Experiments with acoustic waves guided along the mechanically free surface of an unconsolidated granular packed structure provide information on the elasticity of granular media at very low pressures that are naturally controlled by the gravitational
acceleration and the depth beneath the surface. Comparison of the determined dispersion relations for guided surface acoustic modes with a theoretical model reveals the dependencies of the elastic moduli of the granular medium on pressure. The experiments confirm recent theoretical predictions that relaxation of the disordered granular packing through non-affine motion leads to a peculiar scaling of shear rigidity with pressure near the jamming transition corresponding to zero pressure. Unexpectedly, and in disagreement with the most of the available theories, the bulk modulus depends on pressure in a very similar way to the shear modulus.
We employ granular hydrodynamics to investigate a paradigmatic problem of clustering of particles in a freely cooling dilute granular gas. We consider large-scale hydrodynamic motions where the viscosity and heat conduction can be neglected, and one
arrives at the equations of ideal gas dynamics with an additional term describing bulk energy losses due to inelastic collisions. We employ Lagrangian coordinates and derive a broad family of exact non-stationary analytical solutions that depend only on one spatial coordinate. These solutions exhibit a new type of singularity, where the gas density blows up in a finite time when starting from smooth initial conditions. The density blowups signal formation of close-packed clusters of particles. As the density blow-up time $t_c$ is approached, the maximum density exhibits a power law $sim (t_c-t)^{-2}$. The velocity gradient blows up as $sim - (t_c-t)^{-1}$ while the velocity itself remains continuous and develops a cusp (rather than a shock discontinuity) at the singularity. The gas temperature vanishes at the singularity, and the singularity follows the isobaric scenario: the gas pressure remains finite and approximately uniform in space and constant in time close to the singularity. An additional exact solution shows that the density blowup, of the same type, may coexist with an ordinary shock, at which the hydrodynamic fields are discontinuous but finite. We confirm stability of the exact solutions with respect to small one-dimensional perturbations by solving the ideal hydrodynamic equations numerically. Furthermore, numerical solutions show that the local features of the density blowup hold universally, independently of details of the initial and boundary conditions.
Potassium intercalation in graphite is investigated by first-principles theory. The bonding in the potassium-graphite compound is reasonably well accounted for by traditional semilocal density functional theory (DFT) calculations. However, to investi
gate the intercalate formation energy from pure potassium atoms and graphite requires use of a description of the graphite interlayer binding and thus a consistent account of the nonlocal dispersive interactions. This is included seamlessly with ordinary DFT by a van der Waals density functional (vdW-DF) approach [Phys. Rev. Lett. 92, 246401 (2004)]. The use of the vdW-DF is found to stabilize the graphite crystal, with crystal parameters in fair agreement with experiments. For graphite and potassium-intercalated graphite structural parameters such as binding separation, layer binding energy, formation energy, and bulk modulus are reported. Also the adsorption and sub-surface potassium absorption energies are reported. The vdW-DF description, compared with the traditional semilocal approach, is found to weakly soften the elastic response.
We investigate the rheological properties of an assembly of inelastic (but frictionless) particles close to the jamming density using numerical simulation, in which uniform steady states with a constant shear rate $dotgamma$ is realized. The system b
ehaves as a power-law fluid and the relevant exponents are estimated; e.g., the shear stress is proportional to $dotgamma^{1/delta_S}$, where $1/delta_S=0.64(2)$. It is also found that the relaxation time $tau$ and the correlation length $xi$ of the velocity increase obeying power laws: $tausimdotgamma^{-beta}$ and $xisimdotgamma^{-alpha}$, where $beta=0.27(3)$ and $alpha=0.23(3)$.
The electrical properties of a set of seven-helix transmembrane proteins, whose space arrangement (3D structure) is known, are investigated by using regular arrays of the amino acids. These structures, specifically cubes, have topological features si
milar to those shown by the chosen proteins. The theoretical results show a good agreement between the predicted current-voltage characteristics obtained from a cubic array and those obtained from a detailed 3D structure. The agreement is confirmed by available experiments on bacteriorhodopsin. Furthermore, all the analyzed proteins are found to share the same critical behaviour of the voltage-dependent conductance and of its variance. In particular, the cubic arrangement evidences a short plateau of the excess conductance and its variance at high voltages. The results of the present investigation show the possibility to predict the I-V characteristics of multiple-protein sample even in the absence of a detailed knowledge of their 3D structure.
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a stretching domi
nated regime of elasticity. The physics of this crossover is related to the existence of a central-force isostatic point and to the fact that for most gels the bending modulus is small. This crossover induces scaling behavior for the elastic moduli. In particular, for linear elasticity such a scaling law has been demonstrated [Broedersz et al. Nature Physics, 2011 7, 983]. In this work we generalize the scaling to the nonlinear regime with a two-parameter scaling law involving three critical exponents. We test the scaling law numerically for two disordered lattice models, and find a good scaling collapse for the shear modulus in both the linear and nonlinear regimes. We compute all the critical exponents for the two lattice models and discuss the applicability of our results to real systems.
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walks displacement. It i
s shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.
Recently, in an ensemble of small spheres, we proposed a method that converts the force between two large spheres into the pressure on the large spheres surface element. Using it, the density distribution of the small spheres around the large sphere
can be obtained experimentally. In a similar manner, in this letter, we propose a transform theory for surface force apparatus, which transforms the force acting on the cylinder into the density distribution of the small spheres on the cylindrical surface. The transform theory we derived is briefly explained in this letter.
This work investigates the migration of spherical particles of different sizes in a centrifuge-driven deterministic lateral displacement (c-DLD) device. Specifically, we use a scaled-up model to study the motion of suspended particles through a squar
e array of cylindrical posts under the action of centrifugation. Experiments show that separation of particles by size is possible depending on the orientation of the driving acceleration with respect to the array of posts (forcing angle). We focus on the fractionation of binary suspensions and measure the separation resolution at the outlet of the device for different forcing angles. We found excellent resolution at intermediate forcing angles, when large particles are locked to move at small migration angles but smaller particles follow the forcing angle more closely. Finally, we show that reducing the initial concentration (number) of particles, approaching the dilute limit of single particles, leads to increased resolution in the separation.
In 1983 Felderhof, Ford and Cohen gave microscopic explanation of the famous Clausius-Mossotti formula for the dielectric constant of nonpolar dielectric. They based their considerations on the cluster expansion of the dielectric constant, which rela
tes this macroscopic property with the microscopic characteristics of the system. In this article, we analyze the cluster expansion of Felderhof, Ford and Cohen by performing its resummation (renormalization). Our analysis leads to the ring expansion for the macroscopic characteristic of the system, which is an expression alternative to the cluster expansion. Using similarity of structures of the cluster expansion and the ring expansion, we generalize (renormalize) the Clausius-Mossotti approximation. We apply our renormalized Clausius-Mossotti approximation to the case of the short-time transport properties of suspensions, calculating the effective viscosity and the hydrodynamic function with the translational self-diffusion and the collective diffusion coefficient. We perform calculations for monodisperse hard-sphere suspensions in equilibrium with volume fraction up to 45%. To assess the renormalized Clausius-Mossotti approximation, it is compared with numerical simulations and the Beenakker-Mazur method. The results of our renormalized Clausius-Mossotti approximation lead to comparable or much less error (with respect to the numerical simulations), than the Beenakker-Mazur method for the volume fractions below $ phi approx 30% $ (apart from a small range of wave vectors in hydrodynamic function). For volume fractions above $phi approx 30 %$, the Beenakker-Mazur method gives in most cases lower error, than the renormalized Clausius-Mossotti approximation.
