We address the problem of the rectifying effect of heat conduction at macroscopic size. A design for a macroscopic thermal rectifier based on the macroscopic thermal conductivity of materials is introduced, and then realizations of the design are shown by numerical simulations and phenomenological estimations.

In this paper we consider solvable model systems on which finite-time work is done. For the systems and changes in state considered, there is no entropic change and the ensuing work distribution is Gaussian. We focus on the fluctuations in the work for such systems, arising from system-bath interactions and finite system recurrences, and study the resulting effect of dynamical broadening on the corresponding distribution $P\left(e^{-{\beta }_{0}W}\right)$. This allows us to describe the dependence of $P\left(e^{-{\beta }_{0}W}\right)$ on time and system-bath interactions. From the long-time behavior of the work fluctuations and $P\left(e^{-{\beta }_{0}W}\right)$, we clarify both (i) when a stochastic treatment of the dynamics may be legitimately invoked and (ii) how information on the system-bath interaction for stochastic, near-equilibrium, systems may be extracted for such processes where a final temperature is well defined.

We study, by numerical simulation, the compaction dynamics of frictional hard disks in two dimensions, subjected to vertical shaking. Shaking is modeled by a series of vertical expansion of the disk packing, followed by dynamical recompression of the assembly under the action of gravity. The second phase of the shake cycle is based on an efficient event-driven molecular-dynamics algorithm. We analyze the compaction dynamics for various values of friction coefficient and coefficient of normal restitution. We find that the time evolution of the density is described by $\rho \left(t\right)={\rho }_{\infty }-\Delta \rho E_{\alpha }[-{(t∕\tau )}^{\alpha }]$, where $E_{\alpha }$ denotes the Mittag-Leffler function of order $0<\alpha <1$. The parameter $\tau$ is found to decay with tapping intensity $\Gamma$ according to a power law $\tau \propto {\Gamma }^{-\gamma }$, where parameter $\gamma$ is almost independent on the material properties of grains. Also, an expression for the grain mobility during the compaction process has been obtained. We characterize the local organization of disks in terms of contact connectivity and distribution of the Delaunay “free” volumes. Our analysis at microscopic scale provides evidence that compaction is mainly due to a decrease of the number of the largest pores. An interpretation of the memory effects observed for a discontinuous shift in tapping intensity $\Gamma$ is provided by the analysis of the time evolution of connectivity numbers and volume distribution of pores.

Spontaneous formation of treelike patterns which developed during evaporation of the solvent from a phase-separated bilayer resulting from a binary polymer solution spin-coated onto a solid substrate has been studied. The initial bilayer consists of a poly(isobutyl methacrylate) (BMA) layer on top of a nitrocellulose (NC) solution layer. During evaporation, the top BMA layer becomes unstable and transforms into short ridges. Finally, the inhomogeneous evaporation of the solvent from the NC solution layer connects the BMA ridges to treelike patterns. To support our model, we present results of a complementary experiment based on casting of the BMA solution on an inclined glass substrate.

We have developed a fully nonlocal model to describe the dynamic behavior of nematic liquid-crystal elastomers. The free energy, incorporating both elastic and nematic contributions, is a function of the material displacement vector and the orientational order parameter tensor. The free energy cost of spatial variations of these order parameters is taken into account through nonlocal interactions rather than through the use of gradient expansions. We also give an expression for the Rayleigh dissipation function. The equations of motion for displacement and orientational order are obtained from the free energy and the dissipation function by the use of a Lagrangian approach. We examine the free energy and the equations of motion in the limit of long-wavelength and small-amplitude variations of the displacement and the orientational order parameter. We compare our results with those in the literature. If the scalar order parameter is held fixed, we recover the usual viscoelastic theory for nematic liquid crystals.

We have observed large pores in the membrane of giant vesicles in an aqueous medium. The lifetime of the pores can reach $2\min$ and their size (a few micrometers) enables their visualization by fluorescence microscopy. These pores are obtained thanks to a destabilization of the membrane due to the synergistic action of a cone-shaped and nitrobenzodiazole (NBD) labeled phospholipid illuminated in the presence of dithionite. The opening of the pore occurs immediately after illumination starts so that it can be accurately triggered. A concomitant decrease of the vesicle radius is observed; we interpret it as a solubilization of the membrane. Depending on the rate of this solubilization, long- or short-lived pores were observed. At the transition between both regimes for a $30\mu \mathrm{m}$ vesicle, the solubilization rate was about $1∕300{\mathrm{s}}^{-1}$. In order to interpret these observations, we have revisited the current model of pore opening to take into account this solubilization. This proposed model along with simulations enables us to prove that solubilization explains why the large long-lived pores are observed even in an aqueous medium. The model also predicts the solubilization rate at the transition between a single long-lived pore and a cascade of short-lived pores.

We examine several approaches on how to use the transmission and reflection amplitudes as functions of the modulation frequency of the laser’s intensity to reconstruct the position-dependent scattering coefficient for a simple turbid medium. We explore the region where the contrast between the coefficient and its spatially averaged value is large enough such that perturbative methods fail. We show that in the case of a transillumination geometry, the knowledge of the transmission profile alone is not sufficient for unique image reconstruction, whereas the reflection spectrum allows for a complete inversion. We demonstrate the invertibility for media sampled at only a few positions.

The dimensional crossover phenomena of heat conduction is studied by a two-dimensional (2D) Fermi-Pasta-Ulam lattice. The 2D divergence law of the thermal conductivity is confirmed by the simulations results. The divergence law of the thermal conductivity will change from the 2D class to 1D class as $\delta =N_y∕N_x$ decreases, here $N_y$ is the size in transverse direction and $N_x$ in longitude direction. The simulation’s results suggest that the dimensional crossover happens in ${\delta }^{*}\to 0$ as $N_x\to \infty$.

Bacteria and their bacteriophages are the most abundant, widespread, and diverse groups of biological entities on the planet. In an attempt to understand how the interactions between bacteria, virulent phages, and temperate phages might affect the diversity of these groups, we developed a stochastic network model for examining the coevolution of these ecologies. In our approach, nodes represent whole species or strains of bacteria or phages, rather than individuals, with “speciation” and extinction modeled by duplication and removal of nodes. Phage-bacteria links represent host-parasite relationships and temperate-virulent phage links denote prophage-encoded resistance. The effect of horizontal transfer of genetic information between strains was also included in the dynamical rules. The observed networks evolved in a highly dynamic fashion but the ecosystems were prone to collapse (one or more entire groups going extinct). Diversity could be stably maintained in the model only if the probability of speciation was independent of the diversity. Such an effect could be achieved in real ecosystems if the speciation rate is primarily set by the availability of ecological niches.

The self-force experienced by a semicircular conducting loop of circular cross section is evaluated analytically using the Lorentz force expression and shown to agree with the result of the partially analytical and partially numerical calculations quoted in the paper of Cavalleri et al. [Phys. Rev. E 58, 2505 (1998)].

One-dimensional detrended fluctuation analysis (DFA) and multifractal detrended fluctuation analysis (MFDFA) are widely used in the scaling analysis of fractal and multifractal time series because they are accurate and easy to implement. In this paper we generalize the one-dimensional DFA and MFDFA to higher-dimensional versions. The generalization works well when tested with synthetic surfaces including fractional Brownian surfaces and multifractal surfaces. The two-dimensional MFDFA is also adopted to analyze two images from nature and experiment, and nice scaling laws are unraveled.

We computed the self-organization process of a monodisperse collection of spherical micrometer-sized particles trapped in a two-dimensional thin liquid film isothermally dried on a chemically inert substrate. The substrate is either flat or indented to create linear stripes on its surface. The numerical results are illustrated and discussed in the light of experimental ones obtained from the drying of a water-based suspension of diamond particles $(d_{50}=10\mathrm{\mu }\mathrm{m})$ on a glass substrate. The drying of the suspension on a flat substrate leads to the formation of linear patterns and small clusters of micrometer-sized particles distributed over the whole surface of the substrate, whereas the drying of the suspension on an indented substrate leads to the aggregation of the particles along one side of the stripe which has a higher roughness than the other side of the stripe. This is an easy experimental way to obtain colloidal self-organized patterns.

We study the effect of folding ridges on the scaling properties of randomly crumpled sheets of different kinds of paper in the folded and unfolded states. We found that the mean ridge length scales with the sheet size with the scaling exponent $\mu$ determined by the competition between bending and stretching deformations in the folded sheet. This scaling determines the mass fractal dimension of randomly folded balls $D_M=2∕\mu$. We also found that surfaces of crumpled balls, as well as unfolded sheets, both display self-affine invariance with $\zeta ={\nu }_{\mathrm{ph}}$, if $\mu ⩽{\nu }_{\mathrm{ph}}$, where ${\nu }_{\mathrm{ph}}=3∕4$ is the size exponent for crumpled phantom membrane, or both exhibit an intrinsically anomalous roughness characterized by the universal local roughness exponent $\zeta =0.72\pm 0.04$ and the material dependent global roughness exponent $\alpha =\mu$, when $\mu >{\nu }_{\mathrm{ph}}$. The physical implications of these findings are discussed.

We have performed an experimental study of the transition of rolling-grain ripples toward vortex ripples. In particular, we have looked for the influence of the grains’ diameter, the frequency of oscillation, and the grains’ cohesion. We demonstrate that the rolling-grain ripples are transient patterns which do appear as soon as we are close to the threshold for grain motion, whereas vortex ripples are always the final patterns observed and are the only patterns observed if one is far from the threshold for grain motion. Our results show that the “elasticity” (i.e., the tendency to modify the wavelength by either compression or dilatation) of the vortex ripples explains several discrepancies with respect to the observed evolutions and measurements reported so far in the literature.

The properties of many heterogeneous media depend on both the surface roughness and the local variations of the optical properties. An effective optical interface is usually invoked to describe the characteristics of such media. Using approaches specific to near-field optics, the two influences can be decoupled and a quantitative assessment of their contributions can be performed. It is also shown that a discrete random-walk model can be used to determine the magnitude of the dielectric constant fluctuations at subwavelength scales which, in turn, describe the morphology of optically inhomogeneous media.

Motivated by studies of comblike structures, we present a generalization of the classical diffusion equation to model anisotropic, anomalous diffusion. We assume that the diffusive flux is given by a diffusion tensor acting on the gradient of the probability density, where each component of the diffusion tensor can have its own scaling law. We also assume scaling laws that have an explicit power-law dependence on space and time. Solutions of the proposed generalized diffusion equation are consistent with previously derived asymptotic results for the probability density on comblike structures.

We use analytic and numerical methods to analyze the dynamics of vortices following the quench of a type-II superconductor under the application of an external magnetic field. In three dimensions, in the absence of a field, the spacing between vortices scales with time $t$ with an exponent $\varphi =0.414\pm 0.01$, in a thin sheet of a superconductor, the scaling exponent is $\varphi =0.294\pm 0.01$. When an external magnetic field $h$ is applied, the vortices are confined with respect to the length scale of the Abrikosov lattice, leading to a crossover between the power-law scaling length scale and the lattice length scale. From this we suggest a one-parameter scaling of $\dot{r}$ with $h$ and $r$ that is consistent with numerical data.

Unidirectional motion of solitons can take place, although the applied force has zero average in time, when the spatial symmetry is broken by introducing a potential $V\left(x\right)$, which consists of periodically repeated cells with each cell containing an asymmetric array of strongly localized inhomogeneities at positions $x_i$. A collective coordinate approach shows that the positions, heights, and widths of the inhomogeneities (in that order) are the crucial parameters so as to obtain an optimal effective potential $U_{\mathit{opt}}$ that yields a maximal average soliton velocity. $U_{\mathit{opt}}$ essentially exhibits two features: double peaks consisting of a positive and a negative peak, and long flat regions between the double peaks. Such a potential can be obtained by choosing inhomogeneities with opposite signs (e.g., microresistors and microshorts in the case of long Josephson junctions) that are positioned close to each other, while the distance between each peak pair is rather large. These results of the collective variable theory are confirmed by full simulations for the inhomogeneous sine-Gordon system.

Preceding molecular dynamics simulations of biomolecular interactions, the molecule of interest is often equilibrated with respect to an initial configuration. This so-called equilibration stage is required because the input structure is typically not within the equilibrium phase space of the simulation conditions, particularly in systems as complex as proteins, which can lead to artifactual trajectories of protein dynamics. The time at which nonequilibrium effects from the initial configuration are minimized—what we will call the equilibration time—marks the beginning of equilibrium phase-space exploration. Note that the identification of this time does not imply exploration of the entire equilibrium phase space. We have found that current equilibration methodologies contain ambiguities that lead to uncertainty in determining the end of the equilibration stage of the trajectory. This results in equilibration times that are either too long, resulting in wasted computational resources, or too short, resulting in the simulation of molecular trajectories that do not accurately represent the physical system. We outline and demonstrate a protocol for identifying the equilibration time that is based on the physical model of Normal Mode Analysis. We attain the computational efficiency required of large-protein simulations via a stretched exponential approximation that enables an analytically tractable and physically meaningful form of the root-mean-square deviation of atoms comprising the protein. We find that the fitting parameters (which correspond to physical properties of the protein) fluctuate initially but then stabilize for increased simulation time, independently of the simulation duration or sampling frequency. We define the end of the equilibration stage—and thus the equilibration time—as the point in the simulation when these parameters attain constant values. Compared to existing methods, our approach provides the objective identification of the time at which the simulated biomolecule has entered an energetic basin. For the representative protein considered, bovine pancreatic trypsin inhibitor, existing methods indicate a range of $0.2–10\mathrm{ns}$ of simulation until a local minimum is attained. Our approach identifies a substantially narrower range of $4.5–5.5\mathrm{ns}$, which will lead to a much more objective choice of equilibration time.

Long nonlinear two-dimensional traveling waves on a film driven by laminar gas flow are investigated numerically via solving Navier-Stokes equations. The evolution of their shape, amplitude, and speed with increasing Reynolds number is studied. The existence of solitary waves is demonstrated. A comparison between shear driven and gravity-capillary waves is made and discussed. It is shown that shear driven waves as compared to gravity driven waves are much higher for equal film Reynolds numbers and much slower for equal wave amplitudes.