Two universality classes for thermal transport in one-dimensional oscillator systems are proposed. In class A the asymptotic behavior of the frequency dependent thermal conductivity is $\kappa \left(\omega \right)\sim {\omega }^{-1/2}$, whereas the bulk viscosity is finite. In class B the asymptotic behavior of the thermal conductivity is $\kappa \sim {\omega }^{-\alpha }$, where $\alpha <0.4$, and the frequency dependent bulk viscosity has the same asymptotic behavior as the thermal conductivity. It is further proposed that the criterion for membership in class A is that the ratio of specific heat capacities $\gamma \equiv c_P/c_V=1$. A one-dimensional cubic-plus-quartic coupled oscillator is examined at conditions for which $\gamma =1$ but $P\ne 0$. It is found that the system belongs to class A, in agreement with the proposed criterion. Additionally, it is proposed that examination of whether a system has a well-defined bulk Prandtl number is a more reliable way of determining whether a system is in class A or class B.

We present a study of the fiber bundle model using equal load-sharing dynamics where the breaking thresholds of the fibers are drawn randomly from a power-law distribution of the form $p\left(b\right)\sim b^{-1}$ in the range ${10}^{-\beta }$ to ${10}^{\beta }$. Tuning the value of $\beta$ continuously over a wide range, the critical behavior of the fiber bundle has been studied both analytically as well as numerically. Our results are: (i) The critical load ${\sigma }_c(\beta ,N)$ for the bundle of size $N$ approaches its asymptotic value ${\sigma }_c\left(\beta \right)$ as ${\sigma }_c(\beta ,N)={\sigma }_c\left(\beta \right)+A{N}^{-1/\nu \left(\beta \right)}$, where ${\sigma }_c\left(\beta \right)$ has been obtained analytically as ${\sigma }_c\left(\beta \right)={10}^{\beta }/(2\beta eln10)$ for $\beta \ge {\beta }_u=1/(2ln10)$, and for $\beta <{\beta }_u$ the weakest fiber failure leads to the catastrophic breakdown of the entire fiber bundle, similar to brittle materials, leading to ${\sigma }_c\left(\beta \right)={10}^{-\beta }$; (ii) the fraction of broken fibers right before the complete breakdown of the bundle has the form $1-1/(2\beta ln10)$; (iii) the distribution $D\left(\Delta \right)$ of the avalanches of size $\Delta$ follows a power-law $D\left(\Delta \right)\sim {\Delta }^{-\xi }$ with $\xi =5/2$ for $\Delta \gg {\Delta }_c\left(\beta \right)$ and $\xi =3/2$ for $\Delta \ll {\Delta }_c\left(\beta \right)$, where the crossover avalanche size ${\Delta }_c\left(\beta \right)=2/{(1-e{10}^{-2\beta })}^2$.

In this paper we address the problem of computing state-dependent feedback controls for path integral control problems. To this end we generalize the path integral control formula and utilize this to construct parametrized state-dependent feedback controllers. In addition, we show a relation between control and importance sampling: Better control, in terms of control cost, yields more efficient importance sampling, in terms of effective sample size. The optimal control provides a zero-variance estimate.

We study the critical Casimir force for a film geometry in the Ising universality class. We employ a homogeneous adsorption preference on one of the confining surfaces, while the opposing surface exhibits quenched random disorder, leading to a random local adsorption preference. Disorder is characterized by a parameter $p$, which measures, on average, the portion of the surface that prefers one component, so that $p=0,1$ correspond to homogeneous adsorption preference. By means of Monte Carlo simulations of an improved Hamiltonian and finite-size scaling analysis, we determine the critical Casimir force. We show that by tuning the disorder parameter $p$, the system exhibits a crossover between an attractive and a repulsive force. At $p=1/2$, disorder allows to effectively realize Dirichlet boundary conditions, which are generically not accessible in classical fluids. Our results are relevant for the experimental realizations of the critical Casimir force in binary liquid mixtures.

We study the survival probability and the first-passage time distribution for a Brownian motion in a planar wedge with infinite absorbing edges. We generalize existing results obtained for wedge angles of the form $\pi /n$ with $n$ a positive integer to arbitrary angles, which in particular cover the case of obtuse angles. We give explicit and simple expressions of the survival probability and the first-passage time distribution in which the difference between an arbitrary angle and a submultiple of $\pi$ is contained in three additional terms. As an application, we obtain the short-time development of the survival probability in a wedge of arbitrary angle.

This article presents a new force model for performing quantitative simulations of dense granular materials. Interactions between multiple contacts (MC) on the same grain are explicitly taken into account. Our readily applicable MC-DEM method retains all the advantages of discrete-element method simulations and does not require the use of costly finite-element methods. The new model closely reproduces our recent experimental measurements, including contact force distributions in full 3D, at all compression levels of the packing up to the experimental maximum limit of 13%. Comparisons with classic simulations using the nondeformable spheres approach, as well as with alternative models for interactions between multiple contacts, are provided. The success of our model, compared to these alternatives, demonstrates that interactions between multiple contacts on each grain must be included for dense granular packings.

In this paper we demonstrate the presence of anisotropic stress correlations in the simulated two-dimensional liquids. Whereas the temporal correlation of macroscopic shear stress is known to contribute to viscosity via the Green-Kubo formula, the general question regarding angular dependence of the spatial correlation among atomic-level stresses in liquids without external shear has not been explored. We observed the apparent anisotropicity with well-defined symmetry which can be explained in terms of the elastic continuum theory by Eshelby. In addition, we found that the shear stress correlation is screened compared to the prediction by the elastic continuum theory, and the screening length depends on temperature and follows the power law, suggesting divergence around the glass transition temperature. The success of the Eshelby theory to explain the anisotropy of the stress correlations justifies the idea that the mismatch between the atom and its nearest neighbor cage produces the atomic-level stress as well as the long-range stress fields.

We model the packing structure of a marginally jammed bulk ensemble of polydisperse spheres. To this end we expand on the granocentric model [Clusel et al., Nature (London) 460, 611 (2009)], explicitly taking into account rattlers. This leads to a relationship between the characteristic parameters of the packing, such as the mean number of neighbors and the fraction of rattlers, and the radial distribution function $g\left(r\right)$. We find excellent agreement between the model predictions for $g\left(r\right)$ and packing simulations, as well as experiments on jammed emulsion droplets. The observed quantitative agreement opens the path towards a full structural characterization of jammed particle systems for imaging and scattering experiments.

The KvAP potassium channel is representative of a family of voltage-gated ion channels where the membrane potential is sensed by a transmembrane helix containing several positively charged arginines. Previous work by Wang and Zocchi [A. Wang and G. Zocchi, PLoS ONE 6, e18598 (2011)] showed how a negatively charged polyelectrolyte attached in proximity to the voltage sensing element can bias the opening probability of the channel. Here we introduce three phosphorylation sites at the same location and show that the response curve of the channel shifts by about 20 mV upon phosphorylation, while other characteristics such as the single-channel conductance are unaffected. In summary, we construct an artificial phosphorylation site which confers allosteric regulation to the channel.

We present a minimal one-dimensional deterministic continuous dynamical system that exhibits chaotic behavior and complex transport properties. Our model is an overdamped rocking ratchet with finite dissipation, that is periodically kicked with a $\delta$ function driving force, without finite inertia terms or temporal or spatial stochastic forces. To our knowledge this is the simplest model reported in the literature for a ratchet, with this complex behavior. We develop an analytical approach that predicts many key features of the system, such as current reversals, as well as the presence of chaotic behavior and bifurcation. Our analytical approach allows us to study the transition from regular to chaotic motion as well as a tangent bifurcation associated with this transition. We show that our approach can be easily extended to other types of periodic driving forces. The square wave is shown as an example.

Capillary forces determine the shape of a liquid interface. Although often not considered, elastic solids with a free surface are also subjected to surface forces and these become important for materials of low Young's modulus. Here we consider two equivalent problems where a capillary free surface deforms due to vortices: (i) in a steady viscous flow [solved by Jeong and Moffatt, J. Fluid Mech. 241, 1 (1992)], and (ii) in an elastic medium. The equations of linear incompressible elasticity and viscous flow are strictly identical, and the two-dimensional problems that we consider are solved using complex variable methods. Despite the similarity, the kinematics of the free surface is very different for the viscous and elastic cases. We show for the present problem that these kinematics result in displacement and velocity fields of different topology. Unexpectedly, the resulting surface deflections are even of opposite sign.

We report measurements and simulations of the time-evolving rms velocity distribution in an ultracold neutral plasma. A strongly coupled ultracold neutral ${\mathrm{Ca}}^{+}$ plasma is generated by photoionizing laser-cooled atoms close to threshold. A fraction of these ions is then promoted to the second ionization state to form a mixed ${\mathrm{Ca}}^{+}\text{−}{\mathrm{Ca}}^{2+}$ plasma. By varying the time delay between the first and the second ionization events, a minimum in ion heating is achieved. We show that the Coulomb strong-coupling parameter $\Gamma$ increases by a factor of 1.4 to a maximum value of 3.6. A pure ${\mathrm{Ca}}^{2+}$ plasma would have $\Gamma =6.8$, moving these strongly coupled systems closer to the regime of liquid-like correlations.

We study the Brownian motion of a particle bound by a harmonic potential and immersed in a fluid with a uniform shear flow. We describe this problem first in terms of a linear Fokker-Planck equation which is solved to obtain the probability distribution function for finding the particle in a volume element of its associated phase space. We find the explicit form of this distribution in the stationary limit and use this result to show that both the equipartition law and the equation of state of the trapped particle are modified from their equilibrium form by terms increasing as the square of the imposed shear rate. Subsequently, we propose an alternative description of this problem in terms of a generalized Langevin equation that takes into account the effects of hydrodynamic correlations and sound propagation on the dynamics of the trapped particle. We show that these effects produce significant changes, manifested as long-time tails and resonant peaks, in the equilibrium and nonequilibrium correlation functions for the velocity of the Brownian particle. We implement numerical simulations based on molecular dynamics and multiparticle collision dynamics, and observe a very good quantitative agreement between the predictions of the model and the numerical results, thus suggesting that this kind of numerical simulations could be used as complement of current experimental techniques.

We introduce the leaf-excluded percolation model, which corresponds to independent bond percolation conditioned on the absence of leaves (vertices of degree one). We study the leaf-excluded model on the square and simple-cubic lattices via Monte Carlo simulation, using a worm-like algorithm. By studying wrapping probabilities, we precisely estimate the critical thresholds to be $0.3552475\left(8\right)$ (square) and $0.185022\left(3\right)$ (simple-cubic). Our estimates for the thermal and magnetic exponents are consistent with those for percolation, implying that the phase transition of the leaf-excluded model belongs to the standard percolation universality class.

Liquid crystalline polymer stabilized blue phases (PSBPs) are candidate materials for next generation electro-optic switching devices because they form a self-organized three-dimensional periodic structure and exhibit a fast response time of submillisecond order. Considering the crystallographic structures of PSBPs, it is intuitive to believe that the electro-optic effect would depend on the direction of the applied electric field; however, this relationship has not yet been investigated. In this study, we prepared two kinds of samples in which the (110) and (200) planes were oriented parallel to the substrates, and investigated the electro-optic Kerr effect as a field was applied between the two substrates. The two samples exhibited differing behaviors, with the Kerr coefficient of the (110)-oriented sample being larger by 20% than that of the (200)-oriented sample. These results imply that the electro-optic Kerr effect of PSBPs is not isotropic but anisotropic, just like cubic optical crystals.

We use a bath of chaotic surface waves in water to mechanically and macroscopically mimic the thermal behavior of a short articulated chain with only nearest-neighbor interactions. The chaotic waves provide isotropic and random agitation to which a temperature can be ascribed, allowing the chain to passively explore its degrees of freedom in analogy to thermal motion. We track the chain in real time and infer end-to-end potentials using Boltzmann statistics. We extrapolate our results, by using Monte Carlo simulations of self-avoiding polymers, to lengths not accessible in our system. In the long-chain limit we demonstrate universal scaling of the statistical parameters of all chains in agreement with well-known predictions for self-avoiding walks. However, we find that the behavior of chains below a characteristic length scale fundamentally differs. We find that short chains have much greater compressional stiffness than would be expected. However, chains rapidly soften as length increases to meet with expected scalings.

An analytical approach is proposed for the investigation of the conductivity properties of DNA. The charge mobility of DNA is studied based on an extended Peyrard-Bishop-Holstein model when the charge carrier is also subjected to an external electrical field. We have obtained the values of some of the system parameters, such as the electron-lattice coupling constant, by using the mean Lyapunov exponent method. On the other hand, the electrical current operator is calculated directly from the lattice operators. Also, we have studied Landauer resistance behavior with respect to the external field, which could serve as the interface between chaos theory tools and electronic concepts. We have examined the effect of two types of electrical fields (dc and ac) and variation of the field frequency on the current flowing through DNA. A study of the current-voltage $\left(I\text{−}V\right)$ characteristic diagram reveals regions with a (quasi-)Ohmic property and other regions with negative differential resistance (NDR). NDR is a phenomenon that has been observed experimentally in DNA at room temperature. We have tried to study the affected agents in charge transfer phenomena in DNA to better design nanostructures.

We study a generic model for the polarization and motility of self-propelled soft objects, biological cells, or biomimetic systems, interacting with a viscous substrate. The active forces generated by the cell on the substrate are modeled by means of oscillating force multipoles at the cell-substrate interface. Symmetry breaking and cell polarization for a range of cell sizes naturally “emerge” from long range mechanical interactions between oscillating units, mediated both by the intracellular medium and the substrate. However, the harnessing of cell polarization for motility requires substrate-mediated interactions. Motility can be optimized by adapting the oscillation frequency to the relaxation time of the system or when the substrate and cell viscosities match. Cellular noise can destroy mechanical coordination between force-generating elements within the cell, resulting in sudden changes of polarization. The persistence of the cell's motion is found to depend on the cell size and the substrate viscosity. Within such a model, chemotactic guidance of cell motion is obtained by directionally modulating the persistence of motion, rather than by modulating the instantaneous cell velocity, in a way that resembles the run and tumble chemotaxis of bacteria.

Information processing in living cells frequently involves an exchange of peripheral membrane proteins between the cytosol and organelle membranes. The typical time scale $\tau$ of these association-dissociation cycles is commonly quantified in vivo via fluorescence recovery after photobleaching (FRAP). Contrary to common assumptions, we show here that $\tau$ values determined by FRAP depend on the size and number of target structures. Hence, FRAP times alone are insufficient to draw conclusions about the proteins' binding kinetics. In contrast, extracting primary molecular association and dissociation rates from FRAP approaches provides a size-independent and therefore robust measure for the proteins' binding kinetics. We support our theoretical considerations with experiments on the small GTPase Arf-1 that transiently associates with Golgi membranes: While Arf-1 recovery times in untreated cells and in cells with disrupted microtubules are significantly different, the molecular kinetic rates are shown to be the same in both cases.