This paper presents an experimental approach to identify the sources of instabilities in arc plasma devices. The phenomena of demixing in arcs have been utilized to explore the characteristics of different instabilities. Problems in explaining the observed behavior with our current understanding of the phenomena are discussed. Hydrogen is used as a secondary gas with argon as the primary plasma gas for this study. Results indicate that the observed behavior such as steady, takeover, and restrike modes of instabilities in arcs may essentially originate from the thin boundary layer over the anode wall primarily at the location of the anodic arc root. The bulk core flow apparently does not play any significant role in such instabilities. Arc currents rather than flow rates control the behavior of the instabilities in frequency space. Bifurcation of the system behavior and evidence for the existence of quadratic zones in flow space of binary gas mixtures separating steady and unsteady behavior are discussed.

The generalized Langevin equation is useful for modeling a wide range of physical processes. Unfortunately its parameters, especially the memory function, are difficult to determine for nontrivial processes. We establish relations between a time-discrete generalized Langevin model and discrete multivariate autoregressive (AR) or autoregressive moving average models (ARMA). This allows a wide range of discrete linear methods known from time series analysis to be applied. In particular, the determination of the memory function via the order of the respective AR or ARMA model is addressed. The method is illustrated on a one-dimensional test system and subsequently applied to the molecular dynamics time series of a biomolecule that exhibits an interesting relationship between the solvent method used, the respective molecular conformation, and the depth of the memory.

We introduce a stochastic algorithm that acts as a prime-number generator. The dynamics of this algorithm gives rise to a continuous phase transition, which separates a phase where the algorithm is able to reduce a whole set of integers into primes and a phase where the system reaches a frozen state with low prime density. We present both numerical simulations and an analytical approach in terms of an annealed approximation, by means of which the data are collapsed. A critical slowing-down phenomenon is also outlined.

In this article we obtain a fundamental measure functional for the model of aligned hard hexagons in the plane. Our aim is not just to provide a functional for an admittedly academic model, but to investigate the structure of fundamental measure theory. A model of aligned hard hexagons has similarities with the hard disk model. Both share “lost cases,” i.e. admit configurations of three particles in which there is pairwise overlap but not triple overlap. These configurations are known to be problematic for fundamental measure functionals, which are not able to capture their contribution correctly. This failure lies in the inability of these functionals to yield a correct low density limit of the third order direct correlation function. Here we derive the functional by projecting aligned hard cubes on the plane $x+y+z=0$. The correct dimensional crossover behavior of these functionals permits us to follow this strategy. The functional of aligned hard cubes, however, does not have lost cases, so neither had the resulting functional for aligned hard hexagons. The latter exhibits, in fact, a peculiar structure as compared to the one for hard disks. It depends on a uniparametric family of weighted densities through an additional term not appearing in the functional for hard disks. Apart from studying the freezing of this system, we discuss the implications of the functional structure for further developments of fundamental measure theory.

The early stage of fractal porphyrin diffusion-limited aggregation (DLA), induced by addition of a polyamine, is observed in aqueous solution by enhanced Raman scattering and fluorescence quenching. The enhancement of Raman scattering is due to nonlinear optical properties typical of fractal composites. Although this early stage (reaction-limited aggregation) has been theoretically predicted (by mean-field theory and molecular dynamics simulation), it is experimentally difficult to observe. During this initial stage, fluorescence quenching gives direct information on the decrease of the concentration of monomeric porphyrins, whereas Raman scattering (through characteristic vibrational modes of the aggregate) reports on the concentration of porphyrins in the aggregated form. These small clusters constitute the seeds for the DLA aggregation process leading to micrometric-sized fractals.

In order to form magnetic filaments or chains, aqueous suspensions of superparamagnetic colloidal particles were aggregated under the action of an external magnetic field in the presence of different amounts of an indifferent 1:1 electrolyte (KBr). This allowed the influence of the anisotropic magnetic and isotropic electrostatic interactions on the aggregation behavior of these electric double-layered magnetic particles to be studied. Dynamic light scattering was used for monitoring the average diffusion coefficient of the magnetic filaments formed. Hydrodynamic equations were employed for obtaining the average chain lengths from the experimental mean diffusion coefficients. The results show that, for the same exposure time to the magnetic field, the average filament size is monotonously related to the amount of electrolyte added. The chain growth behavior was found to follow a power law with a similar exponent for all electrolyte concentrations used in this work. The time evolution of the average filament size can be rescaled such that all the curves collapse on a single master curve. Since the electrolyte added does not have any effect on the scaling behavior, the mechanism of aggregation seems to be completely controlled by the dipolar interaction. However, electrolyte addition not only controls the range of the total interaction between the particles, but also enhances the growth rate of the aggregation process. Taking into account the anisotropic character of these aggregation processes we propose a kernel that depends explicitly on the range of the dipolar interaction. The corresponding solutions of the Smoluchowski equation combined with theoretical models for the diffusion and light scattering by rigid rods reproduce the measured time evolution of the average perpendicular aggregate diffusion coefficient quite satisfactorily.

We study two aspects of the elasticity of smectic-$A$ elastomers that make these materials genuinely and qualitatively different from conventional uniaxial rubbers. Under strain applied parallel to the layer normal, monodomain smectic-$A$ elastomers exhibit a drastic change in Young’s modulus above a threshold strain value of about $3\%$, as has been measured in experiments by [Nishikawa and Finkelmann, Macromol. Chem. Phys. 200, 312 (1999)]. Our theory predicts that such strains induce a transition to a smectic-$C$-like state and that it is this transition that causes the change in elastic modulus. We calculate the stress-strain behavior as well as the tilt of the smectic layers and the molecular orientation for strain along the layer normal, and we compare our findings with the experimental data. We also study the electroclinic effect in chiral smectic-$A^{*}$ elastomers. According to experiments by [Lehmann et al., Nature (London) 410, 447 (2001)] and [Köhler et al., Appl. Phys. A 80, 381 (2003)], this effect leads in smectic-$A^{*}$ elastomers to a giant or, respectively, at least very large lateral electrostriction. Incorporating polarization into our theory, we calculate the height change of smectic-$A^{*}$ elastomer films in response to a lateral external electric field, and we compare this result to the experimental findings.

The recently proposed statistical temperature molecular dynamics (STMD) algorithm [Kim et al., Phys. Rev. Lett. 97, 050601 (2006)] is used as the core of an optimization algorithm, statistical temperature annealing (STA), for finding low-lying energy minima of complex potential energy landscapes. Since STMD realizes a random walk in energy, the idea is simply to initiate repeated minimizations from configurations in the low-energy segments of STMD trajectories. STA is tested in structural optimization of various off-lattice $AB$ and extended $AB$ protein models in two and three dimensions with different chain lengths. New putative ground states were found for the two- and three-dimensional $AB$ 55-mer, and for the three-dimensional extended $AB$ 21-mer and 55-mer. The distinct folding features of the models are analyzed in terms of the statistical temperature and other representations of the structure of the potential energy landscape. It is shown that the characteristic behavior of the statistical temperature undergoes a qualitative change with the inclusion of a torsional potential in the extended $AB$ model, as the more rigid backbone makes the potential energy landscape more funnel-like.

We present an exact theoretical test of Jarzynski’s equality (JE) for reversible volume-switching processes of an ideal gas system. The exact analysis shows that the prediction of JE for the free energy difference is the same as the work done on the gas system during the reversible process that is dependent on the shape of path of the reversible volume-switching process.

Experimentally well-characterized proteins that are small enough to be computationally tractable provide useful information for refining existing all-atom force fields. This is used by us for reparametrizing a recently developed all-atom force field. Relying on high statistics parallel tempering simulations of a designed 20 residue $\beta$-sheet peptide, we propose incremental changes that improve the force field’s range of applicability.

For nonassociated, glass-forming liquids and polymers, thermodynamic scaling of structural relaxation times and viscosities is an empirical fact, demonstrated by various groups for dozens of materials. The $P$ and $T$ invariance of the isochoric fragility follows directly from this scaling. Apparent inconsistencies with these statements were reported recently by Grzybowski et al. [A. Grzybowski, K. Grzybowska, J. Zioło, and M. Paluch, Phys. Rev. E 74, 041503 (2006)]; however, the putative inconsistencies arise from use at higher pressures of parameters to correlate the isobaric and isochoric fragilities that are valid only for ambient pressure.

Our recent paper [A. Grzybowski, K. Grzybowska, J. Zioło, and M. Paluch, Phys. Rev. E 74, 041503 (2006)] tested the correlations between isobaric and isochoric fragilities, $m_P$ and $m_V$, as well as the scaling exponent $\gamma$ under elevated pressure conditions. The preceding paper [R. Casalini and C. M. Roland, Phys. Rev. E 76, 013501 (2007)] is a Comment by the authors of the correlations originally determined for atmospheric pressure. In this Reply we present our point of view on criticisms contained in the Comment. We clarify and maintain our previously drawn conclusions.

We propose a mechanism for generating snakelike motion in a micrometer-scale, responsive, synthetic material, which thereby undergoes net movement in a fluid (i.e., swimming). By responsive material, we refer to a material that can expand or contract in response to a chemical concentration change. The concentrations of the chemical species are modeled by simple reaction-diffusion equations with suitably chosen source terms. Using linear stability analysis, we isolate the key properties of the material and reaction rate parameters.

The evolution of large-scale fluctuations in a monodisperse dilute suspension sedimenting in a wall-bounded container is considered on the basis of a continuum model. The case when the velocity fluctuations are comparable with the Stokes settling velocity is studied. Small deformations of the sedimentation front is replaced by a flat interface with a surface force distribution. The front holds position ensuring the vertical fluid velocity across the front to be small. So it acts approximately as a no-slip wall. The mechanisms of the fluctuation decay are the convection of large-scale concentration disturbances and the sedimentation-front deformations.

The efficiency of Monte Carlo samplers is dictated not only by energetic effects, such as large barriers, but also by entropic effects that are due to the sheer volume that is sampled. The latter effects appear in the form of an entropic mismatch or divergence between the direct and reverse trial moves. We provide lower and upper bounds for the average acceptance probability in terms of the Rényi divergence of order $1∕2$. We show that the asymptotic finitude of the entropic divergence is the necessary and sufficient condition for nonvanishing acceptance probabilities in the limit of large dimension. Furthermore, we demonstrate that the upper bound is reasonably tight by showing that the exponent is asymptotically exact for systems made up of a large number of independent and identically distributed subsystems. For the last statement, we provide an alternative proof that relies on the reformulation of the acceptance probability as a large deviation problem. The reformulation also leads to a class of low-variance estimators for strongly asymmetric distributions. We show that the entropy divergence causes a decay in the average displacements with the number of dimensions $n$ that are simultaneously updated. For systems that have a well-defined thermodynamic limit, the decay is demonstrated to be $n^{-1∕2}$ for random-walk Monte Carlo and $n^{-1∕6}$ for smart Monte Carlo (SMC). Numerical simulations of the Lennard-Jones 38 (${\mathrm{LJ}}_{38}$) cluster show that SMC is virtually as efficient as the Markov chain implementation of the Gibbs sampler, which is normally utilized for Lennard-Jones clusters. An application of the entropic inequalities to the parallel tempering method demonstrates that the number of replicas increases as the square root of the heat capacity of the system.

Inspired by, and using methods of optimization derived from classical three-dimensional electrostatics we have found a four-dimensional polytope, new to our knowledge, with a high degree of symmetry in terms of the lengths of sides—64 of the 80 vertices have twelve nearest neighbors with the same four nearest neighbor distances, and the other 16 vertices have ten nearest neighbors with distances that are two of the four nearest neighbor distances for the set of 64 vertices. We give and illustrate a simple geometric method to visualize this configuration and other configurations in four, eight, and sixteen dimensions.

We use the method of Balister, Bollobás, and Walters [Random Struct. Algorithms 26, 392 (2005)] to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices. In our computer calculations, the emphasis is on simplicity and ease of verification, rather than obtaining the best possible results. Nevertheless, we obtain intervals of width at most 0.0005 in all cases.

We investigate the mechanism of heat conduction in ordered and disordered harmonic one-dimensional chains within the quantum mechanical Langevin method. In the case of disordered chains we find indications for normal heat conduction, which means that there is a finite temperature gradient, but we cannot clearly decide whether the heat resistance increases linearly with the chain length. Furthermore, we observe characteristic quantum mechanical features like the Bose-Einstein statistics of the occupation numbers of the normal modes, freezing of the heat conductivity, and influence of the entanglement within the chain on the current. For the ordered chain we recover some classical results like a vanishing temperature gradient and a heat flux independent of the length of the chain.

A self-consistent molecular dynamics (SCMD) formulation is presented for electric-field-mediated transport of water and ions through a nanochannel connected to reservoirs or baths. The SCMD formulation is compared with a uniform field MD approach, where the applied electric field is assumed to be uniform, for $2\mathrm{nm}$ and $3.5\mathrm{nm}$ wide nanochannels immersed in a $0.5M$ KCl solution. Reservoir ionic concentrations are maintained using the dual-control-volume grand canonical molecular dynamics technique. Simulation results with varying channel height indicate that the SCMD approach calculates the electrostatic potential in the simulation domain more accurately compared to the uniform field approach, with the deviation in results increasing with the channel height. The translocation times and ionic fluxes predicted by uniform field MD can be substantially different from those predicted by the SCMD approach. Our results also indicate that during a $2\mathrm{ns}$ simulation time ${\mathrm{K}}^{+}$ ions can permeate through a $1\mathrm{nm}$ channel when the applied electric field is computed self-consistently, while the permeation is not observed when the electric field is assumed to be uniform.

We present experimental measurements of the cholesteric-smectic phase transition of suspensions of charged semiflexible rods as a function of rod flexibility and surface charge. The rod particles consist of the bacteriophage M13 and closely related mutants, which are structurally identical to M13, but vary either in contour length and therefore ratio of persistence length to contour length, or surface charge. Surface charge is altered in two ways; by changing solution $p\mathrm{H}$ and by comparing M13 with $fd$ virus, a virus which differs from M13 only by the substitution of a single charged amino acid for a neutral one per viral coat protein. Phase diagrams are measured as a function of particle length, particle charge, and ionic strength. The experimental results are compared with existing theoretical predictions for the phase behavior of flexible rods and charged rods.