The total elastic stiffness of two contacting bodies with a microscopically rough interface has an interfacial contribution $K$ that is entirely attributable to surface roughness. A quantitative understanding of $K$ is important because it can dominate the total mechanical response and because it is proportional to the interfacial contributions to electrical and thermal conductivity in continuum theory. Numerical simulations of the dependence of $K$ on the applied squeezing pressure $p$ are presented for nominally flat elastic solids with a range of surface roughnesses. Over a wide range of $p$, $K$ rises linearly with $p$. Sublinear power-law scaling is observed at small $p$, but the simulations reveal that this is a finite-size effect. We derive accurate, analytical expressions for the exponents and prefactors of this low-pressure scaling of $K$ by extending the contact mechanics theory of Persson to systems of finite size. In agreement with our simulations, these expressions show that the onset of the low-pressure scaling regime moves to lower pressure as the system size increases.

Exact solutions for symmetric on-site discrete breathers (DBs) are obtained in a forced-damped linear chain with on-site vibro-impact constraints. The damping in the system is caused by inelastic impacts; the forcing functions should satisfy conditions of periodicity and antisymmetry. Global conditions for existence and stability of the DBs are established by a combination of analytic and numeric methods. The DB can lose its stability through either pitchfork, or Neimark-Sacker bifurcations. The pitchfork bifurcation is related to the internal dynamics of each individual oscillator. It is revealed that the coupling can suppress this type of instability. To the contrary, the Neimark-Sacker bifurcation occurs for relatively large values of the coupling, presumably due to closeness of the excitation frequency to a boundary of the propagation zone of the chain. Both bifurcation mechanisms seem to be generic for the considered type of forced-damped lattices. Some unusual phenomena, like nonmonotonous dependence of the stability boundary on the forcing amplitude, are revealed analytically for the initial system and illustrated numerically for small periodic lattices.

We investigate dynamics of an active particle in which shape deformations occur spontaneously. In two dimensions, the deformations are expanded in terms of the Fourier series and the couplings of different modes are taken into consideration truncated up to lower orders. We focus our attention on the special symmetrical structure between the coupled equations of $n$- and $2n$-mode deformations for $n=1$, and those for $n=2$. We show that an oscillatory bifurcation occurs for $n=2$, which corresponds mathematically to the bifurcation for $n=1$ where a straight motion becomes unstable and a circular motion appears. At the oscillatory state, the particle undergoes either a spinning motion or a standing oscillation of shape deformations.

In pipe, channel, and boundary layer flows turbulence first occurs intermittently in space and time: at moderate Reynolds numbers domains of disordered turbulent motion are separated by quiescent laminar regions. Based on direct numerical simulations of pipe flow we argue here that the spatial intermittency has its origin in a nearest neighbor interaction between turbulent regions. We further show that in this regime turbulent flows are intrinsically intermittent with a well-defined equilibrium turbulent fraction but without ever assuming a steady pattern. This transition scenario is analogous to that found in simple models such as coupled map lattices. The scaling observed implies that laminar intermissions of the turbulent flow will persist to arbitrarily large Reynolds numbers.

We propose an approach to the description of orientational phase transitions that utilizes the specific features of orientational energy and entropy. The approach is applied to building a model for nematic phases in materials with nonpolar parallelepiped-type molecules with symmetry $D_{2h}$. The model operates with complex order parameters, generalizes the Landau–de Gennes theory, and predicts the existence of a biaxial nematic phase for the fourth-order expansion of free energy.

We study two-dimensional frustrated but nondisordered systems applying a replica approach to a stripe-forming model with competing interactions. The phenomenology of the model is representative of several well-known systems, like high-Tc superconductors and ultrathin ferromagnetic films, which have been the subject of intense research. We establish the existence of a glass transition to a nonergodic regime accompanied by an exponential number of long-lived metastable states, responsible for slow dynamics and nonequilibrium effects.

We present a systematic numerical investigation of the shear strength and structure of granular packings composed of irregular polyhedral particles. The angularity of the particles is varied by increasing the number of faces from 8 (octahedronlike shape) to 596. We find that the shear strength increases with angularity up to a maximum value and saturates as the particles become more angular (below 46 faces). At the same time, the packing fraction increases to a peak value but declines for more angular particles. We analyze the connectivity and anisotropy of the microstructure by considering both the contacts and branch vectors joining particle centers. The increase of the shear strength with angularity is shown to be due to a net increase of the fabric and force anisotropies but at higher particle angularity a rapid falloff of the fabric anisotropy is compensated by an increase of force anisotropy, leading thus to the saturation of shear strength.

Molecular dynamics (MD) and Monte Carlo (MC) methods are used to determine the spin-pair correlation function $G^{*}\left(t\right)$ for the diffusion of bulk water in three dimensions (3D) and pore water in two dimensions (2D) and quasi-two dimensions (Q2D). The correlation function is required for the determination of the nuclear magnetic resonance spin-lattice and spin-spin relaxation times $T_1$ and $T_2$. It is shown that the analytic form of the powder-average correlation function, introduced by Sholl [Sholl, J. Phys. C: Solid State Phys. 7, 3378 (1974)] for the diffusion of spins on a 3D lattice, is of general validity. An analytic expression for $G^{*}\left(t\right)$ for a uniform spin fluid is derived in 2D. An analytic expression for the long-time behavior of $G^{*}\left(t\right)$ is derived for spins diffusing on 3D, 2D, and Q2D lattices. An analytic correction term, which accounts for spin pairs outside the scope of the numerical simulations, is derived for 3D and 2D and shown to improve the accuracy of the simulations. The contributions to $T_1$ due to translational and rotational motion obtained from the MD simulation of bulk water at 300 K are 7.4 s and $10\pm 1$ s, respectively, at 150 MHz, leading to an overall time of $4.3\pm 0.4$ s compared to the experimental value of 3.8 s. In Q2D systems, in which water is confined by alpha-quartz surfaces to thicknesses of 1–5 nm, $T_1$ for both translational and rotational relaxation is reduced due to the orientation and adsorption of spins at the surfaces. A method of parametrizing the MC lattice-diffusion simulations in 3D, 2D, and Q2D systems is presented. MC results for $G^{*}\left(t\right)$ for 3D and 2D systems are found to be consistent with an analytic uniform fluid model for $t\gtrsim 40$ ps. The value of $T_1$ for translational diffusion obtained from the MC simulation of bulk water is found to be 4.8 s at 15 MHz. $G^{*}\left(t\right)$ obtained from MC simulations of Q2D systems, where water is confined by hard walls, is found to execute a distinct transition from 3D to 2D behavior. The $T_1$ is found to be similar to the 3D bulk water result at all pore thicknesses.

We study the problem of the self-assembly of nanoparticles (NPs) into finite mesoscopic structures with a programmed local morphology and complex overall shape. Our proposed building blocks are NPs that are directionally functionalized with DNA. The combination of directionality and selectivity of interactions allows one to avoid unwanted metastable configurations, which have been shown to lead to slow self-assembly kinetics even in much simpler systems. With numerical simulations, we show that a variety of target mesoscopic objects can be designed and self-assembled in near perfect yield. They include cubes, pyramids, boxes, and even an Empire State Building model. We summarize our findings with a set of design strategies that leads to the successful self-assembly of a wide range of mesostructures.

Particle diffusion in condensed matters driven by thermal gradient, the so-called Ludwig-Soret effect, has been investigated for about 160 years, but up to the present, seldom do theories on atomic level understand a series of puzzles in relevant experiments. In this work, we derived an expression of Soret coefficient for atomic diffusion in condensed matter from a single atom statistic model with relevant parameters expressed in terms of atomic mass and the potential profile felt by the guest atom without empirical parameters. The reality of the model was strictly tested by molecular dynamics simulations, especially the result for He atom diffusing on graphene sheet, which suggests the Soret effect may be used to separate ${}^3$He from ${}^4$He.

We study numerically the geometrical and free-energy fluctuations of a static one-dimensional (1D) interface with a short-range elasticity, submitted to a quenched random-bond Gaussian disorder of finite correlation length $\xi >0$ and at finite temperature $T$. Using the exact mapping from the static 1D interface to the 1+1 directed polymer (DP) growing in a continuous space, we focus our analysis on the disorder free energy of the DP end point, a quantity which is strictly zero in the absence of disorder and whose sample-to-sample fluctuations at a fixed growing time $t$ inherit the statistical translation invariance of the microscopic disorder explored by the DP. Constructing a new numerical scheme for the integration of the Kardar-Parisi-Zhang evolution equation obeyed by the free energy, we address numerically the time and temperature dependence of the disorder free-energy fluctuations at fixed finite $\xi$. We examine, on one hand, the amplitude ${\tilde{D}}_t$ and effective correlation length ${\tilde{\xi }}_t$ of the free-energy fluctuations and, on the other hand, the imprint of the specific microscopic disorder correlator on the large-time shape of the free-energy two-point correlator. We observe numerically the crossover to a low-temperature regime below a finite characteristic temperature $T_c\left(\xi \right)$, as previously predicted by Gaussian variational method computations and scaling arguments and extensively investigated analytically in [Phys. Rev. E 87, 042406 (2013)]. Finally, we address numerically the time and temperature dependence of the roughness $B\left(t\right)$, which quantifies the DP end point transverse fluctuations, and we show how the amplitude ${\tilde{D}}_{\infty }(T,\xi )$ controls the different regimes experienced by $B\left(t\right)$—in agreement with the analytical predictions of a DP toy model approach.

We describe the complex time dependence of the buildup of force exerted by a clamped photoelastomer under illumination. Nonlinear (non-Beer) absorption leads to a bleaching wave of a significant cis isomer dye concentration deeply penetrating the solid with a highly characteristic dynamics. We fit our experimental response at one temperature to obtain material parameters. Force-time data can be matched at all other temperatures with no fitting required; our model provides a universal description of this unusual dynamics. The description is unambiguous since these are clamped systems where gross polymer motion is suppressed as a possible source of anomalous dynamics. Future experiments are suggested.

In this article, we investigate the spontaneous emission properties of radiating molecules embedded in a chiral nematic liquid crystal, under the assumption that the electronic transition frequency is close to the photonic edge mode of the structure, i.e., at resonance. We take into account the transition broadening and the decay of electromagnetic field modes supported by the so-called “mirrorless”cavity. We employ the Jaynes-Cummings Hamiltonian to describe the electron interaction with the electromagnetic field, focusing on the mode with the diffracting polarization in the chiral nematic layer. As known in these structures, the density of photon states, calculated via the Wigner method, has distinct peaks on either side of the photonic band gap, which manifests itself as a considerable modification of the emission spectrum. We demonstrate that, near resonance, there are notable differences between the behavior of the density of states and the spontaneous emission profile of these structures. In addition, we examine in some detail the case of the logarithmic peak exhibited in the density of states in two-dimensional photonic structures and obtain analytic relations for the Lamb shift and the broadening of the atomic transition in the emission spectrum. The dynamical behavior of the atom-field system is described by a system of two first-order differential equations, solved using the Green's-function method and the Fourier transform. The emission spectra are then calculated and compared with experimental data.

Previously electric-field-induced transitions from helical to planar structures in bulk liquid crystals were considered to take place with unwinding of helix. We show that the transition to the planar structure in polar smectic with frustrating interlayer interaction can occur without unwinding but through the formation of a periodic modulated structure with successive left-hand and right-hand sense of rotation in every half period. With field the amplitude of the left-right rotation decreases and a planar structure is formed. This mechanism of transition can take place in the short-pitch Sm$C_{\alpha }^{*}$ phase formed as a result of frustrating interaction.

From a coarse-grained perspective, the motif of a self-activating species, activating a second species that acts as its own repressor, is widely found in biological systems, in particular in genetic systems with inherent oscillatory behavior. Here we consider a specific realization of this motif as a genetic circuit, termed the bistable frustrated unit, in which genes are described as directly producing proteins. Upon an improved resolution in time, we focus on the effect that inherent time scales on the underlying scale can have on the bifurcation patterns on a coarser scale. Time scales are set by the binding and unbinding rates of the transcription factors to the promoter regions of the genes. Depending on the ratio of these rates to the decay times of both proteins, the appropriate averaging procedure for obtaining a coarse-grained description changes and leads to sets of deterministic equations, which considerably differ in their bifurcation structure. In particular, the desired intermediate range of regular limit cycles fades away when the binding rates of genes are not fast as compared to the decay time of the proteins. Our analysis illustrates that the common topology of the widely found motif alone does not imply universal features in the dynamics.

A molecular dynamics simulation method is used to study the translocation of a single strand DNA through nanopores opened on graphene membranes. Simulation results uncover that the translocation time for four DNA strands (20G, 20A, 20T, and 20C) is proportional to the size of the four DNA bases. However, the change of the ionic current is caused not only by the physical blockade of the DNA, but also induced by the change of the ion distribution once the negatively charged DNA enters the nanopore. An electric double layer will be formed and causes higher cation and lower anion concentration near the DNA strand surface, which makes the ionic current blockade not sensitive to the base size for a single-layer graphene nanopore. Increasing the graphene membrane thickness can enhance the DNA physical blockage effect on ionic current and improve the nanopore sensitivity to the four DNA bases.

We present the results of a detailed numerical study of a model for the sharing and sorting of information in a community consisting of a large number of agents. The information gathering takes place in a sequence of mutual bipartite interactions where randomly selected pairs of agents communicate with each other to enhance their knowledge and sort out the common information. Although our model is less restricted compared to the well-established naming game, the numerical results strongly indicate that the whole set of exponents characterizing this model are different from those of the naming game and they assume nontrivial values. Finally, it appears that in analogy to the emergence of clusters in the phenomenon of percolation, one can define clusters of agents here having the same information. We have studied in detail the growth of the largest cluster in this article and performed its finite-size scaling analysis.

Finite-time Lyapunov exponents of generic chaotic dynamical systems fluctuate in time. These fluctuations are due to the different degree of stability across the accessible phase space. A recent numerical study of spatially extended systems has revealed that the diffusion coefficient $D$ of the Lyapunov exponents (LEs) exhibits a nontrivial scaling behavior, $D\left(L\right)\sim L^{-\gamma }$, with the system size $L$. Here, we show that the wandering exponent $\gamma$ can be expressed in terms of the roughening exponents associated with the corresponding “Lyapunov surface.” Our theoretical predictions are supported by the numerical analysis of several spatially extended systems. In particular, we find that the wandering exponent of the first LE is universal: in view of the known relationship with the Kardar-Parisi-Zhang equation, $\gamma$ can be expressed in terms of known critical exponents. Furthermore, our simulations reveal that the bulk of the spectrum exhibits a clearly different behavior and suggest that it belongs to a possibly unique universality class, which has, however, yet to be identified.