The disconnectivity graph (DG) is widely used to represent energy landscapes. Although powerful numerical methods have been developed to construct DGs for continuous potential-energy surfaces, they have difficulties in applications to discrete Hamiltonians as the case of spin-glass models. When the configuration space is large, brute force enumeration of all configurations to build a DG is not practical. We propose an alternative approach to construct DGs based on recursive partition of Monte Carlo samples from microcanonical ensembles. To characterize energy landscapes, we define the local density of states (LDOS) on a DG, with which one can compute many thermodynamic properties over local energy basins for any temperature. Estimation of LDOS is developed with DG construction. We further propose the concepts of tree entropy and local escape probability, both of which are functions of local density of states, to capture the symmetry and the roughness of a Boltzmann distribution, respectively. Our approach is applied to a study of the Sherrington-Kirkpatrick spin-glass model with $N$ varying between 20 and 100 spins. We observe that the energy landscape is extremely asymmetric and there exists a sharp increase in local escape probability preceding the transition from spin glass to paramagnetic phase.

In bulk systems the calculation of the main thermodynamic quantities leads to the same expectation values in the thermodynamic limit, regardless of the choice of the statistical ensemble. Single linear molecules can be still regarded as statistical systems, where the thermodynamic limit is represented by infinitely long chains. The question of equivalence between different ensembles is not at all obvious and has been addressed in the literature, with sometimes contradicting conclusions. We address this problem by studying the scaling properties of the ensemble difference for two different chain models as a function of the degree of polymerization. By characterizing the scaling behavior of the difference between the isotensional (Gibbs) and isometric (Helmholtz) ensembles in the transition from the low-stretching to the high-stretching regime, we show that ensemble equivalence cannot be reached for macroscopic chains in the low force regime, and we characterize the transition from the inequivalence to the equivalence regime.

Insulating particles can become highly electrified during powder handling, volcanic eruptions, and the wind-blown transport of dust, sand, and snow. Measurements in these granular systems have found that smaller particles generally charge negatively, while larger particles charge positively. These observations are puzzling since particles in these systems are generally chemically identical and thus have no contact potential difference. We show here that simple geometry leads to a net transfer of electrons from larger to smaller particles, in agreement with these observations. We integrate this charging mechanism into the first quantitative charging scheme for a granular system of identical insulators and show that its predictions are in agreement with measurements. Our theory thus seems to provide an explanation for the hitherto puzzling phenomenon of the size-dependent charging of granular systems of identical insulators.

Starting from the kinetic equations for the fluctuations and correlations of a dilute gas of inelastic hard spheres or disks, a Boltzmann-Langevin equation for the one-particle distribution function of the homogeneous cooling state is constructed. This equation is the linear Boltzmann equation with a fluctuating white-noise term. Balance equations for the fluctuating hydrodynamic fields are derived. New fluctuating forces appear as compared with the elastic limit. The particular case of the transverse velocity field is investigated in detail. Its fluctuations can be described by means of a Langevin equation, but exhibiting two main differences with the Landau-Lifshitz theory: the noise is not white, and its second moment is not determined by the shear viscosity. This shows that the fluctuation-dissipation relations for molecular fluids do not straightforwardly carry over to inelastic gases. The theoretical predictions are shown to be in good agreement with molecular-dynamics simulation results.

We present the results of first-principles calculations for the electron tunnel current through hydrogen-bonded DNA base pairs and for (deoxy)nucleoside-nucleobase pairs. Electron current signals either through a base pair or through a deoxynucleoside-nucleobase pair are a potential mechanism for recognition or identification of the DNA base on a single-stranded DNA polymer. Four hydrogen-bonded complexes are considered: guanine-cytosine, diaminoadenine-thymine, adenine-thymine, and guanine-thymine. First, the electron tunneling properties are examined through their complex band structure (CBS) and the metal contact’s Fermi-level alignment. For gold contacts, the metal Fermi level lies near the highest occupied molecular orbital for all DNA base pairs. The decay constant determined by the complex band structure at the gold Fermi level shows that tunnel current decays more slowly for base pairs with three hydrogen bonds (guanine-cytosine and diaminoadenine-thymine) than for base pairs with two hydrogen bonds (adenine-thymine and guanine-thymine). The decay length and its dependence on hydrogen-bond length are examined. Second, the conductance is computed using density functional theory Green’s-function scattering methods and these results agree with estimates made from the tunneling decay constant obtained from the CBS. Changing from a base pair to a deoxynucleoside-nucleobase complex shows a significant decrease in conductance. It also becomes difficult to distinguish the current signal by only the number of hydrogen bonds.

We report observations of in vitro DNA compaction into toroids in the absence of any condensing agent. The DNA toroid formation is induced by geometry confinement from microdroplets on mica surfaces. With AFM imaging we show that the confined DNA molecules may take the form of random coils or semiordered folded loops with large microdroplets, while they readily take the form of compact and ordered toroids when the microdroplet sizes are small enough. To better understand these phenomena, we carried out coarse-grained Brownian dynamics simulation, obtaining results that were in good agreement with the experimental observations. The simulation reveals that the toroid formation is sensitive to not only the microdroplet size, but also the DNA stiffness.

The proposed model demonstrates the allosteric role of the two-domain region of the receptor protein in the increased lifetimes of biological receptor/ligand bonds subjected to an external force. The interaction between the domains is represented by a bounded potential, containing two minima corresponding to the attached and separated conformations of the two protein domains. The dissociative potential with a single minimum describing receptor/ligand binding fluctuates between deep and shallow states, depending on whether the domains are attached or separated. A number of valuable analytic expressions are derived and are used to interpret experimental data for two catch bonds. The P-selectin/P-selectin-glycoprotein-ligand-1 (PSGL-1) bond is controlled by the interface between the epidermal growth factor (EGF) and lectin domains of P-selectin, and the type 1 fimbrial adhesive protein (FimH)/mannose bond is governed by the interface between the lectin and pilin domains of FimH. Catch-binding occurs in these systems when the external force stretches the receptor proteins and increases the interdomain distance. The allosteric effect is supported by independent measurements, in which the domains are kept separated by attachment of another ligand. The proposed model accurately describes the experimentally observed anomalous behavior of the lifetimes of the P-selectin/PSGL-1 and FimH/mannose complexes as a function of applied force and provides valuable insights into the mechanism of catch-binding.

We study a system of self-propelled agents with the restricted vision. The field of vision of each agent is only a sector of disk bounded by two radii and the included arc. The inclination of these two radii is characterized by the view angle. The consideration of restricted vision is closer to the reality because natural swarms usually do not have a panoramic view. Interestingly, we find that there exists an optimal view angle, leading to the fastest direction consensus. The value of the optimal view angle depends on the density, the interaction radius, the absolute velocity of swarms, and the strength of noise. Our findings may invoke further efforts and attentions to explore the underlying mechanism of the collective motion.

This Rapid Communication presents an analytical study of the bouncing of a completely inelastic ball on a vertically vibrated plate. The interplay of saddle-node and period-doubling bifurcations leads to an intricate structure of the bifurcation diagram with uncommon properties, such as an infinity of bifurcation cascades in a finite range of the control parameter $\Gamma$. A pseudochaotic behavior, consisting in arbitrarily long and complex periodic sequences, is observed through this generic system.

We study the dynamics of spatiotemporal pattern formation in a nonlinear proliferation system (e.g., cell division supported on a field of nutrition), in which the mechanism of activation and its self-suppression is simultaneously implemented. This dynamical model has been numerically realized with coupled cellular automata (CA), and various long-standing spatiotemporal patterns have been observed. Among others, a successive generation of traveling waves by implanting a spot of cells onto the field consisting of nutrition and activator is particularly interesting. This takes place despite the fact that the present reaction network has a stable fixed point and therefore autonomous temporal oscillatory does not exist in the mean field. Indeed, the reaction-diffusion equation method (RD) applied to this network reproduces only a single excitable wave and soon falls into a steady state (a fixed point) without the following propagating waves. This system, having a stable fixed point, is an excitable system of different kind from the FitzHugh-Nagumo model in that it can generate a pulse propagating outwards by adding only a single cell onto it from outside the system. The present excitation upon dropping a cell is amplified to macroscopic level by a hidden dynamics of oscillation between the activation and its self-suppression. A pulse thus generated is propagated in space time with the help of diffusion. Through a precise comparison between CA and RD, it is found that a very small amount of residue of the cells and activators, which are left unburned in the stochastic treatment of reactions by the CA, becomes a seed to excite the system and generate the next pulse wave. This newly born wave can leave another seed of reaction in the field after its propagation. Based on this analysis, we account for the appearance of other patterns observed. A possible control of these patterns by varying the spatial distribution of initial concentration of the relevant agents such as the activator is also discussed.

We investigate the effect of confinement on drop formation in microfluidic devices. The presence or absence of drop formation is studied for two immiscible coflowing liquids in a microfluidic channel, where the channel width is considerably larger than the channel height. We show that stability of the inner fluid thread depends on the channel geometry: when the width of the inner fluid is comparable to or larger than the channel height, hydrodynamic instabilities are suppressed, and a stable jet that does not break into drops results; otherwise, the inner fluid breaks into drops, in either a dripping or jetting regime. We present a model that accounts for the data and experimentally exploit this effect of geometric confinement to induce the breakup of a jet at a spatially defined location.

It is shown that linear separation relations are fundamental objects for integration by quadratures of Stäckel-separable Liouville-integrable systems (the so-called Stäckel systems). These relations are further employed for the classification of Stäckel systems. Moreover, we prove that any Stäckel-separable Liouville-integrable system can be lifted to a bi-Hamiltonian system of Gel’fand-Zakharevich type. In conjunction with other known result this implies that the existence of bi-Hamiltonian representation of Liouville-integrable systems is a necessary condition for Stäckel separability.

We present a unified scaling theory for the structural behavior of polymers embedded in a disordered energy substrate. An optimal polymer configuration is defined as the polymer configuration that minimizes the sum of interacting energies between the monomers and the substrate. The fractal dimension of the optimal polymer in the limit of strong disorder (SD) was found earlier to be larger than the fractal dimension in weak disorder (WD). We introduce a scaling theory for the crossover between the WD and SD limits. For polymers of various sizes in the same disordered substrate we show that polymers with a small number of monomers $N⪡N^{\ast }$ will behave as in SD, while large polymers with length $N⪢N^{\ast }$ will behave as in WD. This implies that small polymers will be relatively more compact compared to large polymers even in the same substrate. The crossover length $N^{\ast }$ is a function of $\nu$ and $a$, where $\nu$ is the percolation correlation length exponent and $a$ is the parameter which controls the broadness of the disorder. Furthermore, our results show that the crossover between the strong and weak disorder limits can be seen even within the same polymer configuration. If one focuses on a segment of size $n⪡N^{\ast }$ within a long polymer $\left(N⪢N^{\ast }\right)$ that segment will have a higher fractal dimension compared to a segment of size $n⪢N^{\ast }$.

We propose a comprehensive dynamical model for cooperative motion of self-propelled particles, e.g., flocking, by combining well-known elements such as velocity-alignment interactions, spatial interactions, and angular noise into a unified Lagrangian treatment. Noise enters into our model in an especially realistic way: it incorporates correlations, is highly nonlinear, and it leads to a unique collective behavior. Our results show distinct stability regions and an apparent change in the nature of one class of noise-induced phase transitions, with respect to the mean velocity of the group, as the range of the velocity-alignment interaction increases. This phase-transition change comes accompanied with drastic modifications of the microscopic dynamics, from nonintermittent to intermittent. Our results facilitate the understanding of the origin of the phase transitions present in other treatments.

In this paper, we study exactly the thermal conductance for a low dimensional system represented by two coupled massive Brownian particles, both directly and via a Green-Kubo expression. Both approaches give exactly the same result. We also obtain exactly the steady-state probability distribution for that system by means of time averaging.

In a recent paper [Phys. Rev. Lett. 100, 164101 (2008)] and within the context of quantized chaotic billiards, random plane-wave and semiclassical theoretical approaches were applied to an example of a relatively new class of statistical measures, i.e., measures involving both complete spatial integration and energy summation as essential ingredients. A quintessential example comes from the desire to understand the short-range approximation to the first-order ground-state contribution of the residual Coulomb interaction. Billiards, fully chaotic or otherwise, provide an ideal class of systems on which to focus as they have proven to be successful in modeling the single-particle properties of a Landau-Fermi liquid in typical mesoscopic systems, i.e., closed or nearly closed quantum dots. It happens that both theoretical approaches give fully consistent results for measure averages, but that somewhat surprisingly for fully chaotic systems the semiclassical theory gives a much improved approximation for the fluctuations. Comparison of the theories highlights a couple of key shortcomings inherent in the random plane-wave approach. This paper contains a complete account of the theoretical approaches, elucidates the two shortcomings of the oft-relied-upon random plane-wave approach, and treats non-fully-chaotic systems as well.

We propose a Monte Carlo methodology for the joint estimation of unobserved dynamic variables and unknown static parameters in chaotic systems. The technique is sequential, i.e., it updates the variable and parameter estimates recursively as new observations become available, and, hence, suitable for online implementation. We demonstrate the validity of the method by way of two examples. In the first one, we tackle the estimation of all the dynamic variables and one unknown parameter of a five-dimensional nonlinear model using a time series of scalar observations experimentally collected from a chaotic ${\text{CO}}_2$ laser. In the second example, we address the estimation of the two dynamic variables and the phase parameter of a numerical model commonly employed to represent the dynamics of optoelectronic feedback loops designed for chaotic communications over fiber-optic links.

We propose the use of mixing strategies to accelerate the convergence of the common iterative algorithms utilized in quantum optimal control theory (QOCT). We show how the nonlinear equations of QOCT can be viewed as a “fixed-point” nonlinear problem. The iterative algorithms for this class of problems may benefit from mixing strategies, as it happens, e.g., in the quest for the ground-state density in Kohn-Sham density-functional theory. We demonstrate, with some numerical examples, how the same mixing schemes utilized in this latter nonlinear problem may significantly accelerate the QOCT iterative procedures.

We consider the critical spin-spin correlation function of the Ashkin-Teller and Baxter models. By using path-integral techniques in the continuum description of these models in terms of fermion fields, we show that the correlation decays with distance with the same critical exponent as the Ising model. The procedure is straightforwardly extended to take into account the presence of a line defect. Thus we find that in these altered models the critical index of the magnetic correlation on the defect coincides with the one of the defective two-dimensional Ising or Bariev model.

We present a mean field model for coagulation $\left(A+A\to A\right)$ and annihilation $\left(A+A\to 0\right)$ reactions on lattices of traps with a distribution of depths reflected in a distribution of mean escape times. The escape time from each trap is exponentially distributed about the mean for that trap, and the distribution of mean escape times is a power law. Even in the absence of reactions, the distribution of particles over sites changes with time as particles are caught in ever deeper traps, that is, the distribution exhibits aging. Our main goal is to explore whether the reactions lead to further (time dependent) changes in this distribution.