We experimentally study how the cholesteric pitch $P$ depends on the equilibrium pitch $P_0$ in planar liquid crystal (LC) cells with both strong and semistrong anchoring conditions. The cholesteric phase was induced by dissolution in the nematic LC of the right-handed chiral dopant 7-dehydrocholesterol (7-DHC, provitamin ${\text{D}}_3$) which transforms to left-handed tachysterol under the action of uv irradiation at the wavelength of 254 nm. By using the model of photoreaction kinetics we obtain the dependencies of isomer concentrations and, therefore, of the equilibrium pitch on the uv irradiation dose. The cholesteric pitch was measured as a function of irradiation time using the polarimetry method. In this method, the pitch is estimated from the experimental data on the irradiation time dependence of the ellipticity of light transmitted through the LC cells. It is found that the resulting dependence of the twist parameter $2D/P$ ($D$ is the cell thickness) on the free twisting number parameter $2D/P_0$ shows jumplike behavior and agrees well with the known theoretical results for the anchoring potential of Rapini-Papoular form.

Transcription factors (TFs) with regulatory action at multiple promoter targets is the rule rather than the exception, with examples ranging from the cAMP receptor protein (CRP) in E. coli that regulates hundreds of different genes simultaneously to situations involving multiple copies of the same gene, such as plasmids, retrotransposons, or highly replicated viral DNA. When the number of TFs heavily exceeds the number of binding sites, TF binding to each promoter can be regarded as independent. However, when the number of TF molecules is comparable to the number of binding sites, TF titration will result in correlation (“promoter entanglement”) between transcription of different genes. We develop a statistical mechanical model which takes the TF titration effect into account and use it to predict both the level of gene expression for a general set of promoters and the resulting correlation in transcription rates of different genes. Our results show that the TF titration effect could be important for understanding gene expression in many regulatory settings.

We derive some analytical results of a well-known model for quasispherical vesicles in a linear shear flow at low deformability. Attention is focussed on the oscillatory regimes: the tumbling (TB) mode, vacillating-breathing (VB) mode, and the transition from vacillating-breathing to tumbling, depending on a control parameter $\Gamma$. It is shown that, during the VB-to-TB transition ($\Gamma =1$), the vesicle momentarily attains its maximal extension in the vorticity direction and transits through a circular profile in the shear plane for which the radius is exactly determined. In addition, we provide an explicit analytical expression for the effective membrane tension for different types of motions. We find a critical bending number below which the membrane undergoes compression at each instant and show that, during the VB-to-TB transition, a fourth-order membrane deformation is possible.

Nonlinear classical oscillators can be excited to high energies by a weak driving field provided the drive frequency is properly chirped. This process is known as autoresonance (AR). We find that for a large class of oscillators, it is sufficient to consider only the first harmonic of the motion when studying AR, even when the dynamics is highly nonlinear. The first harmonic approximation is also used to relate AR in an asymmetric potential to AR in a “frequency equivalent” symmetric potential and to study the autoresonance breakdown phenomenon.

We study spatial localization in the generalized Swift-Hohenberg equation with either quadratic-cubic or cubic-quintic nonlinearity subject to spatially heterogeneous forcing. Different types of forcing (sinusoidal or Gaussian) with different spatial scales are considered and the corresponding localized snaking structures are computed. The results indicate that spatial heterogeneity exerts a significant influence on the location of spatially localized structures in both parameter space and physical space, and on their stability properties. The results are expected to assist in the interpretation of experiments on localized structures where departures from spatial homogeneity are generally unavoidable.

We consider a Kuramoto model of coupled oscillators that includes quenched random interactions of the type used by van Hemmen in his model of spin glasses. The phase diagram is obtained analytically for the case of zero noise and a Lorentzian distribution of the oscillators' natural frequencies. Depending on the size of the attractive and random coupling terms, the system displays four states: complete incoherence, partial synchronization, partial antiphase synchronization, and a mix of antiphase and ordinary synchronization.

How the nonstationarity in the atmosphere turbulent vertical velocity series affects its organization degree of multiscale structures is quantified by permutation entropy (PE) and complexity-entropy causality plane (CECP), and marked PE and CECP differences are detected between the nonstationary and stationary series. We find that the value of PE is lower in the nonstationary vertical velocity series than the stationary counterparts. Both types of series locate near the region of the higher complexity value in the CECP as chaotic systems, but the PE is smaller and the complexity degree is larger in the nonstationary series than the stationary with smaller time delays. Due to the close relationship between PE and the multiscale Shannon entropy, we show that the PE and CECP can be also taken as an indicator to quantify the different organization degrees of the multiscale structures existing between the stationary and nonstationary surface vertical velocity records.

Coriolis force effects on shear flows are important in geophysical and astrophysical contexts. We report a study on the linear stability and the transient energy growth of the plane Couette flow with system rotation perpendicular to the shear direction. External rotation causes linear instability. At small rotation rates, the onset of linear instability scales inversely with the rotation rate and the optimal transient growth in the linearly stable region is slightly enhanced $\sim {\mathrm{Re}}^2$. The corresponding optimal initial perturbations are characterized by roll structures inclined in the streamwise direction and are twisted under external rotation. At large rotation rates, the transient growth is significantly inhibited and hence linear stability analysis is a reliable indicator for instability.

In low-temperature superfluid helium, viscosity is zero and vorticity takes the form of discrete vortex filaments of fixed circulation and atomic thickness. We present numerical evidence of three-dimensional inverse energy transfer from small length scales to large length scales in superfluid turbulence generated by a flow of vortex rings. We argue that the effect arises from the anisotropy of the flow, which favors vortex reconnections of vortex loops of the same polarity, and that it has been indirectly observed in the laboratory. The effect opens questions about analogies with related processes in ordinary turbulence.

The diffusive dynamics of a particle in a medium with space-dependent friction coefficient is studied within the framework of the inertial Langevin equation. In this description, the ambiguous interpretation of the stochastic integral, known as the Itô-Stratonovich dilemma, is avoided since all interpretations converge to the same solution in the limit of small time steps. We use a newly developed method for Langevin simulations to measure the probability distribution of a particle diffusing in a flat potential. Our results reveal that both the Itô and Stratonovich interpretations converge very slowly to the uniform equilibrium distribution for vanishing time step sizes. Three other conventions exhibit significantly improved accuracy: (i) the “isothermal” (Hänggi) convention, (ii) the Stratonovich convention corrected by a drift term, and (iii) a newly proposed convention employing two different effective friction coefficients representing two different averages of the friction function during the time step. We argue that the most physically accurate dynamical description is provided by the third convention, in which the particle experiences a drift originating from the dissipation instead of the fluctuation term. This feature is directly related to the fact that the drift is a result of an inertial effect that cannot be well understood in the Brownian, overdamped limit of the Langevin equation.

This work is motivated by recent progress in information theory and signal processing where the so-called spatially coupled design of systems leads to considerably better performance. We address relevant open questions about spatially coupled systems through the study of a simple Ising model. In particular, we consider a chain of Curie-Weiss models that are coupled by interactions up to a certain range. Indeed, it is well known that the pure (uncoupled) Curie-Weiss model undergoes a first-order phase transition driven by the magnetic field, and furthermore in the spinodal region such systems are unable to reach equilibrium in subexponential time if initialized in the metastable state. In contrast, the spatially coupled system is instead able to reach the equilibrium even when initialized to the metastable state. The equilibrium phase propagates along the chain in the form of a traveling wave. Here we study the speed of the wave front and the so-called termination cost—i.e., the conditions necessary for the propagation to occur. We reach several interesting conclusions about optimization of the speed and the cost.

Particle tracking and displacement covariance matrix techniques are employed to investigate the phonon dispersion relations of two-dimensional colloidal glasses composed of soft, thermoresponsive microgel particles whose temperature-sensitive size permits in situ variation of particle packing fraction. Bulk, $B$, and shear, $G$, moduli of the colloidal glasses are extracted from the dispersion relations as a function of packing fraction, and variation of the ratio $G/B$ with packing fraction is found to agree quantitatively with predictions for jammed packings of frictional soft particles. In addition, $G$ and $B$ individually agree with numerical predictions for frictional particles. This remarkable level of agreement enabled us to extract an energy scale for the interparticle interaction from the individual elastic constants and to derive an approximate estimate for the interparticle friction coefficient.

The propagation of subdiffusion-reaction fronts is studied in the framework of a model recently suggested by Fedotov [Phys. Rev. E 81, 011117 (2010)]. An exactly solvable model with a piecewise linear reaction function is considered. A drastic difference between the cases of normal diffusion and subdiffusion has been revealed. While in the case of normal diffusion, a traveling wave solution between two locally stable phases always exists, and is unique, in the case of the subdiffusion such solutions do not exist. The numerical simulation shows that the velocity of the front decreases with time according to a power law. The only kind of fronts moving with a constant velocity are waves which propagate solely due to the reaction, with a vanishing subdiffusive flux.

A key quantity characterizing a time-periodically forced quantum system coupled to a heat bath is the energy flowing in the steady state through the system into the bath, where it is dissipated. We derive a general expression which allows one to compute this energy dissipation rate for a heat bath consisting of a large number of harmonic oscillators and work out two analytically solvable model examples. In particular, we distinguish between genuine transitions effectuating a change of the systems's Floquet state and pseudotransitions preserving that state; the latter are shown to yield an important contribution to the total dissipation rate. Our results suggest possible driving-mediated heating and cooling schemes on the quantum level. They also indicate that a driven system does not necessarily occupy only a single Floquet state when in contact with a zero-temperature bath.