We show that within the dipole approximation the complex polarizability of shelled particles of arbitrary shape can be written as the volume of the particle times a weighted average of the electric field in the particle, with weights determined by the differences in permittivities between the shells and the external, possibly lossy media. To calculate the electric field we use an adaptive-mesh finite-element method which is very effective in handling the irregular domains, material inhomogeneities, and complex boundary conditions usually found in biophysical applications. After extensive tests with exactly solvable models, we apply the method to four types of hematic cells: platelets, T-lymphocytes, erythrocytes, and stomatocytes. Realistic shapes of erythrocytes and stomatocytes are generated by a parametrization in terms of Jacobi elliptic functions. Our results show, for example, that if the average polarizability is the main concern, a confocal ellipsoid may be used as a model for a normal erythrocyte, but not for a stomatocyte. A comparison with experimental electrorotation data shows quantitatively the effect of an accurate geometry in the derivation of electrical cell parameters from fittings of theoretical models to the experimental data.

A condensation transition was predicted for growing technological networks evolving by preferential attachment and competing quality of their nodes, as described by the fitness model. When this condensation occurs, a node acquires a finite fraction of all the links of the network. Earlier studies based on steady-state degree distribution and on the mapping to Bose-Einstein condensation were able to identify the critical point. Here we characterize the dynamics of condensation and we present evidence that below the condensation temperature there is a slow down of the dynamics and that a single node (not necessarily the best node in the network) emerges as the winner for very long times. The characteristic time $t^{*}$ at which this phenomenon occurs diverges both at the critical point and at $T\to 0$ when new links are attached deterministically to the highest quality node of the network.

An electromagnetic wave (EMW) interacting with the moving singularity of the charged particle flux undergoes the reflection and absorption as well as frequency change due to Doppler effect and nonlinearity. The singularity corresponding to a caustic in plasma flow with inhomogeneous velocity can arise during the breaking of the finite amplitude Langmuir waves due to nonlinear effects. A systematic analysis of the wave-breaking regimes and caustics formation is presented and the EMW reflection coefficients are calculated.

Accelerator processors like the new Cell processor are extending the traditional platforms for scientific computation, allowing orders of magnitude more floating-point operations per second (flops) compared to standard central processing units. However, they currently lack double-precision support and support for some IEEE 754 capabilities. In this work, we develop a lattice-Boltzmann (LB) code to run on the Cell processor and test the accuracy of this lattice method on this platform. We run tests for different flow topologies, boundary conditions, and Reynolds numbers in the range $\mathrm{Re}=6–350$. In one case, simulation results show a reduced mass and momentum conservation compared to an equivalent double-precision LB implementation. All other cases demonstrate the utility of the Cell processor for fluid dynamics simulations. Benchmarks on two Cell-based platforms are performed, the Sony Playstation3 and the QS20/QS21 IBM blade, obtaining a speed-up factor of 7 and 21, respectively, compared to the original PC version of the code, and a conservative sustained performance of 28 gigaflops per single Cell processor. Our results suggest that choice of IEEE 754 rounding mode is possibly as important as double-precision support for this specific scientific application.

Recent multicolor photon-echo experiments revealed a long-lasting quantum coherence between excitations on the donor and acceptor in photosynthetic systems. Identifying the origin of the quantum coherence is essential to fully understand photosynthesis. Here we present a generic model in which a strong intermolecular steric restoring force in densely packed pigment-protein complexes results in a spatial correlation in conformational (static) variations of chromophores, which in turn induces an effective coupling between high-frequency (dynamic) fluctuations in donor and acceptor. The spatially correlated static and dynamic fluctuations provide a favorable environment to maintain quantum coherence, which can consistently explain the photon-echo measurements.

The elastic properties of micrometer-sized hollow colloidal particles obtained by emulsion templating are probed by nanoindentation measurements in which point forces are applied to solvent-filled particles supported on a flat substrate. We show that the shells respond linearly up to forces of $7–21\mathrm{nN}$, where the indentation becomes of the order of the shell thickness $(20–40\mathrm{nm})$. In the linear region, the particle deformation is reversible. The measured Young’s modulus $(\sim 200\mathrm{MPa})$ is comparable to values for stiff rubbers or soft polymers. At larger applied force, we observe a crossover into a nonlinear regime, where the shells assume a buckled shape. Here, the force increases approximately as the square root of the indentation, in agreement with the theory of elasticity of thin shells. We also observe permanent deformation of the shells after probing them repetitively beyond the linear regime. Finally, the measured elastic properties of the shells nicely explain their spontaneous buckling in solution and due to drying.

The wings of the giant wasp Megascolia procer javanensis are opaque and iridescent. The origin of the blue-green iridescence is studied in detail, using reflection spectroscopy, scanning electron microscopy, and physical modeling. It is shown that the structure responsible for the iridescence is a single homogeneous transparent chitin layer covering the whole surface of each wing. The opacity is essentially due to the presence of melanin in the stratified medium which forms the mechanical core of the wing.

Budding from the plasma membrane of the host cell is an indispensable step in the life cycle of the human immunodeficiency virus (HIV), which belongs to a large family of enveloped RNA viruses, retroviruses. Unlike regular enveloped viruses, retrovirus budding happens concurrently with the self-assembly of the main retrovirus protein subunits (called Gag protein after the name of the genetic material that codes for this protein: Group-specific AntiGen) into spherical virus capsids on the cell membrane. Led by this unique budding and assembly mechanism, we study the free energy profile of retrovirus budding, taking into account the Gag-Gag attraction energy and the membrane elastic energy. We find that if the Gag-Gag attraction is strong, budding always proceeds to completion. During early stage of budding, the zenith angle of partial budded capsids, $\alpha$, increases with time as $\alpha \propto t^{1∕2}$. However, if the Gag-Gag attraction is weak, a metastable state of partial budding appears. The zenith angle of these partially spherical capsids is given by ${\alpha }_0\simeq {({\tau }^2∕\kappa \sigma )}^{1∕4}$ in a linear approximation, where $\kappa$ and $\sigma$ are the bending modulus and the surface tension of the membrane, and $\tau$ is a line tension of the capsid proportional to the strength of Gag-Gag attraction. Numerically, we find ${\alpha }_0<0.3\pi$ without any approximations. Using experimental parameters, we show that HIV budding and assembly always proceed to completion in normal biological conditions. On the other hand, by changing Gag-Gag interaction strength or membrane rigidity, it is relatively easy to tune it back and forth between complete budding and partial budding. Our model agrees reasonably well with experiments observing partial budding of retroviruses including HIV.

Using replica-exchange multicanonical Monte Carlo simulation, the aggregates of two homopolymers were numerically investigated through the microcanonical analysis method. The microcanonical entropy showed one convex function in the transition region, leading to a negative microcanonical specific heat. The origin of temperature backbending was the rearrangement of the segments during the process of aggregation; this aggregation process proceeded via a nucleation and growth mechanism. It was observed that the segments with a sequence number from 10 to 13 in the polymer chain have leading effects on the aggregation.

We investigate the effect of long-range diffusive mixing on stochastic processes taking place on low-dimensional catalytic supports. As a working example, the cyclic lattice Lotka-Volterra (LLV) model is used which is conservative at the mean-field level and demonstrates fractal patterns and local oscillations when realized on low-dimensional lattice supports. We show that the local oscillations are synchronized when a weak, long-range, diffusive process is added to LLV and global oscillations of limit cycle type emerge. This phenomenon is demonstrated as a nonequilibrium phase transition and takes place when the mixing-to-reaction rate $p$ (order parameter) is above a critical point $p_c$. The value of the critical point is shown to depend on the kinetic parameters. The global oscillations in this case emerge as a result of phase synchronization between local oscillations on sublattices.

The construction of the trace formula for open dielectric cavities is examined in detail. Using the Krein formula it is shown that the sum over cavity resonances can be written as a sum over classical periodic orbits for the motion inside the cavity. The contribution of each periodic orbit is the product of the two factors. The first is the same as in the standard trace formula and the second is connected with the product of reflection coefficients for all points of reflection with the cavity boundary. Two asymptotic terms of the smooth resonance counting function related with the area and the perimeter of a convex cavity are derived. The coefficient of the perimeter term differs from the one for closed cavities due to unusual high-energy asymptotics of the $\mathbf{S}$ matrix for the scattering on the cavity. Corrections to the leading semi-classical formula are briefly discussed. Obtained formulas agree well with numerical calculations for circular dielectric cavities.

An analytical model for the linear Richtmyer-Meshkov instability in solids under conditions of high-energy density is presented, in order to describe the evolution of small perturbations at the solid-vacuum interface. The model shows that plasticity determines the maximum perturbation amplitude and provides simple scaling laws for it as well as for the time when it is reached. After the maximum amplitude is reached, the interface remains oscillating with a period that is determined by the elastic shear modulus. Extensive two-dimensional simulations are presented that show excellent agreement with the analytical model. The results suggest the possibility to experimentally evaluate the yield strength of solids under dynamic conditions by using a Richtmyer-Meshkov-instability-based technique.

The simulation of a stationary fluid flow past an obstacle by the lattice Boltzmann method (LBM) in two dimensions is discussed. The combination of second-order expressions for far-field boundary conditions and a suitable treatment of the no-slip boundary condition at the obstacle surface with the nested grid-refinement technique can be applied to the LBM, resulting in a highly efficient method for the treatment of exterior flows. Furthermore, via replacing the nested time stepping by local time stepping, the resolution process can be substantially accelerated. A highly accurate drag coefficient was used to make an error assessment for various no-slip boundary conditions imposed on the obstacle surface. The analysis showed that the equilibrium method for treating the no-slip conditions is superior to halfway bounce-back and full-way bounce-back no-slip conditions when the relaxation time $\tau =1$. Also a $\tau$-dependence test was made to evaluate the performance of different methods in the treatment of the no-slip boundary conditions.

Using molecular dynamics simulations of a generic model, we observe strain hardening in highly cross-linked polymer glasses under tensile deformation. We show that formation of microvoids, without bond breaking, constitutes the microscopic origins of strain hardening. A well-defined functional form is observed for the void size distribution that is consistent with voids in dense equilibrium Lennard-Jones particle packings, independent of strain. Microvoid-based strain hardening is not observed in a separate model with tetrahedral bond angle constraints, indicating that flexible cross-linkers are the key factor in the development of strain hardening behavior.

One-dimensional Brownian motion starting from the origin at time $t=0$, conditioned to return to the origin at time $t=1$ and to stay positive during time interval $0<t<1$, is called the Bessel bridge with duration 1. We consider an $N$-particle system of such Bessel bridges conditioned never to collide with each other in $0<t<1$, which is the continuum limit of the vicious walk model in watermelon configuration with a wall. Distributions of maximum values of paths attained in the time interval $t∊(0,1)$ are studied to characterize the statistics of random patterns of the repulsive paths on the spatiotemporal plane. For the outermost path, the distribution function of maximum value is exactly determined for general $N$. We show that the present $N$-path system of noncolliding Bessel bridges is realized as the positive-eigenvalue process of the $2N\times 2N$ matrix-valued Brownian bridge in the symmetry class C. Using this fact, computer simulations are performed and numerical results on the $N$ dependence of the maximum-value distributions of the inner paths are reported. The present work demonstrates that the extreme-value problems of noncolliding paths are related to random matrix theory, the representation theory of symmetry, and number theory.

In this paper we have explored a model for self-induced aggregation of Brownian particles incorporating non-Markovian and non-Gaussian character of the associated random noise processes. The time evolution of each individual is guided by an overdamped Langevin equation of motion with a nonlocal drift arising out of the imbalance in the local distribution of the other individuals. Our simulation results show that colored noise enhances the tendency of cluster formation. Another observation is that the critical noise variance decreases at first with increase in noise correlation time followed by an increase after exhibiting a minimum. Furthermore, in the long time limit the cluster number in the aggregation process exhibits depletion with time following a power law with an exponent which increases remarkably with non-Markovian character of the noise processes.

We present an efficient method to determine the Fourier-Laplace transform of the joint $n$-point probability distribution of a continuous-time random walk for arbitrary finite $n$. Additionally, we devise a recursive procedure with which it is possible to calculate the Laplace transforms of the multipoint correlation functions without having to determine the joint probability distributions first. The methods are used on several examples with both independent and dependent distributions for the waiting time and the spatial step size.

We describe an experimental and computational investigation of the ordered and disordered phases of a vibrating thin, dense granular layer composed of identical metal spheres. We compare the results from spheres with different amounts of inelasticity and show that inelasticity has a strong effect on the phase diagram. We also report the melting of an ordered phase to a homogeneous disordered liquid phase at high vibration amplitude or at large inelasticities. Our results show that dissipation has a strong effect on ordering and that in this system ordered phases are absent entirely in highly inelastic materials.

It is shown that the deviations of the experimental statistics of six chaotic acoustic resonators from Wigner-Dyson random matrix theory predictions are explained by a recent model of random missing levels. In these resonatorsa made of aluminum plates a the larger deviations occur in the spectral rigidity (SRs) while the nearest-neighbor distributions (NNDs) are still close to the Wigner surmise. Good fits to the experimental NNDs and SRs are obtained by adjusting only one parameter, which is the fraction of remaining levels of the complete spectra. For two Sinai stadiums, one Sinai stadium without planar symmetry, two triangles, and a sixth of the three-leaf clover shapes, was found that 7%, 4%, 7%, and 2%, respectively, of eigenfrequencies were not detected.

We determine the scaling exponents of polymer translocation (PT) through a nanopore by extensive computer simulations of various microscopic models for chain lengths extending up to $N=800$ in some cases. We focus on the scaling of the average PT time $\tau \sim N^{\alpha }$ and the mean-square change of the PT coordinate, $⟨s^2\left(t\right)⟩\sim t^{\beta }$. We find $\alpha =1+2\nu$ and $\beta =2∕\alpha$ for unbiased PT in two dimensions (2D) and three dimensions (3D). The relation $\alpha \beta =2$ holds for driven PT in 2D, with a crossover from $\alpha \approx 2\nu$ for short chains to $\alpha \approx 1+\nu$ for long chains. This crossover is, however, absent in 3D where $\alpha =1.42\pm 0.01$ and $\alpha \beta \approx 2.2$ for $N\approx 40-800$.