We study theoretically the kinetics of mRNA translocation in the wild-type (WT) Escherichia coli ribosome, which is composed of a small $30\mathrm{S}$ and large $50\mathrm{S}$ subunit, and the ribosomes with mutations to some intersubunit bridges such as B1a, B4, B7a, and B8. The theoretical results reproduce well the available in vitro experimental data on the biphasic kinetics of the forward mRNA translocation catalyzed by elongation factor G (EF-G) hydrolyzing GTP, which can be best fit by the sum of two exponentials, and the monophasic kinetics of the spontaneous reverse mRNA translocation in the absence of the elongation factor, which can be best fit by a single-exponential function, in both the WT and mutant ribosomes. We show that both the mutation-induced increase in the maximal rate of the slow phase for the forward mRNA translocation and that in the rate of the spontaneous reverse mRNA translocation result from a reduction in the intrinsic energy barrier to resist the rotational movements between the two subunits, giving the same degree of increase in the two rates. The mutation-induced increase in the maximal rate of the fast phase for the forward mRNA translocation results mainly from the increase in the rate of the ribosomal unlocking, a conformational change in the ribosome that widens the mRNA channel for the mRNA translocation to take place, which could be partly due to the effect of the mutation on the intrasubunit 30S head rotation. Moreover, we study the translation rate of the WT and mutant ribosomes. It is shown that the translation rate versus the concentration of EF-G–GTP does not follow the Michaelis-Menten (MM) kinetics, which is in sharp contrast to the general property of other enzymes that the rate of the enzymatic reaction versus the concentration of a substrate follows the MM kinetics. The physical origin of this non-MM kinetics for the ribosome is revealed.

Finite-sized populations of spiking elements are fundamental to brain function but also are used in many areas of physics. Here we present a theory of the dynamics of finite-sized populations of spiking units, based on a quasirenewal description of neurons with adaptation. We derive an integral equation with colored noise that governs the stochastic dynamics of the population activity in response to time-dependent stimulation and calculate the spectral density in the asynchronous state. We show that systems of coupled populations with adaptation can generate a frequency band in which sensory information is preferentially encoded. The theory is applicable to fully as well as randomly connected networks and to leaky integrate-and-fire as well as to generalized spiking neurons with adaptation on multiple time scales.

Small-world networks—complex networks characterized by a combination of high clustering and short path lengths—are widely studied using the paradigmatic model of Watts and Strogatz (WS). Although the WS model is already quite minimal and intuitive, we describe an alternative formulation of the WS model in terms of a distance-dependent probability of connection that further simplifies, both practically and theoretically, the generation of directed and undirected WS-type small-world networks. In addition to highlighting an essential feature of the WS model that has previously been overlooked, namely the equivalence to a simple distance-dependent model, this alternative formulation makes it possible to derive exact expressions for quantities such as the degree and motif distributions and global clustering coefficient for both directed and undirected networks in terms of model parameters.

Diffusion can be strongly affected by ballistic flights (long jumps) as well as long-lived sticking trajectories (long sticks). Using statistical inference techniques in the spirit of Granger causality, we investigate the appearance of long jumps and sticks in molecular-dynamics simulations of diffusion in a prototype system, a benzene molecule on a graphite substrate. We find that specific fluctuations in certain, but not all, internal degrees of freedom of the molecule can be linked to either long jumps or sticks. Furthermore, by changing the prevalence of these predictors with an outside influence, the diffusion of the molecule can be controlled. The approach presented in this proof of concept study is very generic and can be applied to larger and more complex molecules. Additionally, the predictor variables can be chosen in a general way so as to be accessible in experiments, making the method feasible for control of diffusion in applications. Our results also demonstrate that data-mining techniques can be used to investigate the phase-space structure of high-dimensional nonlinear dynamical systems.

Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as pointlike objects moving along trajectories with a constant velocity. Interaction with medium boundaries alters this velocity and may often result in a reflection of the drift trajectory. Such reflections have diverse characteristics and are known to be highly nonspecular in general. In this context we apply the theory of response functions, which via numerically computable integrals, reduces the reaction-diffusion equations governing the whole excitable medium to the dynamics of just the rotation center and rotation phase of a spiral wave. Spiral reflection trajectories are computed by this method for both small- and large-core spiral waves in the Barkley model. Such calculations provide insight into the process of reflection as well as explanations for differences in trajectories across parameters, including the effects of incidence angle and forcing amplitude. Qualitative aspects of these results are preserved far beyond the asymptotic limit of weak boundary effects and slow resonant drift.

Convergent cross-mapping (CCM) is a technique for computing specific kinds of correlations between sets of times series. It was introduced by Sugihara et al. [Science 338, 496 (2012).] and is reported to be “a necessary condition for causation” capable of distinguishing causality from standard correlation. We show that the relationships between CCM correlations proposed by Sugihara et al. do not, in general, agree with intuitive concepts of “driving” and as such should not be considered indicative of causality. It is shown that the fact that the CCM algorithm implies causality is a function of system parameters for simple linear and nonlinear systems. For example, in a circuit containing a single resistor and inductor, both voltage and current can be identified as the driver depending on the frequency of the source voltage. It is shown that the CCM algorithm, however, can be modified to identify relationships between pairs of time series that are consistent with intuition for the considered example systems for which CCM causality analysis provided nonintuitive driver identifications. This modification of the CCM algorithm is introduced as “pairwise asymmetric inference” (PAI) and examples of its use are presented.

We investigate localization of low-energy modes of the Laplacian with a point scatterer on a rectangular plate. We observe that the point scatterer acts as a barrier confining the low-level modes to one side of the plate while assuming the Dirichlet boundary condition at a point does not induce this type of localization. This low-energy phenomenon extends to higher modes as we increase the eccentricity of the plate.

In this study we present direct numerical simulation results of the Richtmyer-Meshkov instability (RMI) initiated by $\text{Ma}=1.05,\text{Ma}=1.2$, and $\text{Ma}=1.5$ shock waves interacting with a perturbed planar interface between air and $S{F}_6$. At the lowest shock Mach number the fluids slowly mix due to viscous diffusion, whereas at the highest shock Mach number the mixing zone becomes turbulent. When a minimum critical Taylor microscale Reynolds number is exceeded, an inertial range spectrum emerges, providing further evidence of transition to turbulence. The scales of turbulent motion, i.e., the Kolmogorov length scale, the Taylor microscale, and the integral length, scale are presented. The separation of these scales is found to increase as the Reynolds number is increased. Turbulence statistics, i.e., the probability density functions of the velocity and its longitudinal and transverse derivatives, show a self-similar decay and thus that turbulence evolving from RMI is not fundamentally different from isotropic turbulence, though nominally being only isotropic and homogeneous in the transverse directions.

The solution of the inverse scattering problem for the one-dimensional Schrödinger equation is given by the Marchenko equation. Recently, a Marchenko-type equation has been derived for three-dimensional (3D) acoustic wave fields, whose solution has been shown to recover the Green's functions from points within the medium to its exterior, using only single-sided scattered data. Here we extend this approach to 3D vectorial wave fields that satisfy the elastodynamic wave equation and recover Green's functions from points interior to an elastic, solid-state medium from purely external and one-sided measurements. The method is demonstrated in a solid-earth-like model to construct Green's functions using only subsurface sources, from earth-surface force and deformation sources and particle velocity and stress measurements.

We analyze the properties of naturally formed nanobubbles in Lennard-Jones molecular dynamics simulations of liquid-to-vapor nucleation in the boiling and the cavitation regimes. The large computational volumes provide a realistic environment at unchanging average temperature and liquid pressure, which allows us to accurately measure properties of bubbles from their inception as stable, critically sized bubbles, to their continued growth into the constant speed regime. Bubble gas densities are up to $50\%$ lower than the equilibrium vapor densities at the liquid temperature, yet quite close to the gas equilibrium density at the lower gas temperatures measured in the simulations: The latent heat of transformation results in bubble gas temperatures up to $25\%$ below those of the surrounding bulk liquid. In the case of rapid bubble growth—typical for the cavitation regime—compression of the liquid outside the bubble leads to local temperature increases of up to $5\%$, likely significant enough to alter the surface tension as well as the local viscosity. The liquid-vapor bubble interface is thinner than expected from planar coexistence simulations by up to $50\%$. Bubbles near the critical size are extremely nonspherical, yet they quickly become spherical as they grow. The Rayleigh-Plesset description of bubble-growth gives good agreement in the cavitation regime.

We discuss the numerically stable, spectral-domain computation and extraction of the scattered electromagnetic field excited by distributed sources embedded in planar-layered environments, where each layer may exhibit arbitrary and independent electrical and magnetic anisotropic response and loss profiles. This stands in contrast to many standard spectral-domain algorithms that are restricted to computing the fields radiated by Hertzian dipole sources in planar-layered environments where the media possess azimuthal-symmetric material tensors (i.e., isotropic, and certain classes of uniaxial, media). Although computing the scattered field, particularly when due to distributed sources, appears (from the analytical perspective, at least) relatively straightforward, different procedures within the computation chain, if not treated carefully, are inherently susceptible to numerical instabilities and (or) accuracy limitations due to the potential manifestation of numerically overflown and (or) numerically unbalanced terms entering the chain. Therefore, primary emphasis herein is given to effecting these tasks in a numerically stable and robust manner for all ranges of physical parameters. After discussing the causes behind, and means to mitigate, these sources of numerical instability, we validate the algorithm's performance against closed-form solutions. Finally, we validate and illustrate the applicability of the proposed algorithm in case studies concerning active remote sensing of marine hydrocarbon reserves embedded deep within lossy, planar-layered media.

We study diffusion on a periodic billiard table with an infinite horizon in the limit of narrow corridors. An effective trapping mechanism emerges according to which the process can be modeled by a Lévy walk combining exponentially distributed trapping times with free propagation along paths whose precise probabilities we compute. This description yields an approximation of the mean squared displacement of infinite-horizon billiards in terms of two transport coefficients, which generalizes to this anomalous regime the Machta-Zwanzig approximation of normal diffusion in finite-horizon billiards [J. Machta and R. Zwanzig, Phys. Rev. Lett. 50, 1959 (1983)].

We study the statistics of the condition number $\kappa ={\lambda }_{\max }/{\lambda }_{\min }$ (the ratio between largest and smallest squared singular values) of $N\times M$ Gaussian random matrices. Using a Coulomb fluid technique, we derive analytically and for large $N$ the cumulative $\mathcal{P}(\kappa <x)$ and tail-cumulative $\mathcal{P}(\kappa >x)$ distributions of $\kappa$. We find that these distributions decay as $\mathcal{P}(\kappa <x)\approx exp[-\beta N^2{\Phi }_{-}\left(x\right)]$ and $\mathcal{P}(\kappa >x)\approx exp[-\beta N{\Phi }_{+}\left(x\right)]$, where $\beta$ is the Dyson index of the ensemble. The left and right rate functions ${\Phi }_{\pm }\left(x\right)$ are independent of $\beta$ and calculated exactly for any choice of the rectangularity parameter $\alpha =M/N-1>0$. Interestingly, they show a weak nonanalytic behavior at their minimum $\langle \kappa \rangle$ (corresponding to the average condition number), a direct consequence of a phase transition in the associated Coulomb fluid problem. Matching the behavior of the rate functions around $\langle \kappa \rangle$, we determine exactly the scale of typical fluctuations $\sim O\left(N^{-2/3}\right)$ and the tails of the limiting distribution of $\kappa$. The analytical results are in excellent agreement with numerical simulations.

In this work we study the thermal rectification efficiency of a one-dimensional mass-graded anharmonic oscillator lattice at large system sizes. A modest increase in rectification is observed. When the magnitude of the mass gradient scales with the system size, the aforementioned effect increases substantially. This result can be unmistakeably attributed to an asymmetry in the local temperature profile obtained for the employed parameter values.

It is difficult to relate the properties of liquids and glasses directly to their structure because of complexity in the structure that defies precise definition. The potential energy landscape (PEL) approach is a very insightful way to conceptualize the structure-property relationship in liquids and glasses, particularly the effect of temperature and history. However, because of the highly multidimensional nature of the PEL it is hard to determine, or even visualize, the actual details of the energy landscape. In this article we introduce a modified concept of the local energy landscape (LEL), which is limited in phase space, and demonstrate its usefulness using molecular dynamics simulation on a simple liquid at high temperatures. The local energy landscape is given as a function of the local coordination number, the number of the nearest-neighbor atoms. The excitation in the LEL corresponds to the so-called β-relaxation process. The LEL offers a simple but useful starting point to discuss complex phenomena in liquids and glasses.

Inspired by microscopic Paramecia which use trichocyst extrusion to propel themselves away from thermal aggression, we propose a macroscopic experiment to study the stability of a slender beam extruded in a highly viscous fluid. Piano wires were extruded axially at constant speed in a tank filled with corn syrup. The force necessary to extrude the wire was measured to increase linearly at first until the compressive viscous force causes the wire to buckle. A numerical model, coupling a lengthening elastica formulation with resistive-force theory, predicts a similar behavior. The model is used to study the dynamics at large time when the beam is highly deformed. It is found that at large time, a large deformation regime exists in which the force necessary to extrude the beam at constant speed becomes constant and length independent. With a proper dimensional analysis, the beam can be shown to buckle at a critical length based on the extrusion speed, the bending rigidity, and the dynamic viscosity of the fluid. Hypothesizing that the trichocysts of Paramecia must be sized to maximize their thrust per unit volume as well as avoid buckling instabilities, we predict that their bending rigidity must be about $3\times {10}^{-9}\mathrm{N}\mu {\mathrm{m}}^2$. The verification of this prediction is left for future work.

Many-particle effects in escapes of hard disks from a square box via a hole are discussed in a viewpoint of dynamical systems. Starting from $N$ disks in the box at the initial time, we calculate the probability $P_n\left(t\right)$ for at least $n$ disks to remain inside the box at time $t$ for $n=1,2,...,N$. At early times, the probabilities $P_n\left(t\right),n=2,3,...,N-1$, are described by superpositions of exponential decay functions. On the other hand, after a long time the probability $P_n\left(t\right)$ shows a power-law decay $\sim t^{-2n}$ for $n\ne 1$, in contrast to the fact that it decays with a different power law $\sim t^{-n}$ for cases without any disk-disk collision. Chaotic or nonchaotic properties of the escape systems are discussed by the dynamics of a finite-time largest Lyapunov exponent, whose decay properties are related with those of the probability $P_n\left(t\right)$.

A two-level atomic system as a working substance is used to set up a refrigerator consisting of two quantum adiabatic and two isochoric processes (two constant-frequency processes ${\omega }_a$ and ${\omega }_b$ with ${\omega }_a<{\omega }_b)$, during which the two-level system is in contact with two heat reservoirs at temperatures $T_h$ and $T_c(<T_h)$. Considering finite-time operation of two isochoric processes, we derive analytical expressions for cooling rate $R$ and coefficient of performance (COP) $\varepsilon$. The COP at maximum $\chi (=\varepsilon R)$ figure of merit is numerically determined, and it is proved to be in nice agreement with the so-called Curzon and Ahlborn COP ${\varepsilon }_{\text{CA}}=\sqrt{1+{\varepsilon }_C}-1$, where ${\varepsilon }_C=T_c/(T_h-T_c)$ is the Carnot COP. In the high-temperature limit, the COP at maximum $\chi$ figure of merit, ${\varepsilon }^{*}$, can be expressed analytically by ${\varepsilon }^{*}={\varepsilon }_{+}\equiv \left(\sqrt{9+8{\varepsilon }_C}-3\right)/2$, which was derived previously as the upper bound of optimal COP for the low-dissipation or minimally nonlinear irreversible refrigerators. Within the context of irreversible thermodynamics, we prove that the value of ${\varepsilon }_{+}$ is also the upper bound of COP at maximum $\chi$ figure of merit when we regard our model as a linear irreversible refrigerator.

The mode-coupling theory of the glass transition treats the dynamics of supercooled liquids in terms of two-point density correlation functions. Here we consider a generalized, hierarchical formulation of schematic mode-coupling equations in which the full basis of multipoint density correlations is taken into account. By varying the parameters that control the effective contributions of higher-order correlations, we show that infinite hierarchies can give rise to both sharp and avoided glass transitions. Moreover, small changes in the form of the coefficients result in different scaling behaviors of the structural relaxation time, providing a means to tune the fragility in glass-forming materials. This demonstrates that the infinite-order construct of generalized mode-coupling theory constitutes a powerful and unifying framework for kinetic theories of the glass transition.