Our prior work has shown that high quality ($Q$) factor whispering gallery modes (WGMs) in liquid microdroplets can potentially induce single-photon-level nonlinear effects through radiation pressure on the interface. However, little is known about the nonlinear effects of other processes involving scattering force and thermocapillarity. In this study, we establish a numerical framework that can calculate the fluid motion and the resultant nonlinearity induced by the optical scattering force and thermocapillarity. Then, we compare the magnitude of various nonlinear optofluidic processes induced by the radiation pressure, the thermocapillary effect, the scattering-induced optical force, and the Kerr effect. Using realistic fluid parameters, we show that the radiation pressure due to the WGM produces the strongest nonlinear optofluidic effect.

In this Comment we point out some shortcomings in two papers [N. Laskin, Phys. Rev. E 62, 3135 (2000); N. Laskin, Phys. Rev. E 66, 056108 (2002)]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from a place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to an arbitrary destination.

The fractional uncertainty relation is a mathematical formulation of Heisenberg's uncertainty principle in the framework of fractional quantum mechanics. Two mistaken statements presented in the Comment have been revealed. The origin of each mistaken statement has been clarified and corrected statements have been made. A map between standard quantum mechanics and fractional quantum mechanics has been presented to emphasize the features of fractional quantum mechanics and to avoid misinterpretations of the fractional uncertainty relation. It has been shown that the fractional probability current equation is correct in the area of its applicability. Further studies have to be done to find meaningful quantum physics problems with involvement of the fractional probability current density vector and the extra term emerging in the framework of fractional quantum mechanics.

Stochastic systems characterized by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position dependent and obeys a power-law form attributed to the underlying self-similar structure. Both the one- and two-dimensional cases are analyzed. The random walk description involves a position-dependent waiting time distribution. On the other hand, the stochastic dynamics is formulated in terms of the subordination technique where the random time generator is position dependent. The first passage time problem is addressed by evaluating a first passage time density distribution and an escape rate. The influence of the medium nonhomogeneity on those quantities is demonstrated; moreover, the dependence of the escape rate on the stability index and the memory parameter is evaluated. Results indicate essential differences between the Gaussian case and the case involving Lévy flights.

A network of neurons in the central nervous system collectively represents information by its spiking activity states. Typically observed states, i.e., code words, occupy only a limited portion of the state space due to constraints imposed by network interactions. Geometrical organization of code words in the state space, critical for neural information processing, is poorly understood due to its high dimensionality. Here, we explore the organization of neural code words using retinal data by computing the entropy of code words as a function of Hamming distance from a particular reference codeword. Specifically, we report that the retinal code words in the state space are divided into multiple distinct clusters separated by entropy-gaps, and that this structure is shared with well-known associative memory networks in a recallable phase. Our analysis also elucidates a special nature of the all-silent state. The all-silent state is surrounded by the densest cluster of code words and located within a reachable distance from most code words. This code-word space structure quantitatively predicts typical deviation of a state-trajectory from its initial state. Altogether, our findings reveal a non-trivial heterogeneous structure of the code-word space that shapes information representation in a biological network.

Methylation of mammalian DNA occurs primarily at CG dinucleotides. These CpG sites are located nonrandomly in the genome, tending to occur within high density clusters of CpGs (islands) or within large regions of low CpG density. Cluster methylation tends to be bimodal, being dominantly unmethylated or mostly methylated. For CpG clusters near promoters, low methylation is associated with transcriptional activity, while high methylation is associated with gene silencing. Alternative CpG methylation states are thought to be stable and heritable, conferring localized epigenetic memory that allows transient signals to create long-lived gene expression states. Positive feedback where methylated CpG sites recruit enzymes that methylate nearby CpGs, can produce heritable bistability but does not easily explain that as clusters increase in size or density they change from being primarily methylated to primarily unmethylated. Here, we show that an interaction between the methylation state of a cluster and its occupancy by nucleosomes provides a mechanism to generate these features and explain genome wide systematics of CpG islands.

We analyze ultrasensitivity in a model of Vibrio harveyi quorum sensing. We consider a feedforward model consisting of two biochemical networks per cell. The first represents the interchange of a signaling molecule (autoinducer) between the cell cytoplasm and an extracellular domain and the binding of intracellular autoinducer to cognate receptors. The unbound and bound receptors within each cell act as kinases and phosphotases, respectively, which then drive a second biochemical network consisting of a phosphorylation-dephosphorylation cycle. We ignore subsequent signaling pathways associated with gene regulation and the possible modification in the production rate of an autoinducer (positive feedback). We show how the resulting quorum sensing system exhibits ultrasensitivity with respect to changes in cell density. We also demonstrate how quorum sensing can protect against the noise amplification of fast environmental fluctuations in comparison to a single isolated cell.

Magnetoactive elastomers (MAEs) are composite materials comprised of micrometer-sized ferromagnetic particles in a nonmagnetic elastomer matrix. A single-particle mechanism of magnetostriction in MAEs, assuming the rotation of a soft magnetic, mechanically rigid particle with uniaxial magnetic anisotropy in magnetic fields is identified and considered theoretically within the framework of an alternative model. In this mechanism, the total magnetic anisotropy energy of the filling particles in the matrix is the sum over single particles. Matrix displacements in the vicinity of the particle and the resulting direction of the magnetization vector are calculated. The effect of matrix deformation is pronounced well if the magnetic anisotropy coefficient $K$ is much larger than the shear modulus µ of the elastic matrix. The feasibility of the proposed magnetostriction mechanism in soft magnetoactive elastomers and gels is elucidated. The magnetic-field-induced internal stresses in the matrix lead to effects of magnetodeformation and may increase the elastic moduli of these composite materials.

We propose a theoretical explanation for the long-standing problem of the anomalous critical behavior of the heat capacity near the smectic-$A$–hexatic phase transition. Experiments find a large specific heat critical exponent $\alpha =0.5–0.7$, which is inconsistent with a small negative value $\alpha \approx -0.01$ expected for the three-dimensional $XY$ universality class. We show that most of the observed features can be explained by treating simultaneously fluctuations of the hexatic orientational and translational (positional) order parameters. Assuming that the translational correlation length ${\xi }_{tr}$ is much larger than the hexatic correlation length ${\xi }_h$, we calculate the temperature dependence of the heat capacity in the critical region near the smectic-$A$–hexatic phase transition. Our results are in quantitative agreement with the calorimetric experimental data.

The linear hydrodynamic stability of a model for confined quasi-two-dimensional granular gases is analyzed. The system exhibits homogeneous hydrodynamics, i.e., there are macroscopic evolution equations for homogeneous states. The stability analysis is carried out around all these states and not only the homogeneous steady state reached eventually by the system. It is shown that in some cases the linear analysis is not enough to reach a definite conclusion on the stability, and molecular dynamics simulation results are presented to elucidate these cases. The analysis shows the relevance of nonlinear hydrodynamic contributions to describe the behavior of spontaneous fluctuations occurring in the system, that lead even to the transitory formation of clusters of particles. The conclusion is that the system is always stable. The relevance of the results for describing the instabilities of confined granular gases observed experimentally is discussed.

A mesoscopic model of amorphous plasticity is discussed in the context of depinning models. After embedding in a $d+1$-dimensional space, where the accumulated plastic strain lives along the additional dimension, the gradual plastic deformation of amorphous media can be regarded as the motion of an elastic manifold in a disordered landscape. While the associated depinning transition leads to scaling properties, the quadrupolar Eshelby interactions at play in amorphous plasticity induce specific additional features like shear-banding and weak ergodicity breakdown. The latters are shown to be controlled by the existence of soft modes of the elastic interaction, the consequence of which is discussed in the context of depinning.

We consider thermal transport in low-dimensional disordered harmonic networks of coupled masses. Utilizing known results regarding Anderson localization, we derive the actual dependence of the thermal conductance $G$ on the length $L$ of the sample. This is required by nanotechnology implementations because for such networks Fourier's law $G\propto 1/L^{\alpha }$ with $\alpha =1$ is violated. In particular we consider “glassy” disorder in the coupling constants and find an anomaly which is related by duality to the Lifshitz-tail regime in the standard Anderson model.

Here we measure the hindered diffusion of an optically confined nanoparticle in the direction normal to a surface, and we use this to determine the particle-surface interaction profile in terms of the absolute height. These studies are performed using the evanescent field of an optically excited single-mode silicon nitride waveguide, where the particle is confined in a height-dependent potential energy well generated from the balance of optical gradient and surface forces. Using a high-speed cmos camera, we demonstrate the ability to capture the short time-scale diffusion dominated motion for 800-nm-diam polystyrene particles, with measurement times of only a few seconds per particle. Using established theory, we show how this information can be used to estimate the equilibrium separation of the particle from the surface. As this measurement can be made simultaneously with equilibrium statistical mechanical measurements of the particle-surface interaction energy landscape, we demonstrate the ability to determine these in terms of the absolute rather than relative separation height. This enables the comparison of potential energy landscapes of particle-surface interactions measured under different experimental conditions, enhancing the utility of this technique.

It is always some constraint that yields any nontrivial structure from statistical averages. As epitomized by the Boltzmann distribution, the energy conservation is often the principal constraint acting on mechanical systems. Here we investigate a different type: the topological constraint imposed on “space.” Such a constraint emerges from the null space of the Poisson operator linking an energy gradient to phase space velocity and appears as an adiabatic invariant altering the preserved phase space volume at the core of statistical mechanics. The correct measure of entropy, built on the distorted invariant measure, behaves consistently with the second law of thermodynamics. The opposite behavior (decreasing entropy and negative entropy production) arises in arbitrary coordinates. An ensemble of rotating rigid bodies is worked out. The theory is then applied to up-hill diffusion in a magnetosphere.

We present an analytical and numerical study of the parking lot model (PLM) of granular relaxation and make a connection to the aging dynamics of dense colloids. As we argue, the PLM is a Kinetically Constrained Model which features astronomically large equilibration times and displays a characteristic aging behavior on all observable time scales. The density of parked cars displays quasi-equilibrium Gaussian fluctuations interspersed by increasingly rare intermittent events, quakes, which can lead to an increase of the density to new record values. Defining active clusters as the shortest domains of parked cars which must be rearranged to allow further insertions, we find that their typical length grows logarithmically with time for low enough temperatures and show how the number of active clusters on average gradually decreases as the system approaches equilibrium. We further characterize the aging process in terms of the statistics of the record-sized fluctuations in the interstitial free volume which lead to quakes and show that quakes are uncorrelated and that they can be approximately described as a Poisson process in logarithmic time.

We propose a nanostructure control method which uses slowly ramping parameters. We demonstrate the dynamics of this method in both a nonlinear classical system and a quantum system. When a quantum mechanical two-level atom (quantum dot) is irradiated by an electric field with a slowly increasing frequency, there exists a sudden transition from ground (excited) to excited (ground) state. This occurs when the ramping rate is smaller than the square of the Rabi frequency. The transition arises when its “instant frequency”—the time derivative of the driving field phase—matches the resonance frequency, satisfying the Fermi golden rule. We also find that the parameter ramping is an efficient control manner for classical nanomechanical shuttles. For ramping of driving amplitudes, the shuttle's mechanical oscillation is amplified and even survives when the ramping is stopped outside the original oscillation region. This strange oscillation is due to the entrance into a multistable dynamic region in phase space. For ramping of driving frequencies, an onset of oscillation arises when the instant frequency enters the oscillation region. Thus, regardless of being classical or quantum, the instant frequency is physically relevant. We discuss in which conditions the dynamic control is efficient.

A central issue in the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate with a—in principle, any—network a differentiable object (a Riemannian manifold) whose volume is used to define the entropy. The effectiveness of the latter in measuring network complexity is successfully proved through its capability of detecting a classical phase transition occurring in both random graphs and scale-free networks, as well as of characterizing small exponential random graphs, configuration models, and real networks.

We present a theoretical framework for the linear and nonlinear viscoelastic properties of reversibly crosslinked networks of semiflexible polymers. In contrast to affine models where network strain couples to the polymer end-to-end distance, in our model strain rather serves to locally distort the network structure. This induces bending modes in the polymer filaments, the properties of which are slaved to the surrounding network structure. Specifically, we investigate the frequency-dependent linear rheology, in particular in combination with crosslink binding-unbinding processes. We also develop schematic extensions to describe the nonlinear response during creep measurements as well as during constant strain-rate ramps.

We study glassy dynamics using a simulation of three soft Brownian particles confined to a two-dimensional circular region. If the circular region is large, the disks freely rearrange, but rearrangements are rarer for smaller system sizes. We directly measure a one-dimensional free-energy landscape characterizing the dynamics. This landscape has two local minima corresponding to the two distinct disk configurations, separated by a free-energy barrier that governs the rearrangement rate. We study several different interaction potentials and demonstrate that the free-energy barrier is composed of a potential-energy barrier and an entropic barrier. The heights of both of these barriers depend on temperature and system size, demonstrating how non-Arrhenius behavior can arise close to the glass transition.

We report optical birefringence data for a series of mixtures of the liquid crystals octylcyanobiphenyl (8CB) and decylcyanobiphenyl (10CB). Nematic order parameter $S$ data in the nematic and smectic $A$ phases have been derived from phase angle changes obtained in temperature scans with a rotating analyzer method. These $S$ values have been used to arrive at values for possible entropy discontinuities at the smectic $A$ to nematic phase transition temperature $T_{NA}$. The 10CB mole fraction dependence of the obtained entropy discontinuities could be well fitted with a crossover function consistent with the mean-field free-energy expression with a nonzero cubic term arising from the coupling between the smectic-$A$ order parameter and the orientational order parameter director fluctuations in the Halperin-Lubensky-Ma theory. The obtained results are in good agreement with existing results from adiabatic scanning calorimetry. By exploiting the fact that the temperature derivative of the order parameter $S\left(T\right)$ near $T_{NA}$ exhibits the same power law divergence as the specific heat capacity, we have extracted the effective critical exponent $\alpha$ values for the compositions under study. The critical exponent $\alpha$ has been observed to reach the tricritical value ${\alpha }_{\mathrm{TCP}}=0.5$ for the 10CB mole fraction of $x=0.330$.