This paper revisits one of the puzzling behaviors in a developable cone (d-cone), the shape obtained by pushing a thin sheet into a circular container of radius $R$ by a distance $\eta$. The mean curvature was reported to vanish at the rim where the d-cone is supported. We investigate the ratio of the two principal curvatures versus sheet thickness $h$ over a wider dynamic range than was used previously, holding $R$ and $\eta$ fixed. Instead of tending toward 1 as suggested by previous work, the ratio scales as ${(h/R)}^{1/3}$. Thus the mean curvature does not vanish for very thin sheets as previously claimed. Moreover, we find that the normalized rim profile of radial curvature in a d-cone is identical to that in a “c-cone” which is made by pushing a regular cone into a circular container. In both c-cones and d-cones, the ratio of the principal curvatures at the rim scales as ${(R/h)}^{5/2}F/\left(Y{R}^2\right)$, where $F$ is the pushing force and $Y$ is the Young's modulus. Scaling arguments and analytical solutions confirm the numerical results.

Many investigators have coupled the Lees-Edwards boundary conditions (LEBCs) and suspension methods in the framework of the lattice Boltzmann method to study the pure bulk properties of particle-fluid suspensions. However, these suspension methods are all link-based and are more or less exposed to the disadvantages of violating Galilean invariance. In this paper, we have coupled LEBCs with a node-based suspension method, which is demonstrated to be Galilean invariant in benchmark simulations. We use the coupled algorithm to predict the viscosity of a particle-fluid suspension at very low Reynolds number, and the simulation results are in good agreement with the semiempirical Krieger-Dougherty formula.

Newton's cradle for two balls with Hertzian interactions is considered as a hybrid system, and this makes it possible to derive return maps for the motion between collisions in an exact form despite the fact that the three-halves interaction law cannot be solved in closed form. The return maps depend on a constant whose value can only be determined numerically, but solutions can be written down explicitly in terms of this parameter, and we compare this with the results of simulations. The results are in fact independent of the details of the interaction potential.

The density of states $g\left(\varepsilon \right)$ is frequently used to calculate the temperature-dependent properties of a thermodynamic system. Here a derivation is given for calculating the warped density of states $g^{*}\left(\varepsilon \right)$ resulting from the addition of a perturbation. The method is validated for a classical Heisenberg model of bcc Fe and the errors in the free energy are shown to be second order in the perturbation. Taking the perturbation to be the difference between a first-principles quantum-mechanical energy and a corresponding classical energy, this method can significantly reduce the computational effort required to calculate $g\left(\varepsilon \right)$ for quantum systems using the Wang-Landau approach.

Cells propel themselves along a substrate by organizing structures at the leading edge called lamellipodia that contain the actin network, myosin, integrin, and other proteins. In this article, we describe a quantitative model that couples the response of stretch-sensitive proteins in the lamellipodia to the dynamics of the actin cytoskeleton, therefore allowing the cell to respond to different substrate stiffnesses. Using this model, we predict the various phases of dynamics possible, including continuous protrusion, unstable retractions leading to ruffling, and periodic protrusion-retraction cycles. We explain the necessary conditions for each type of migratory behavior to occur. In particular, we show that, for periodic protrusion-retraction cycles to occur, the stiffness of the substrate must be high, the myosin-dependent maturation rate of nascent to focal adhesions must be high, and the myosin-independent integrin activation rate must be low. In addition, we also predict the dynamics expected at a given substrate stiffness, leading to a quantitative explanation of experimental data that showed that periodic protrusion-retraction cycles disappear when cells are placed on soft substrates. We also suggest experiments with downregulating $\alpha$ actinin and/or talin and upregulating p130Cas and make predictions on what types of migratory dynamics will be observed.

This paper focus on the study of the composition-dependent fourth and fifth virial coefficient of a hard-sphere binary mixture, namely, $B_4\left(s\right)$ and $B_5\left(s\right)$. On one side, the analytical expression of $B_4\left(s\right)$ is revised. In particular, I analyzed the composition-independent term $B_4^{\left[1\right]}\left(s\right)$ included in $B_4\left(s\right)$ and found a simplified form of its exact expression, which has the advantage over that previously published of highlighting the geometric properties of this term. On the other side, using a geometrical approach, I found a set of nonanalytic points of $B_4\left(s\right)$ and $B_5\left(s\right)$ as functions of $s$ by analyzing each of their composition-independent terms.

Total internal reflection fluorescence cross-correlation spectroscopy (TIR-FCCS) has recently [S. Yordanov et al., Optics Express 17, 21149 (2009)] been established as an experimental method to probe hydrodynamic flows near surfaces, on length scales of tens of nanometers. Its main advantage is that fluorescence occurs only for tracer particles close to the surface, thus resulting in high sensitivity. However, the measured correlation functions provide only rather indirect information about the flow parameters of interest, such as the shear rate and the slip length. In the present paper, we show how to combine detailed and fairly realistic theoretical modeling of the phenomena by Brownian dynamics simulations with accurate measurements of the correlation functions, in order to establish a quantitative method to retrieve the flow properties from the experiments. First, Brownian dynamics is used to sample highly accurate correlation functions for a fixed set of model parameters. Second, these parameters are varied systematically by means of an importance-sampling Monte Carlo procedure in order to fit the experiments. This provides the optimum parameter values together with their statistical error bars. The approach is well suited for massively parallel computers, which allows us to do the data analysis within moderate computing times. The method is applied to flow near a hydrophilic surface, where the slip length is observed to be smaller than $10\mathrm{nm}$, and, within the limitations of the experiments and the model, indistinguishable from zero.

We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSYQM), reflectionless scattering, and soliton solutions of integrable partial differential equations. We show that the members of a class of reflectionless Hamiltonians, namely, Akulin's Hamiltonians, are connected via supersymmetric chains to a potential-free Hamiltonian, explaining their reflectionless nature. While the reflectionless property in question has been mentioned in the literature for over two decades, the enabling algebraic mechanism was previously unknown. Our results indicate that the multisoliton solutions of the sine-Gordon and nonlinear Schrödinger equations can be systematically generated via the supersymmetric chains connecting Akulin's Hamiltonians. Our findings also explain a well-known but little-understood effect in laser physics: when a two-level atom, initially in the ground state, is subjected to a laser pulse of the form $V\left(t\right)=(n\hslash /\tau )/\cosh (t/\tau )$, with $n$ being an integer and $\tau$ being the pulse duration, it remains in the ground state after the pulse has been applied, for any choice of the laser detuning.

We develop a modulation theory model based on a Lagrangian formulation to investigate the evolution of dark and gray optical spatial solitary waves for both the defocusing nonlinear Schrödinger (NLS) equation and the nematicon equations describing nonlinear beams, nematicons, in self-defocusing nematic liquid crystals. Since it has an exact soliton solution, the defocusing NLS equation is used as a test bed for the modulation theory applied to the nematicon equations, which have no exact solitary wave solution. We find that the evolution of dark and gray NLS solitons, as well as nematicons, is entirely driven by the emission of diffractive radiation, in contrast to the evolution of bright NLS solitons and bright nematicons. Moreover, the steady nematicon profile is nonmonotonic due to the long-range nonlocality associated with the perturbation of the optic axis. Excellent agreement is obtained with numerical solutions of both the defocusing NLS and nematicon equations. The comparisons for the nematicon solutions raise a number of subtle issues relating to the definition and measurement of the width of a dark or gray nematicon.

We independently determine the bulk and shear moduli of compressed microgel suspensions and the bulk modulus of individual microgel particles and find that the elastic behavior of the suspension reflects the degree of compression of the particles. This feature, which is distinct from other soft materials such as emulsions or foams, can give rise to an unusually large difference between the bulk and shear moduli of the suspension. Our results extend our understanding of soft materials to systems based on compressible objects, opening up possibilities for engineering materials with drastically different responses to shear and compression.

The solution of the problem of the partition function calculation for a Coulomb-like system is proposed. The quantum-field-theory approach is used to give a statistical description of a system of interacting particles with due regard to arbitrary spatially inhomogeneous configurations. Formation of structures in a Coulomb-like system is analyzed and applied to the case of of dusty crystals and two-dimensional colloidal crystals. In the one-dimensional case, an exact solution for the spatial distribution of charged particles is obtained. In the two- dimensional case, the exact partition function for homogeneous distribution of particles is presented. We have analytically derived the necessary condition for the crystal formation in a system of interacting particles in the three-dimensional case.

We report detailed theoretical investigations of the micromechanics and bulk elastic properties of composites consisting of randomly distributed stiff fibers embedded in an elastic matrix in two and three dimensions. Recent experiments [V. Pelletier, N. Gal, P. Fournier, and M. L. Kilfoil, Phys. Rev. Lett. 102, 188303 (2009)] have suggested that the inclusion of stiff microtubules in a softer, nearly incompressible biopolymer matrix can lead to emergent compressibility. This can be understood in terms of the enhancement of the compressibility of the composite relative to its shear compliance as a result of the addition of stiff rodlike inclusions. We show that the Poisson's ratio $\nu$ of such a composite evolves with increasing rod density toward a particular value, or fixed point, independent of the material properties of the matrix, as long as it has a finite initial compressibility. This fixed point is $\nu =1/4$ in three dimensions and $\nu =1/3$ in two dimensions. Our results suggest an important role for stiff filaments such as microtubules and stress fibers in cell mechanics. At the same time, our work has a wider elasticity context, with potential applications to composite elastic media with a wide separation of scales in stiffness of its constituents such as carbon nanotube-polymer composites, which have been shown to have highly tunable mechanics.

We explore the spatial complexity of Conway’s “Game of Life,” a prototypical cellular automaton by means of a geometrical procedure generating a two-dimensional random walk from a bidimensional lattice with periodical boundaries. The one-dimensional projection of this process is analyzed and it turns out that some of its statistical properties resemble the so-called stylized facts observed in financial time series. The scope and meaning of this result are discussed from the viewpoint of complex systems. In particular, we stress how the supposed peculiarities of financial time series are, often, overrated in their importance.

We propose a model of the dynamics of financial assets based on the mean-field framework. This framework allows us to construct a model which includes the interaction among the financial assets reflecting the market structure. Our study is on the cutting edge in the sense of a microscopic approach to modeling the financial market. To demonstrate the effectiveness of our model concretely, we provide a case study, which is the pricing problem of the European call option with short-time memory noise.

We investigate the existence and stability of traveling-wave solutions in a continuum field of nonlocally coupled identical phase oscillators with distance-dependent propagation delays. A comprehensive stability diagram in the parametric space of the system is presented that shows a rich structure of multistable regions and illuminates the relative influences of time delay, the nonlocality parameter and the intrinsic oscillator frequency on the dynamics of these states. A decrease in the intrinsic oscillator frequency leads to a break-up of the stability domains of the traveling waves into disconnected regions in the parametric space. These regions exhibit a tongue structure for high connectivity, whereas they submerge into the stable region of the synchronous state for low connectivity. One finding is the existence of forbidden regions in the parametric space where no phase-locked solutions are possible. We also discover a new class of nonstationary breather states for this model system that are characterized by periodic oscillations of the complex order parameter.

We consider theoretically and numerically a periodic concentration grating induced in a layer of ferrofluid in the presence of the external magnetic field by nonuniform optical heating through photoabsorption. The stationary profiles of the periodic microstructures are governed by the equilibrium of the diffusive, thermodiffusive, and magnetic fluxes. The anisotropy of the diffusion coefficient and the magnetically driven microconvection contribute to the relaxation of these structures. The temperature-concentration coupling is shown to increase the initial effective diffusive relaxation rate by up to 50%. Microconvection dominates in the relaxation process even at small values of the control parameter and rapidly destroys the periodic part of the concentration grating. We describe this process in the weakly nonlinear regime by an approximate Galerkin model.

We consider separately a spin and an oscillator that are coupled to their environment. After a finite interval of random length, the state of the environment changes, and each change causes a random change in the resonance frequency of the spin or vibrational frequency of the oscillator. Mathematically, the evolution of these frequencies is described by a continuous-time random walk. Physically, the stochastic dynamics can be understood as non-Gaussian because the frequency of the system and state of the environment change on comparable time scales. These dynamics are also nonstationary, and so might apply to a nonequilibrium environment. The re-sonance and vibrational spectra of the spin and oscillator, as well as the ensemble-averaged displacement of the oscillator, are investigated in detail. We observe some distinct non-Gaussian features of the dynamics, such as the narrow, leptokurtic shape of the resonance spectrum of the spin and beating of the average oscillator displacement. The convergence to Gaussian dynamics as changes in the environment occur with increasing frequency is also considered. Among other results, we observe narrowing of the resonance and vibrational lines in the Gaussian limit due to a weakening of the system-environment interaction.

We have studied the Jarzynski equality (JE) in van der Pol and Rayleigh oscillators, which are typical deterministic non-Hamiltonian models but not expected to rigorously satisfy the JE because they are not reversible. Our simulations that calculate the contribution to the work $W$ of an applied ramp force with a duration $\tau$ show that the JE approximately holds for a fairly wide range of $\tau$ including $\tau \to 0$ and $\tau \to \infty$, except for $\tau \sim T$, where $T$ denotes the period of relaxation oscillations in the limit cycle. The work distribution function (WDF) is shown to be non-Gaussian with the $U$-shaped structure for a strong damping parameter. The $\tau$ dependence of $R$ $(=-k_{B}T\ln \langle e^{-\beta W}\rangle )$ obtained by our simulations is semiquantitatively elucidated with the use of a simple expression for limit-cycle oscillations, where the bracket $\langle ·\rangle$ expresses an average over the WDF. The result obtained in self-excited oscillators is in contrast with the fact that the JE holds in the Nosé-Hoover oscillator, which also belongs to deterministic non-Hamiltonian models.

The cumulant generating function of time-averaged current is studied from an operational viewpoint. Specifically, for interacting Brownian particles under nonequilibrium conditions, we show that the first derivative of the cumulant generating function is equal to the expectation value of the current in a modified system with an extra force added, where the modified system is characterized by a variational principle. The formula reminds us of Einstein's fluctuation theory in equilibrium statistical mechanics. Furthermore, since the formula leads to the fluctuation-dissipation relation when the linear response regime is focused on, it is regarded as an extension of the linear response theory to that valid beyond the linear response regime. The formula is also related to previously known theories such as the Donsker-Varadhan theory, the additivity principle, and the least dissipation principle, but it is not derived from them. Examples of its application are presented for a driven Brownian particle on a ring subject to a periodic potential.