The Kronecker channel model of wireless communication is analyzed using statistical mechanics methods. In the model, spatial proximities among transmission/reception antennas are taken into account as certain correlation matrices, which generally yield nontrivial dependence among symbols to be estimated. This prevents accurate assessment of the communication performance by naively using a previously developed analytical scheme based on a matrix integration formula. In order to resolve this difficulty, we develop a formalism that can formally handle the correlations in Kronecker models based on the known scheme. Unfortunately, direct application of the developed scheme is, in general, practically difficult. However, the formalism is still useful, indicating that the effect of the correlations generally increase after the fourth order with respect to correlation strength. Therefore, the known analytical scheme offers a good approximation in performance evaluation when the correlation strength is sufficiently small. For a class of specific correlation, we show that the performance analysis can be mapped to the problem of one-dimensional spin systems in random fields, which can be investigated without approximation by the belief propagation algorithm.

We developed an experimental method to generate mechanically stable (MS) packings of frictionless disks and performed coordinated experiments and simulations to characterize MS packings in small systems. For a given system geometry, MS packings occur as discrete, well-separated points in configuration space with probabilities that vary by many orders of magnitude and are robust with respect to the packing preparation. Over a continuous range of system geometries, MS packings occur as distinct geometrical families and only a small fraction of families are sampled via quasistatic dynamics. These results suggest that the most frequent MS packings may dominate the structural and mechanical properties of dense granular media.

We study the effects of intrinsic sequence-dependent curvature for a two-dimensional semiflexible biopolymer with short-range correlation in intrinsic curvatures. We show exactly that when not subjected to any external force, such a system is equivalent to a system with a well-defined intrinsic curvature and a proper renormalized persistence length. We find the exact expression for the distribution function of the equivalent system. However, we show that such an equivalent system does not always exist for the polymer subjected to an external force. We find that under an external force, the effect of sequence disorder depends upon the averaging order, the degree of disorder, and the experimental conditions, such as the boundary conditions. Furthermore, a short to moderate length biopolymer may be much softer or has a smaller apparent persistent length than what would be expected from the “equivalent system.” Moreover, under a strong stretching force and for a long biopolymer, the sequence disorder is immaterial for elasticity. Finally, the effect of sequence disorder may depend upon the quantity considered.

We present experimental measurements of the equilibrium elastic energy of protein-DNA chimeras, for two different sets of attachment points of the DNA “molecular spring” on the surface of the protein. Combining these with measurements of the enzyme’s activity under stress and a mechanical model of the system, we determine how the elastic energy is partitioned between the DNA and the protein. The analysis shows that the protein is mechanically stiffer than the DNA spring.

Sequence alignment is a tool in bioinformatics that is used to find homological relationships in large molecular databases. It can be mapped on the physical model of directed polymers in random media. We consider the finite-temperature version of local sequence alignment for proteins and study the transition between the linear phase and the biologically relevant logarithmic phase, where the free energy grows linearly or logarithmically with the sequence length. By means of numerical simulations and finite-size-scaling analysis, we determine the phase diagram in the plane that is spanned by the gap costs and the temperature. We use the most frequently used parameter set for protein alignment. The critical exponents that describe the parameter-driven transition are found to be explicitly temperature dependent. Furthermore, we study the shape of the (free-) energy distribution close to the transition by rare-event simulations down to probabilities on the order ${10}^{-64}$. It is well known that in the logarithmic region, the optimal score distribution $\left(T=0\right)$ is described by a modified Gumbel distribution. We confirm that this also applies for the free-energy distribution $\left(T>0\right)$. However, in the linear phase, the distribution crosses over to a modified Gaussian distribution.

The coverage dependence of the one-dimensional collective diffusion coefficient is analyzed by using the gradient expansion of the local density. The transition probabilities are written as an expansion of the probabilities of the occupation configurations. Since the detail balance principle determines only a part of the diffusion terms in the expansion, different functional relations are proposed for these terms. The diffusion coefficient is obtained for various choices of these relations. However, some of them seem to be not physically sound and the diffusion coefficient does not behave properly. The range of validity of various expressions for the jump rates is determined and phase diagrams are shown. Besides that, it is shown that the transition state theory guarantees physically suitable behavior of the coefficient of one-dimensional diffusion.

Bacterial cells come in a variety of shapes, determined by the stress-bearing cell wall. Though many molecular details about the cell wall are known, our understanding of how a particular shape is produced during cell growth is at its infancy. Experiments on curved Escherichia coli grown in microtraps, and on naturally curved Caulobacter crescentus, reveal different modes of growth: one preserving arc length and the other preserving radius of curvature. We present a simple model for curved cell growth that relates these two growth modes to distinct but related growth rules—“hooplike growth” and “self-similar growth”—and discuss the implications for microscopic growth mechanisms.

We investigated the agitation induced in a liquid by quasimonodispersed spherical bubbles. For ${\text{Re}}_p$ about 10 and for void fractions ranging from 0.002 to 0.1, the axial velocity fluctuation probability density functions happen to be uniquely determined by the velocity variance. In addition, the variance experiences a rupture from a nonlinear to a quasilinear increase with the volumic concentration. It is shown that the presence of a deficit of neighbors in the wake of any test inclusion forces the screening of velocity disturbances at a finite distance $X$—of order ${\text{Re}}_p/\alpha$—and that the velocity variance does not depend on the system size when the later is large compared with $X$. Finally, the bubble-induced agitation happens to be much stronger for quasimonodispersed than for polydispersed size distributions because of the longer interaction duration between pairs in the former case.

Fiber bundle models (FBMs) are useful tools in understanding failure processes in a variety of material systems. While the fibers and load sharing assumptions are easily described, FBM analysis is typically difficult. Monte Carlo methods are also hampered by the severe computational demands of large bundle sizes, which overwhelm just as behavior relevant to real materials starts to emerge. For large size scales, interest continues in idealized FBMs that assume either equal load sharing (ELS) or local load sharing (LLS) among fibers, rules that reflect features of real load redistribution in elastic lattices. The present work focuses on a one-dimensional bundle of $N$ fibers under LLS where life consumption in a fiber follows a power law in its load, with exponent $\rho$, and integrated over time. This life consumption function is further embodied in a functional form resulting in a Weibull distribution for lifetime under constant fiber stress and with Weibull exponent, $\beta$. Thus the failure rate of a fiber depends on its past load history, except for $\beta =1$. We develop asymptotic results validated by Monte Carlo simulation using a computational algorithm developed in our previous work [Phys. Rev. E 63, 021507 (2001)] that greatly increases the size, $N$, of treatable bundles (e.g., ${10}^6$ fibers in ${10}^3$ realizations). In particular, our algorithm is $\mathcal{O}\left(N\text{ln}N\right)$ in contrast with former algorithms which were $\mathcal{O}\left(N^2\right)$ making this investigation possible. Regimes are found for $\left(\beta ,\rho \right)$ pairs that yield contrasting behavior for large $N$. For $\rho >1$ and large $N$, brittle weakest volume behavior emerges in terms of characteristic elements (groupings of fibers) derived from critical cluster formation, and the lifetime eventually goes to zero as $N\to \infty$, unlike ELS, which yields a finite limiting mean. For $1/2\le \rho \le 1$, however, LLS has remarkably similar behavior to ELS (appearing to be virtually identical for $\rho =1$) with an asymptotic Gaussian lifetime distribution and a finite limiting mean for large $N$. The coefficient of variation follows a power law in increasing $N$ but, except for $\rho =1$, the value of the negative exponent is clearly less than 1/2 unlike in ELS bundles where the exponent remains 1/2 for $1/2<\rho \le 1$. For sufficiently small values $0<\rho ⪡1$, a transition occurs, depending on $\beta$, whereby LLS bundle lifetimes become dominated by a few long-lived fibers. Thus the bundle lifetime appears to approximately follow an extreme-value distribution for the longest lived of a parallel group of independent elements, which applies exactly to $\rho =0$. The lower the value of $\beta$, the higher the transition value of $\rho$, below which such extreme-value behavior occurs. No evidence was found for limiting Gaussian behavior for $\rho >1$ but with $0<\beta \left(\rho +1\right)<1$, as might be conjectured from quasistatic bundle models where $\beta \left(\rho +1\right)$ mimics the Weibull exponent for fiber strength.

We show that the capacity of a complex network that models a city street grid to support congested traffic can be optimized by using routes that collectively minimize the maximum ratio of betweenness to capacity in any link. Networks with a heterogeneous distribution of link capacities and with a heterogeneous transport load are considered. We find that overall traffic congestion and average travel times can be significantly reduced by a judicious use of slower and smaller capacity links.

A given set of data points in some feature space may be associated with a Schrödinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged dynamical scheme using a time-dependent Schrödinger equation. Moreover, we approximate this Hamiltonian formalism by a truncated calculation within a set of Gaussian wave functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states opening up the possibility of exploration of relationships among data points through observation of varying dynamical distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing such as dimensional reduction through singular-value decomposition or feature filtering.

Fractional Gaussian noise (fGn) is an important and widely used self-similar process, which is mainly parametrized by its Hurst exponent $\left(H\right)$. Many researchers have proposed methods for estimating the Hurst exponent of fGn. In this paper we put forward a modified periodogram method for estimating the Hurst exponent based on a refined approximation of the spectral density function. Generalizing the spectral exponent from a linear function to a piecewise polynomial, we obtained a closer approximation of the fGn’s spectral density function. This procedure is significant because it reduced the bias in the estimation of $H$. Furthermore, the averaging technique that we used markedly reduced the variance of estimates. We also considered the asymptotical unbiasedness of the method and derived the upper bound of its variance and confidence interval. Monte Carlo simulations showed that the proposed estimator was superior to a wavelet maximum likelihood estimator in terms of mean-squared error and was comparable to Whittle’s estimator. In addition, a real data set of Nile river minima was employed to evaluate the efficiency of our proposed method. These tests confirmed that our proposed method was computationally simpler and faster than Whittle’s estimator.

Although we can often observe time-series data of many elements, these elements do not always interact with each other. This paper proposes a scheme to estimate the interdependency among observed elements only by time-series data, which is useful for selecting essential elements to optimize multivariate prediction model. Because this estimation is a sort of combinatorial optimization problems, we applied the genetic algorithm as a method to moderate this problem. Through some simulations, we confirmed performance of our method, which can identify interaction of multivariate system and can improve its prediction accuracy. Especially, our method can be applied to predict real foreign-exchange markets even if system has nonstational property and its structure changes dynamically.

We have studied the dynamics of warm dense Li with near-elastic x-ray scattering. Li foils were heated and compressed using shock waves driven by 4-ns-long laser pulses. Separate 1-ns-long laser pulses were used to generate a bright source of 2.96 keV Cl Ly-$\alpha$ photons for x-ray scattering, and the spectrum of scattered photons was recorded at a scattering angle of $120°$ using a highly oriented pyrolytic graphite crystal operated in the von Hamos geometry. A variable delay between the heater and backlighter laser beams measured the scattering time evolution. Comparison with radiation-hydrodynamics simulations shows that the plasma is highly coupled during the first several nanoseconds, then relaxes to a moderate coupling state at later times. Near-elastic scattering amplitudes have been successfully simulated using the screened one-component plasma model. Our main finding is that the near-elastic scattering amplitudes are quite sensitive to the mean ionization state $\overline{Z}$ and by extension to the choice of ionization model in the radiation-hydrodynamics simulations used to predict plasma properties within the shocked Li.

A dynamical approach to recurrent and extreme events is developed focusing on the role of correlations and memory in the structure of the probability distributions and their low-order moments. The procedure is illustrated on homogeneous first and second order Markov chains, non-Markovian and nonhomogeneous processes and deterministic dynamical systems. Substantial differences with classical statistical theory as applied to independent identically distributed random variables are identified.

We discuss a method that allows us to compute the thermodynamic Casimir force at a given temperature in lattice models by performing a single Monte Carlo simulation. It is analogous to the one used by de Forcrand and co-workers in the study of ‘t Hooft loops and the interface tension in $\text{SU}\left(N\right)$ lattice gauge models in four dimensions. We test the method at the example of thin films in the $XY$ universality class. In particular we simulate the improved two-component ${\varphi }^4$ model on the simple cubic lattice. This allows us to compare with our previous study, where we have computed the Casimir force by numerically integrating energy densities over the inverse temperature.

We investigate the long-time behavior of the survival probability $P\left(t\right)$ of a mobile particle in $d$-dimensional continuous Euclidean media doped with noninteracting mobile traps. The particle is strictly subdiffusive, implying that its mean-square displacement grows as $t^{{\gamma }^{\prime }}$ with $0<{\gamma }^{\prime }<1$. Initially, the traps are scattered randomly and their subsequent mean-square displacement grows as $t^{\gamma }$ with $0<\gamma \le 1$. Instantaneous annihilation of the particle takes place upon contact with any of the traps. The solution to this problem is obtained by deriving lower and upper asymptotic bounds of the survival probability and showing that they converge to one another for long times, thereby unambiguously determining the long-time decay of $P\left(t\right)$. For $d\ge 2$ we find that at late times the survival probability is that of the pure target problem (the problem where the particle remains immobile) in agreement with previous studies for the $d=1$ case. These decay laws remain invariant over the whole $\gamma$ range as opposed to the dynamical crossover observed for the case of a purely diffusive particle $\left({\gamma }^{\prime }=1\right)$ where, for $\gamma <2/\left(2+d\right)$, the survival probability becomes that of the so-called trapping problem (the problem where the particle moves in a sea of static traps). This behavior implies that for sufficiently low values of $\gamma \left(\gamma <2/\left(2+d\right)\right)$ the survival probability becomes singular in the limit ${\gamma }^{\prime }\to 1$: trappinglike for ${\gamma }^{\prime }=1$ and targetlike for any ${\gamma }^{\prime }<1$.

Commonly, normal diffusive behavior is characterized by a linear dependence of the second central moment on time, $⟨x^2\left(t\right)⟩\propto t$, while anomalous behavior is expected to show a different time dependence, $⟨x^2\left(t\right)⟩\propto t^{\delta }$ with $\delta <1$ for subdiffusive and $\delta >1$ for superdiffusive motions. Here we explore in details the fact that this kind of qualification, if applied straightforwardly, may be misleading: there are anomalous transport motions revealing perfectly “normal” diffusive character $\left(⟨x^2\left(t\right)⟩\propto t\right)$ yet being non-Markov and non-Gaussian in nature. We use recently developed framework of Monte Carlo simulations which incorporates anomalous diffusion statistics in time and space and creates trajectories of such an extended random walk. For special choice of stability indices describing statistics of waiting times and jump lengths, the ensemble analysis of anomalous diffusion is shown to hide temporal memory effects which can be properly detected only by examination of formal criteria of Markovianity (fulfillment of the Chapman-Kolmogorov equation).