportional to the value of the applied frequency. These two regions are characterized by different amplitudes and phase shifts in the response dynamics.

The phenomenon of stochastic resonance in networks with small-world connectivity is investigated when the coupling strength is adaptive. The effects of the fixed and adaptive couplings on stochastic resonance of the system are discussed. It is found that the resonance is a monotonically increasing function of the adaptive coupling strength, while there is a peak when the coupling strength is fixed. The resonance for the adaptive coupling can reach a much larger value than that for fixed coupling.

Fluctuations can give useful information about the system under study. Here, particle density fluctuations in magnetically confined toroidal plasmas are studied using noise theory. Homogenous and stationary statistics are considered and correlations of fluctuations are calculated for Markovian systems. The relaxation of fluctuations is modeled by the space-fractional diffusion equation. Effects of different parameters of this model on correlations have been obtained. The results identify the two fluctuating regimes observed in experiments, which are related to diffusive and wave propagation of the mass in the system.

Highly nonlinear solitary waves (HNSWs) are stress waves that can form and travel in highly nonlinear systems. They are characterized by a constant spatial wavelength and by a tunable propagation speed, dependent on the wave amplitude. Conventionally, HNSW's are generated in one-dimensional chains of spherical particles by means of a mechanical impact. In this paper, we demonstrate that short-duration laser pulses can be used to generate HNSW's, and we characterize their propagating properties in terms of shape, speed, and duration. We compare the waves’ characteristics with theoretical predictions, finding excellent agreement. In addition a simplified formulation is given to estimate the dynamic contact force generated by laser pulses onto the chain.

A smectic-$A$ (Sm$A$) liquid crystal phase of fluid layers with in-plane polarization $\text{P}$ is shown to exhibit effective conductivity in the semiconducting range during electric-field-induced polarization reorientation, but becomes insulating once the polarization is aligned with the field. Such fluid ferroelectrics sandwiched between highly insulating layers enable electro-optic devices with long-term dc electrostatic control of polarization and optic axis orientation.

Close to sinusoidal substrates, simple fluids may undergo a filling transition, in which the fluid passes from a dry to a filled state, where the interface remains unbent but bound to the substrate. Increasing the surface field, the interface unbinds and a wetting transition occurs. We show that this double-transition sequence may be strongly modified in the case of ordered fluids, such as nematic liquid crystals. Depending on the preferred orientation of the nematic molecules at the structured substrate and at the isotropic-nematic interface, the filling transition may not exist, and the fluid passes directly from a dry to a complete-wet state, with the interface far from the substrate. More interestingly, in other situations, the complete wetting transition may be prevented, and the fluid passes from a dry to a filled state, and remains in this configuration, with the interface always attached to the substrate, even for very large surface fields. Both transitions are observed only for a same substrate in a narrow range of amplitudes.

Ionic size effects are significant in many biological systems. Mean-field descriptions of such effects can be efficient but also challenging. When ionic sizes are different, explicit formulas in such descriptions are not available for the dependence of the ionic concentrations on the electrostatic potential, that is, there is no explicit Boltzmann-type distributions. This work begins with a variational formulation of the continuum electrostatics of an ionic solution with such nonuniform ionic sizes as well as multiple ionic valences. An augmented Lagrange multiplier method is then developed and implemented to numerically solve the underlying constrained optimization problem. The method is shown to be accurate and efficient, and is applied to ionic systems with nonuniform ionic sizes such as the sodium chloride solution. Extensive numerical tests demonstrate that the mean-field model and numerical method capture qualitatively some significant ionic size effects, particularly those for multivalent ionic solutions, such as the stratification of multivalent counterions near a charged surface. The ionic valence-to-volume ratio is found to be the key physical parameter in the stratification of concentrations. All these are not well described by the classical Poisson–Boltzmann theory, or the generalized Poisson–Boltzmann theory that treats uniform ionic sizes. Finally, various issues such as the close packing, limitation of the continuum model, and generalization of this work to molecular solvation are discussed.

Based on the quasi-adiabatic model, the parameters of the bubble interior for a moving single bubble sonoluminescence in water, adiponitrile, and N-methylformamide are calculated for various fluid viscosities. By using a complete form of the hydrodynamic force, the bubble trajectory is calculated for a moving single bubble sonoluminescence (m-SBSL). It is found that as the fluid viscosity increases, the unique circular path changes to an ellipsoidal and then linear form and along this incrementally increase of viscosity the light intensity increases. By using the Bremsstrahlung model to describe the bubble radiation, gradual increase of the viscosity results in brighter emissions. It is found that in fluids with higher viscosity the light intensity decreases as time passes.

A uniformly moving inclusion which locally suppresses the fluctuations of a classical thermally excited field is shown to experience a drag force that depends on the dynamics of the field. It is shown that in a number of cases the linear friction coefficient is dominated by short distance fluctuations and takes a very simple form. Examples where this drag can occur are for stiff objects, such as proteins, nonspecifically bound to more flexible ones such as polymers and membranes.

We study the effective diffusion constant of a Brownian particle linearly coupled to a thermally fluctuating scalar field. We use a path-integral method to compute the effective diffusion coefficient perturbatively to lowest order in the coupling constant. This method can be applied to cases where the field is affected by the particle (an active tracer) and cases where the tracer is passive. Our results are applicable to a wide range of physical problems, from a protein diffusing in a membrane to the dispersion of a passive tracer in a random potential. In the case of passive diffusion in a scalar field, we show that the coupling to the field can, in some cases, speed up the diffusion corresponding to a form of stochastic resonance. Our results on passive diffusion are also confirmed via a perturbative calculation of the probability density function of the particle in a Fokker-Planck formulation of the problem. Numerical simulations on simplified systems corroborate our results.

Brownian particles confined in a two-dimensional enclosure that give rise to a bistable entropic potential are considered. With the introduction of an intermediate lobe, the mean first passage time from one lobe to another through the intermediate shows a turnover behavior with the variation of the stability of the entropic intermediate. The mean escape time shows a minimum for an optimal value of the barrier height of the intermediate state. A three-state model is proposed to explain the nonmonotonic behavior of the entropic transport.

We develop a theory for the eigenvalue density of arbitrary non-Hermitian Euclidean matrices. Closed equations for the resolvent and the eigenvector correlator are derived. The theory is applied to the random Green’s matrix relevant to wave propagation in an ensemble of pointlike scattering centers. This opens a new perspective in the study of wave diffusion, Anderson localization, and random lasing.