The theory of DNA dynamics is exceedingly complex and not easily explained. In the past two decades, by adapting methods of statistical physics, the dynamics of DNA in contact with a thermal bath is widely studied. In this paper, the thermal denaturation of DNA in the framework of the Peyrard-Bishop-Dauxois (PBD) model through the Rényi dimension is investigated. As a result, the Rényi dimension spectrum of the melting transition process reveals the multifractal nature of the dynamics of the Peyrard-Bishop-Dauxois model. Also, it can be concluded that the Rényi dimension ($D_q$) at negative values of $q$ is the characteristic signature of pre-melting and thermal denaturation of DNA. Furthermore, this approach is in excellent agreement with previous experimental studies.

We consider the phase separation in an asymmetrically charged lipid bilayer membrane consisting of neutral and negatively charged lipids that are in contact with in and out ionic solutions having different ionic strengths. The two asymmetric leaflets are coupled through electrostatic interactions. Based on a free-energy approach, the critical point and phase diagrams are calculated for different ionic strengths of the two solutions and coupling parameter. An increase of the coupling constant or asymmetry in the salt concentration between the in and out solutions yields a higher phase-separation temperature because of electrostatic interactions. As a consequence, the phase-coexistence region increases for strong screening (small Debye length). Finally, possible three-phase coexistence regions in the phase diagram are predicted.

The corneal endothelium is a fluid-transporting epithelium. As other similar tissues, it displays an electrical potential of ∼1 mV (aqueous side negative) across the entire layer [transendothelial potential difference (TEPD)]. It appears that this electrical potential is mainly the result of the transport of anions across the cell layer (from stroma to aqueous). There is substantial evidence that the TEPD is related linearly to fluid transport; hence, under proper conditions, its measure could serve as a measure of fluid transport. Furthermore, the TEPD is not steady; instead, it displays a spectrum of frequency components (0–15 Hz) recognized recently using Fourier transforms. Such frequency components appear due to charge-separating (electrogenic) processes mediated by epithelial plasma membrane proteins (both ionic channels and ionic cotransporters). In particular, the endothelial TEPD oscillations of the highest amplitude (1–2 Hz) were linked to the operation of so-called sodium bicarbonate cotransporters. However, no time localization of that activity could be obtained with the Fourier methodology utilized. For that reason we now characterize the TEPD using wavelet analysis with the aim to localize in time the variations in TEPD. We find that the mentioned high-amplitude oscillatory components of the TEPD appear cyclically during the several hours that an endothelial preparation survives in vitro. They have a period of 4.6 ± 0.4 s on average ($n$=4). The wavelet power value at the peak of such oscillations is 1.5 ± 0.1 mV${}^2$ Hz on average ($n$ $=$ 4), and is remarkably narrow in its distribution.

We reveal and give a theoretical explanation for spiral-like structures of periodicity hubs in the biparameter space of a generic dissipative system. We show that organizing centers for “shrimp”-shaped connection regions in the spiral structure are due to the existence of Shilnikov homoclinics near a codimension-2 bifurcation of saddle-foci.

Unexpected formation of regular high-$Q$ whispering gallery modes in a deformed microdisk where the radius is of the order of the vacuum wavelength is explained in terms of partial barriers in phase space. Using a semiclassical approach to determine the action flux of the partial barriers, we successfully predict spectral ranges in which the high-$Q$ modes can exist. Our analysis enables optimization of emission directionality and the $Q$ factor of deformed ultrasmall microcavities.

We report that defocusing cubic media with spatially inhomogeneous nonlinearity, whose strength increases rapidly enough toward the periphery, can support stable bright localized modes. Such nonlinearity landscapes give rise to a variety of stable solitons in all three dimensions, including one-dimensional fundamental and multihump states, two-dimensional vortex solitons with arbitrarily high topological charges, and fundamental solitons in three dimensions. Solitons maintain their coherence in the state of motion, oscillating in the nonlinear potential as robust quasiparticles and colliding elastically. In addition to numerically found soliton families, particular solutions are found in an exact analytical form, and accurate approximations are developed for the entire families, including moving solitons.

An ice sheet that spreads into an ocean is forced to bend owing to its buoyancy and detaches from the bedrock to form a floating ice shelf. The location of the transition between the grounded sheet and the floating shelf, defined as the grounding line, behaves as a free boundary. We develop a model of an elastic grounded sheet resting on a deformable elastic bed and coupled to an elastic floating shelf. We find that the grounding-line position is determined by the geometry of the bed and the bending-buoyancy length scale of the system. These two contributions depend on the reaction modulus of the bed in opposite ways. We show that the structure of the floating shelf depends on the bending-buoyancy length scale only, allowing us to calculate the bending stiffness of the elastic sheet independently of the properties of the bed. Relations between the structure of the floating shelf and the grounding-line position are also developed. Our theoretical predictions agree with laboratory experiments made using thick elastic sheets and a dense salt solution. Our findings may provide new insights into the dynamics near grounding lines, as well as methods to infer the bending stiffness of ice sheets and the grounding-line position from satellite altimetery that can be applied to elastic sheets in general.

We theoretically investigate the possibility of generating pulses in an excitable (asymmetric) semiconductor ring laser (SRL) using optical trigger pulses. We show that the phase difference between the injected field and the electric field inside the SRL determines the direction of the perturbation in phase space. Due to the folded shape of the excitability threshold, this has an important influence on the ability to cross it. A mechanism for exciting multiple consecutive pulses using a single trigger pulse (i.e., multipulse excitability) is revealed. We furthermore investigate the possibility of using asymmetric SRLs in a coupled configuration, which is a first step toward an all-optical neural network using SRLs as building blocks.

Numerical results for kinetic and thermal energy dissipation rates in bubbly Rayleigh-Bénard convection are reported. Bubbles have a twofold effect on the flow: on the one hand, they absorb or release heat to the surrounding liquid phase, thus tending to decrease the temperature differences responsible for the convective motion; but on the other hand, the absorbed heat causes the bubbles to grow, thus increasing their buoyancy and enhancing turbulence (or, more properly, pseudoturbulence) by generating velocity fluctuations. This enhancement depends on the ratio of the sensible heat to the latent heat of the phase change, given by the Jakob number, which determines the dynamics of the bubble growth.

The numerical solution of the nonlinear wave equation on unbounded spatial domain is considered. The artificial boundary method is introduced to reduce the nonlinear problem on unbounded spatial domain to an initial boundary value problem on a bounded domain. Using the unified approach, which is based on the operator splitting method, we construct the efficient nonlinear local absorbing boundary conditions for the nonlinear wave equation, and give the stability analysis of the resulting boundary conditions. Finally, several numerical examples are given to demonstrate the effectiveness of our method.

We present a unique derivation of metadynamics. This work leads to a more robust understanding of the error in the computed free energy than what has been obtained previously. Moreover, a formula for the exact free energy is introduced. The formula can be used to post-process any existing well-tempered metadynamics data, allowing one, in principle, to obtain an exact free energy regardless of the metadynamics parameters.

We derive the quantum mechanical description of overdamped Brownian motion of a particle in a spin bath of two-level atoms. The resulting Smoluchowski equation is used to calculate the rate of escape of the particle from a metastable state. At 0 K the decay rate is finite. We show that while quantization enhances the decay rate, higher temperatures induce thermal saturation, resulting in effective a reduction of the system-bath coupling. The role of coherence is examined.

Exit times for stochastic Ginzburg-Landau classical field theories with two or more coupled classical fields depend on the interval length on which the fields are defined, the potential in which the fields deterministically evolve, and the relative stiffness of the fields themselves. The latter is of particular importance in that physical applications will generally require different relative stiffnesses, but the effect of varying field stiffnesses has not heretofore been studied. In this paper, we explore the complete phase diagram of escape times as they depend on the various problem parameters. In addition to finding a transition in escape rates as the relative stiffness varies, we also observe a critical slowing down of the string method algorithm as criticality is approached.

We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model, and, by performing percolation processes, we get information about topology and resilience properties of the networks themselves. Given the weighted nature of the graphs, different kinds of bond percolation can be studied: stochastic (deleting links randomly) and deterministic (deleting links based on rank weights), each mimicking a different physical process. The evolution of the network is accordingly different, as evidenced by the behavior of the largest component size and of the distribution of cluster sizes. In particular, we can derive that weak ties are crucial in order to maintain the graph connected and that, when they are the most prone to failure, the giant component typically shrinks without abruptly breaking apart; these results have been recently evidenced in several kinds of social networks.

We study the behavior of a yield-stress fluid following the impact of a vertically falling sphere. Since the impact produces shear stresses larger than the yield stress, the material in the vicinity of the impact becomes fluidized. The sphere entrains air when it enters the fluid, and the resulting cavity pinches off below the surface. The upper part of this cavity then rebounds upward. For sufficiently fast impacts, a vertical jet is produced by the cavity collapse. While many aspects of this process are similar to that in Newtonian fluids or granular materials, the rheological properties of our target material change the scaling of the cavity pinch-off depth and have a dramatic effect on the height of the jets. The material returns to a solid-like behavior once the stresses due to the impact have relaxed to below the yield stress, leaving a crater in the surface of the material. We find that the diameter of this crater depends nonmonotonically on the impact speed. The crater shape also changes with speed, reflecting the dynamics of the impact process.

A linear stability analysis is presented to study the self-organized instabilities of a highly compliant elastic cylindrical shell filled with a viscous liquid and submerged in another viscous medium. The prototype closely mimics many components of micro- or nanofluidic devices and biological processes such as the budding of a string of pearls inside cells and sausage-string formation of blood vessels. The cylindrical shell is considered to be a soft linear elastic solid with small storage modulus. When the destabilizing capillary force derived from the cross-sectional curvature overcomes the stabilizing elastic and in-plane capillary forces, the microtube can spontaneously self-organize into one of several possible configurations; namely, pearling, in which the viscous fluid in the core of the elastic shell breaks up into droplets; sausage strings, in which the outer interface of the mircrotube deforms more than the inner interface; and wrinkles, in which both interfaces of the thin-walled mircrotube deform in phase with small amplitudes. This study identifies the conditions for the existence of these modes and demonstrates that the ratios of the interfacial tensions at the interfaces, the viscosities, and the thickness of the microtube play crucial roles in the mode selection and the relative amplitudes of deformations at the two interfaces. The analysis also shows asymptotically that an elastic fiber submerged in a viscous liquid is unstable for $Y=\gamma /\left(G_{e}R\right)>6$ and an elastic microchannel filled with a viscous liquid should rupture to form spherical cavities (pearling) for $Y>2$, where $\gamma$, $G_e$, and $R$ are the surface tension, elastic shear modulus, and radius, respectively, of the fiber or microchannel.

The topology and geometry of closed defect loops is studied in chiral nematic colloids with variable chirality. The colloidal particles with perpendicular surface anchoring of liquid crystalline molecules are inserted in a twisted nematic cell with the thickness that is only slightly larger than the diameter of the colloidal particle. The total twist of the chiral nematic structure in cells with parallel boundary conditions is set to 0, $\pi$, $2\pi$, and $3\pi$, respectively. We use the laser tweezers to discern the number and the topology of the $-1/2$ defect loops entangling colloidal particles. For a single colloidal particle, we observe that a single defect loop is winding around the particle, with the winding pattern being more complex in cells with higher total twist. We observe that colloidal dimers and colloidal clusters are always entangled by one or several $-1/2$ defect loops. For colloidal pairs in $\pi$-twisted cells, we identify at least 17 different entangled structures, some of them exhibiting linked defect loops-Hopf link. Colloidal entanglement is even richer with a higher number of colloidal particles, where we observe not only linked, but also colloidal clusters knotted into the trefoil knot. The experiments are in good agreement with numerical modeling using Landau-de Gennes theory coupled with geometrical and topological considerations using the method of tetrahedral rotation.

The liquid-crystal dimer 1′′,7′′-bis(4-cyanobiphenyl-4′-yl)heptane (CB7CB) exhibits two liquid-crystalline mesophases on cooling from the isotropic phase. The high-temperature phase is nematic; the identification and characterization of the other liquid-crystal phase is reported in this paper. It is concluded that the low-temperature mesophase of CB7CB is a new type of uniaxial nematic phase having a nonuniform director distribution composed of twist-bend deformations. The techniques of small-angle x-ray scattering, modulated differential scanning calorimetry, and dielectric spectroscopy have been applied to establish the nature of the nematic-nematic phase transition and the structural features of the twist-bend nematic phase. In addition, magnetic resonance studies (electron-spin resonance and ${}^2$H nuclear magnetic resonance) have been used to investigate the orientational order and director distribution in the liquid-crystalline phases of CB7CB. The synthesis of a specifically deuterated sample of CB7CB is reported, and measurements showed a bifurcation of the quadrupolar splitting on entering the low-temperature mesophase from the high-temperature nematic phase. This splitting could be interpreted in terms of the chirality of the twist-bend structure of the director. Calculations using an atomistic model and the surface interaction potential with Monte Carlo sampling have been carried out to determine the conformational distribution and predict dielectric and elastic properties in the nematic phase. The former are in agreement with experimental measurements, while the latter are consistent with the formation of a twist-bend nematic phase.

High-resolution x-ray scattering studies of the nonpolar thermotropic liquid crystal 4-$n$-pentylphenylthiol-4′-$n$-octyloxybenzoate ($\overline{8}S5$) in aerosil gel nanonetworks reveal that the aerosil-induced disorder significantly alters both the nematic to smectic-$A$ and smectic-$A$ to smectic-$C$ phase transitions. The limiting $\overline{8}S5$ smectic-$A$ correlation length follows a power-law dependence on the aerosil density in quantitative agreement with the limiting lengths measured previously in other smectic-$A$ liquid crystal gels. The smectic-$A$ to smectic-$C$ liquid crystalline phase transition is altered fundamentally by the presence of the aerosil gel. The onset of the smectic-$C$ phase remains relatively sharp but there is an extended coexistence region where smectic-$A$ and smectic-$C$ domains can exist.