We examine a length scale that characterizes the spatial extent of heterogeneous dynamics in a glass-forming binary hard-sphere mixture up to the mode-coupling volume fraction ${\varphi }_c$. First, we characterize the system’s dynamics. Then, we utilize a method [Phys. Rev. Lett. 105, 217801 (2010)] to extract and analyze the ensemble-independent dynamic susceptibility ${\chi }_4(t)$ and the dynamic correlation length $\xi (t)$ for a range of times between the $\beta$ and $\alpha$ relaxation times. We find that in this time range the dynamic correlation length follows a volume fraction-independent master curve $\xi (t)~\ln (t)$. For longer times, $\xi (t)$ departs from this master curve and remains constant up to the largest time at which we can determine the length accurately. In addition to the previously established correlation ${\tau }_{\alpha }~\exp [\xi ({\tau }_{\alpha })]$ between the $\alpha$ relaxation time, ${\tau }_{\alpha }$, and the dynamic correlation length at this time, $\xi ({\tau }_{\alpha })$, we also find a similar correlation for the diffusion coefficient $D~\exp [\xi ({\tau }_{\alpha }){}^{\theta }]$ with $\theta \approx 0.6$. We discuss the relevance of these findings for different theories of the glass transition.

General symmetry arguments, dating back to de Gennes, dictate that at scales longer than the pitch, the low-energy elasticity of a chiral nematic liquid crystal (cholesteric) and of a Dzyaloshinskii-Morya (DM) spiral state in a helimagnet with negligible crystal symmetry fields (e.g., MnSi, FeGe) is identical to that of a smectic liquid crystal, thereby inheriting its rich phenomenology. Starting with a chiral Frank free energy (exchange and DM interactions of a helimagnet) we present a transparent derivation of the fully nonlinear Goldstone mode elasticity, which involves an analog of the Anderson-Higgs mechanism that locks the spiral orthonormal (director or magnetic moment) frame to the cholesteric (helical) layers. This shows explicitly the reduction of three orientational modes of a cholesteric down to a single-phonon Goldstone mode that emerges on scales longer than the pitch. At a harmonic level our result reduces to that derived many years ago by Lubensky and collaborators.

We describe general characteristics of the Hodgkin-Huxley neuron’s response to a periodic train of short current pulses with Gaussian noise. The deterministic neuron is bistable for antiresonant frequencies. When the stimuli arrive at the resonant frequency the firing rate is a continuous function of the current amplitude $I_0$ and scales as $(I_0-I_{\mathrm{th}}){}^{1/2}$, characteristic of a saddle-node bifurcation at the threshold $I_{\mathrm{th}}$. Intervals of continuous irregular response alternate with integer mode-locked regions with bistable excitation edge. There is an even-all multimodal transition between the 2 : 1 and 3 : 1 states in the vicinity of the main resonance, which is analogous to the odd-all transition discovered earlier in the high-frequency regime. For $I_0<I_{\mathrm{th}}$ and small noise the firing rate has a maximum at the resonant frequency. For larger noise and subthreshold stimulation the maximum firing rate initially shifts toward lower frequencies, then returns to higher frequencies in the limit of large noise. The stochastic coherence antiresonance, defined as a simultaneous occurrence of (i) the maximum of the coefficient of variation and (ii) the minimum of the firing rate vs the noise intensity, occurs over a wide range of parameter values, including monostable regions. Results of this work can be verified experimentally.

The actin cytoskeleton of adherent tissue cells often condenses into filament bundles contracted by myosin motors, so-called stress fibers, which play a crucial role in the mechanical interaction of cells with their environment. Stress fibers are usually attached to their environment at the endpoints, but possibly also along their whole length. We introduce a theoretical model for such contractile filament bundles which combines passive viscoelasticity with active contractility. The model equations are solved analytically for two different types of boundary conditions. A free boundary corresponds to stress fiber contraction dynamics after laser surgery and results in good agreement with experimental data. Imposing cyclic varying boundary forces allows us to calculate the complex modulus of a single stress fiber.

The problem of the helix-coil transition of biopolymers in explicit solvents, such as water, with the ability for hydrogen bonding with a solvent is addressed analytically using a suitably modified version of the Generalized Model of Polypeptide Chains. Besides the regular helix-coil transition, an additional coil-helix or reentrant transition is also found at lower temperatures. The reentrant transition arises due to competition between polymer-polymer and polymer-water hydrogen bonds. The balance between the two types of hydrogen bonding can be shifted to either direction through changes not only in temperature, but also by pressure, mechanical force, osmotic stress, or other external influences. Both polypeptides and polynucleotides are considered within a unified formalism. Our approach provides an explanation of the experimental difficulty of observing the reentrant transition with pressure and underscores the advantage of pulling experiments for studies of DNA. Results are discussed and compared with those reported in a number of recent publications with which a significant level of agreement is obtained.

The dynamics of technological, economic and social phenomena is controlled by how humans organize their daily tasks in response to both endogenous and exogenous stimulations. Queueing theory is believed to provide a generic answer to account for the often observed power-law distributions of waiting times before a task is fulfilled. However, the general validity of the power law and the nature of other regimes remain unsettled. Using anonymized data collected by Google at the World Wide Web level, we identify the existence of several additional regimes characterizing the time required for a population of Internet users to execute a given task after receiving a message. Depending on the under- or over-utilization of time by the population of users and the strength of their response to perturbations, the pure power law is found to be coextensive with an exponential regime (tasks are performed without too much delay) and with a crossover to an asymptotic plateau (some tasks are never performed).

Electric double-layer supercapacitors are a fast-rising class of high-power energy storage devices based on porous electrodes immersed in a concentrated electrolyte or ionic liquid. As yet there is no microscopic theory to describe their surprisingly large capacitance per unit volume (volumetric capacitance) of $~$$100$ F/cm${}^3$, nor is there a good understanding of the fundamental limits on volumetric capacitance. In this paper we present a non-mean-field theory of the volumetric capacitance of a supercapacitor that captures the discrete nature of the ions and the exponential screening of their repulsive interaction by the electrode. We consider analytically and via Monte Carlo simulations the case of an electrode made from a good metal and show that in this case the volumetric capacitance can reach the record values. We also study how the capacitance is reduced when the electrode is an imperfect metal characterized by some finite screening radius. Finally, we argue that a carbon electrode, despite its relatively large linear screening radius, can be approximated as a perfect metal because of its strong nonlinear screening. In this way the experimentally measured capacitance values of $~$$100$ F/cm${}^3$ may be understood.

Rounding border effects at the escape point of open integrable billiards are analyzed via the escape-time statistics and emission angles. The model is the rectangular billiard and the shape of the escape point is assumed to have a semicircular form. Stickiness, chaos, and self-similar structures for the escape times and emission angles are generated inside “backgammon” like stripes of initial conditions. These stripes are born at the boundary between two different emission angles but with the same escape times and when rounding effects increase they start to overlap generating a very rich dynamics. Tiny rounded borders (around $0.1\%$ from the whole billiard size) are shown to be sufficient to generate the sticky motion with power-law decay ${\gamma }_{\mathrm{esc}}=1.27$, while borders larger than $10\%$ are enough to produce escape times related to the chaotic motion. Escape exponents in the interval $1<{\gamma }_{\mathrm{esc}}<2$ are generated due to marginal unstable periodic orbits trapping alternately (in time) regular and chaotic trajectories.

We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semiclassical approximation of this system has an interesting fixed-point bifurcation structure. In the semiclassical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that the bifurcation structure leads to mixed-state entanglement between the nanomechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semiclassical bifurcation. Quantum signatures of the semiclassical limit cycles are presented.

Using numerical simulations, we study the separation of deformable bodies, such as capsules, vesicles, and cells, in deterministic lateral displacement devices, also known as bump arrays. These arrays comprise regular rows of obstacles such as micropillars whose arrangements are shifted between adjacent rows by a fixed amount. We show that, in addition to the zigzag and laterally displaced trajectories that have been observed experimentally, there exists a third type of trajectory which we call dispersive, characterized by seemingly random bumpings off the micropillars. These dispersive trajectories are observed only for large and rigid particles whose diameters are approximately more than half the gap size between micropillars and whose stiffness exceeds approximately $500$ MPa. We then map out the regions in phase space, spanned by the row shift, row separation, particle diameter, and particle deformability, in which the different types of trajectories are expected. We also show that, in this phase space, it is possible to transition from zigzag to dispersive trajectories, bypassing lateral displacement. Experimentally, this is undesirable because it limits the ability of the device to sort particles according to size. Finally, we discuss how our numerical simulations may be of use in device prototyping and optimization.

We present an efficient and exact Monte Carlo algorithm to simulate reversible aggregation of particles with dedicated binding sites. This method introduces a data structure of dynamic bond trees to record clusters and sequences of bond formations. The algorithm achieves a constant time cost for processing cluster association and a cost between $O(\log M)$ and $O(M)$ for processing bond dissociation in clusters with $M$ bonds. The algorithm is statistically exact and can reproduce results obtained by the standard method. We applied the method to simulate a trivalent ligand and a bivalent receptor clustering system and obtained an average scaling of $O(M^{0.45})$ for processing bond dissociation in acyclic aggregation, compared to a linear scaling with the cluster size in standard methods. The algorithm also demands substantially less memory than the conventional method.

Hydrodynamic simulations of strongly attractive rodlike colloids are performed with and without shear flow. In the absence of flow, the isotropic-nematic coexistence becomes isotropic-smectic A, and the interfacial properties clearly vary with increasing attraction strength. In the presence of shear flow, a new collective rotation appears in which the director rotates in the vorticity-flow plane in a similar fashion to the movement of the rotor of a helicopter.

In a recent work [M. Castellana and G. Parisi, Phys. Rev. E 82, 040105(R) (2010)], the large-scale behavior of the simplest non-mean-field spin-glass system has been analyzed, and the critical exponent related to the divergence of the correlation length has been computed at two loops within the $\epsilon$-expansion technique by two independent methods. By performing the explicit calculation of the critical exponents at two loops, one obtains that the two methods yield the same result. This shows that the underlying renormalization group ideas apply consistently in this disordered model, in such a way that an $\epsilon$-expansion can be set up. The question of the extension to high orders of this $\epsilon$-expansion is particularly interesting from the physical point of view. Indeed, once high orders of the series in $\epsilon$ for the critical exponents are known, one could check the convergence properties of the series, and find out if the ordinary series resummation techniques, yielding very accurate predictions for the Ising model, work also for this model. If this is the case, a consistent and predictive non-mean-field theory for such a disordered system could be established. In that regard, in this work we expose the underlying techniques of such a two-loop computation. We show with an explicit example that such a computation could be quite easily automatized, i.e., performed by a computer program, in order to compute high orders of the $\epsilon$-expansion, and so eventually make this theory physically predictive. Moreover, all the underlying renormalization group ideas implemented in such a computation are widely discussed and exposed.

Network structures are reconstructed from dynamical data by respectively naive mean field (nMF) and Thouless-Anderson-Palmer (TAP) approximations. TAP approximation adds simple corrections to the nMF approximation, taking into account the effect of the focused spin on itself via its influence on other neighboring spins. For TAP approximation, we use two methods to reconstruct the network: (a) iterative method; (b) casting the inference formula to a set of cubic equations and solving it directly. We investigate inference of the asymmetric Sherrington-Kirkpatrick (aS-K) model using asynchronous update. The solutions of the set of cubic equations depend on temperature $T$ in the aS-K model, and a critical temperature $T_c\approx 2.1$ is found. The two methods for TAP approximation produce the same results when the iterative method is convergent. Compared to nMF, TAP is somewhat better at low temperatures, but approaches the same performance as temperature increases. Both nMF and TAP approximation reconstruct better for longer data length $L$, but for the degree of improvement, TAP performs better than nMF.

We investigated the mixing and segregation of a system consisting of two different species of particles, having different charges, interacting through a pure Coulomb potential, and confined in a three-dimensional parabolic trap. The structure of the cluster and its normal mode spectrum are analyzed as a function of the relative charge and the relative number of different types of particles. We found that (a) the system can be in a mixed or segregated state depending on the relative charge ratio parameter and (b) the segregation process is mediated by a first or second order structural phase transition which strongly influences the magic cluster properties of the system.

In this paper we analyze some aspects of exponential flights, a stochastic process that governs the evolution of many random transport phenomena, such as neutron propagation, chemical or biological species migration, and electron motion. We introduce a general framework for $d$-dimensional setups and emphasize that exponential flights represent a deceivingly simple system, where in most cases closed-form formulas can hardly be obtained. We derive a number of exact (where possible) or asymptotic results, among which are the stationary probability density for two-dimensional systems, a long-standing issue in physics, and the mean residence time in a given volume. Bounded or unbounded domains as well as scattering or absorbing domains are examined, and Monte Carlo simulations are performed so as to support our findings.

We study the transport of paramagnetic colloidal particles on a patterned magnetic substrate with kinetic Monte Carlo and Brownian dynamics computer simulations. The planar substrate is decorated with point dipoles in either parallel or zigzag stripe arrangements and exposed to an additional external magnetic field that oscillates in time. For the case of parallel stripes we find that the magnitude and direction of the particle current is controlled by the tilt angle of the external magnetic field. The effect is reliably obtained in a wide range of ratios between temperature and magnetic permeability. Particle transport is achieved only when the period of oscillation of the external field is greater than a critical value. For the case of zigzag stripes a current is obtained using an oscillating external field normal to the substrate. In this case, transport is possible only in the vertex of the zigzag, giving rise to a narrow stream of particles. The magnitude and direction of the particle current are found to be controlled by a combination of the zigzag angle and the distance of the colloids from the substrate. Metropolis Monte Carlo and Brownian dynamics simulations predict results that are in good agreement with each other. Using kinetic Monte Carlo we find that at high density the particle transport is hindered by jamming.

Random laser action in organic materials is of great topical interest that is fueled by the rapid development of active compounds and new dye molecules. We propose a pure-diffusive model to describe the strong connection established between a dye-host interaction and the scattering when considering an anisotropic complex fluid. The model considers multiple scattering induced by dielectric tensor fluctuations and a suitable quantistic description for light amplification in order to explain the generation of the narrow-band blue-shifted lasing mode experimentally observed in such systems. We also find that the introduction of a strong intermolecular force field provides the condition to enhance diffusive processes. The agreement between experimental observations and simulations advances the understanding of the physical mechanism behind mode selection in these systems.

Density functional theory (DFT) has been employed in a conformational study of a bent-core PBBC homologous series. IR spectra, GIAO-DFT chemical shielding tensors (CSTs), and molecular susceptibility tensors (MSTs) are theoretically calculated for various optimized conformations established by searching the potential energy surface of each PBBC V-shaped molecule. The IR results could aid the understanding of vibration normal modes, while the MST results can illuminate the alignment properties of the V-shaped molecules in an external magnetic field. CSTs of the aromatic carbons, and those previously measured by the 2D-NMR SUPER technique (with some ${}^{13}\mathrm{C}$ NMR peaks reassigned for correctness based on new DFT calculations), were found to be in good agreement. These verified experimental CSTs are then used to revisit the ${}^{13}\mathrm{C}$ NMR data to yield structural and local orientational order parameters for two members of the PBBC series. The PBBC series studied using the combined DFT-${}^{13}\mathrm{C}$ NMR approach strongly supports the notion that lesser populated conformational states found by DFT could be reached in the studied mesogens 10DClPBBC and 11ClPBBC upon decreasing temperature, as revealed by the change in the bend angle determined by NMR and identified with those of the DFT molecular structures optimized for various conformers.

We develop a theory to explain the origin of the static and dynamical memory effects in transcription-factor-mediated transcription activation. Our results suggest that the following inequality conditions should be satisfied to observe such memory effects: (a) ${\tau }_L\gg max({\tau }_R,{\tau }_E),$ (b) ${\tau }_{\mathit{LT}}\gg {\tau }_T,$ and (c) ${\tau }_I⩾({\tau }_{\mathit{EL}}+{\tau }_{\mathit{TR}})$ where ${\tau }_L$ is the average time required for the looping-mediated spatial interactions of enhancer—transcription-factor complex with the corresponding promoter—RNA-polymerase or eukaryotic RNA polymerase type II (PolII in eukaryotes) complex that is located $L$ base pairs away from the cis-acting element, $({\tau }_R,{\tau }_E)$ are respectively the search times required for the site-specific binding of the RNA polymerase and the transcription factor with the respective promoter and the cis-regulatory module, ${\tau }_{\mathit{LT}}$ is the time associated with the relaxation of the looped-out segment of DNA that connects the cis-acting site and promoter, ${\tau }_T$ is the time required to generate a complete transcript, ${\tau }_I$ is the transcription initiation time, ${\tau }_{\mathit{EL}}$ is the elongation time, and ${\tau }_{\mathit{TR}}$ is the termination time. We have theoretically derived the expressions for the various searching, looping, and loop-relaxation time components. Using the experimentally determined values of various time components we further show that the dynamical memory effects cannot be experimentally observed whenever the segment of DNA that connects the cis-regulatory element with the promoter is not loaded with bulky histone bodies. Our analysis suggests that the presence of histone-mediated compaction of the connecting segment of DNA can result in higher values of looping and loop-relaxation times, which is the origin of the static memory in the transcription activation that is mediated by the memory gene loops in eukaryotes.