Water is the most studied substance on Earth. However, it is not completely understood why its structural and dynamical properties give rise to some anomalous behaviors. Some of them emerge when experiments at low temperatures and/or high pressures are performed. Here we report dielectric measurements on cold water under macroscopically constrained conditions, i.e., water in a large container at constant volume that cannot freeze below the melting point. The inner pressure in these conditions shifts the $\alpha$ relaxation peak to similar frequencies as seen in ice Ih. At 267 K we observe a peculiar response possibly due to the Grotthuss mechanism. At 251 K (the triple point) ice III forms.

Glassy liquid crystalline systems are expected to show significant history-dependent effects. Two model glassy systems are the RAN and SSS (sprinkled silica spin) lattice models. The RAN model is a Lebwohl-Lasher lattice model with locally coupled nematic spins, together with uncorrelated random anisotropy fields at each site, while the SSS model has a finite concentration of impurity spins frozen in random directions. Here Brownian simulation is used to study the effect of different sample histories in the low temperature regime in a three-dimensional ($d=3$) model intermediate between SSS and RAN, in which a finite concentration $p<p_c$ ($p_c$ the percolation threshold) of frozen spins interacts with neighboring nematic spins with coupling $W$. Simulations were performed at temperature $T\sim T_{NI}/2$ ($T_{NI}$ the bulk nematic-isotropic transition temperature) for temperature-quenched and field-quenched histories (TQH and FQH, respectively), as well as for temperature-annealed histories (AH). The first two of these limits represent extreme histories encountered in typical experimental studies. Using long-time averages for equilibrated systems, we calculate orientational order parameters and two-point correlation functions. Finite-size scaling was used to determine the range of the orientational ordering, as a function of coupling strength $W,p$ and sample history. Sample history plays a significant role; for given concentration $p$, as disorder strength $W$ is increased, TQH systems sustain quasi-long-range order (QLRO) and short-range order (SRO). The data are also consistent with a long-range order (LRO) phase at very low disorder strength. By contrast, for FQH and $p\le 0.1$, only LRO and QLRO occur within the range of parameters investigated. The crossover between regimes depends on history, but in general, the FQH phase is more ordered than the AH phase, which is more ordered than the TQH phase. However, at temperatures close to the isotropic-nematic phase transition of pure samples we observe SRO for $p=0.1$ even for FQH. We detect also in the QLRO phase a domain-type structural pattern, consistent with ideas introduced by Giamarchi and Doussal [Phys. Rev. B 52, 1242 (1995)] on superconducting flux lattices. In the weak-disorder limit the orientational correlation length obeys the Larkin-Imry-Ma scaling $\xi \sim D^{-2/(4-d)}$.

Despite the recent progress in physical control and manipulation of various condensed matter, atomic, and particle systems, including individual atoms and photons, our ability to control topological defects remains limited. Recently, controlled generation, spatial translation, and stretching of topological point and line defects have been achieved using laser tweezers and liquid crystals as model defect-hosting systems. However, many modes of manipulation remain hindered by limitations inherent to optical trapping. To overcome some of these limitations, we integrate holographic optical tweezers with a magnetic manipulation system, which enables fully holonomic manipulation of defects by means of optically and magnetically controllable colloids used as “handles” to transfer forces and torques to various liquid crystal defects. These colloidal handles are magnetically rotated around determined axes and are optically translated along three-dimensional pathways while mechanically attached to defects, which, combined with inducing spatially localized nematic-isotropic phase transitions, allow for geometrically unrestricted control of defects, including previously unrealized modes of noncontact manipulation, such as the twisting of disclination clusters. These manipulation capabilities may allow for probing topological constraints and the nature of defects in unprecedented ways, providing the foundation for a tabletop laboratory to expand our understanding of the role defects play in fields ranging from subatomic particle physics to early-universe cosmology.

The glass transition temperature and the dynamics of the $\alpha$ and $\beta$ processes have been investigated using differential scanning calorimetry and dielectric relaxation spectroscopy during successive annealing processes above the glass transition temperature for stacked thin films of poly(methyl methacrylate) (PMMA) of various thicknesses. The glass transition temperature and the dynamics of the $\alpha$ process (segmental motion) of as-stacked PMMA thin films exhibit thin-film-like behavior, insofar as the glass transition temperature is depressed and the dynamics of the $\alpha$ process are faster than those of the bulk system. Annealing at high temperature causes the glass transition temperature to increase from the reduced value and causes the dynamics of the $\alpha$ process to become slower approaching those of the bulk. Contrary to the segmental motion, the relaxation time of the $\beta$ process (local motion) of the stacked PMMA thin films is almost equal to that of the bulk PMMA and is unaffected by the annealing process. However, the relaxation strengths of both the $\alpha$ process and $\beta$ process show a strong correlation between each other. The sum of the relaxation strengths remains almost unchanged, while the individual relaxation strengths change during the annealing process. The fragility index of the stacked PMMA thin films increases with annealing, which suggests that the glassy state of the stacked thin films changes from strong to fragile.

We study a biologically motivated model of overdamped, autochemotactic Brownian agents with concentration-dependent chemotactic sensitivity. The agents in our model move stochastically and produce a chemical ligand at their current position. The ligand concentration obeys a reaction-diffusion equation and acts as a chemoattractant for the agents, which bias their motion towards higher concentrations of the dynamically altered chemical field. We explore the impact of concentration-dependent response to chemoattractant gradients on large-scale pattern formation, by deriving a coarse-grained macroscopic description of the individual-based model, and compare the conditions for emergence of inhomogeneous solutions for different variants of the chemotactic sensitivity. We focus primarily on the so-called receptor-law sensitivity, which models a nonlinear decrease of chemotactic sensitivity with increasing ligand concentration. Our results reveal qualitative differences between the receptor law, the constant chemotactic response, and the so-called log law, with respect to stability of the homogeneous solution, as well as the emergence of different patterns (labyrinthine structures, clusters, and bubbles) via spinodal decomposition or nucleation. We discuss two limiting cases, where the model can be reduced to the dynamics of single species: (I) the agent density governed by a density-dependent effective diffusion coefficient and (II) the ligand field with an effective bistable, time-dependent reaction rate. In the end, we turn to single clusters of agents, studying domain growth and determining mean characteristics of the stationary inhomogeneous state. Analytical results are confirmed and extended by large-scale GPU simulations of the individual based model.

The behavior of a small isolated hydrate-free inclusion (a gas bubble) within a porous matrix filled with methane hydrate and either water or methane gas is analyzed. Simplifying assumptions of spherical symmetry, an infinite uniform porous medium, and negligible effects of background temperature and pressure variations focus the investigation on the features of the dynamics of a single bubble determined by a phase transition. Two solutions are presented: an exact solution of the Stefan problem obtained when the effects of gas and water flow are neglected, and a numerical solution of the full problem. The solutions are in good agreement with each other and with known asymptotic dependencies, confirming that the effects of inertia and convection transport can be neglected in the case of small inclusions. It is found that, after an initial adjustment, the radius of any small bubble decreases with time following a self-similar solution of the Stefan problem. The lifetime of a bubble is evaluated as a function of initial radius and the system's physical parameters. Possible effects of such inclusions on the filtration of methane to the surface and other aspects of the dynamics of hydrate-bearing deposits are discussed.

We present results for entropy and kinetic energy spectra computed from direct numerical simulations for low-Prandtl-number ($\text{Pr}<1$) turbulent flow in Rayleigh-Bénard convection with uniform rotation about a vertical axis. The simulations are performed in a three-dimensional periodic box for a range of the Taylor number ($0\le \text{Ta}\le {10}^8$) and reduced Rayleigh number $r=\text{Ra}/{\text{Ra}}_{\circ }(\text{Ta},\text{Pr})$ ($1.0\times {10}^2\le r\le 5.0\times {10}^3$). The Rossby number Ro varies in the range $1.34\le \text{Ro}\le 73$. The entropy spectrum $E_{\theta }\left(k\right)$ shows bisplitting into two branches for lower values of wave number $k$. The entropy in the lower branch scales with $k$ as $k^{-1.4\pm 0.1}$ for $r>{10}^3$ for the rotation rates considered here. The entropy in the upper branch also shows scaling behavior with $k$, but the scaling exponent decreases with increasing Ta for all $r$. The energy spectrum $E_v\left(k\right)$ is also found to scale with the wave number $k$ as $k^{-1.4\pm 0.1}$ for $r>{10}^3$. The scaling exponent for the energy spectrum and the lower branch of the entropy spectrum vary between $-1.7$ and $-2.4$ for lower values of $r$ ($<$${10}^3$). We also provide some simple arguments based on the variation of the Kolmogorov picture to support the results of simulations.

The flow of fluids and particulate suspensions in realistic models of geological fractures is investigated by lattice Boltzmann numerical simulations. The walls are synthetic self-affine fractal surfaces combined to produce a tight fracture, the fluid is a viscous Newtonian liquid, and the particles are rigid noncolloidal solid spheres. One focus is channeling phenomena, where we compare the fracture aperture, the preferred paths for fluid flow, and the preferred paths for suspended particles. The preferred paths are found to be somewhat similar for pure fluid and particulates and not immediately related to the fracture aperture map. We further investigate the (tensor) stress exerted on the fracture walls. Wall roughness tends to decrease stress by reducing the flow velocities adjacent to it, an effect enhanced by the presence of particulates. Last, we examine the stress probability distributions and their spatial correlation functions.

One goal of photoacoustic tomography (PAT) is to estimate an initial pressure function $\phi$ from pressure data measured at a boundary surrounding the object of interest. This paper is concerned with a time reversal method for PAT that is based on the dissipative wave equation of Nachman, Smith, and Waag [J. Acoust. Soc. Am. 88, 1584 (1990)]. This equation is a correction of the thermoviscous wave equation such that its solution has a finite wave front speed and, in contrast, it can model several relaxation processes. In this sense, it is more accurate than the thermoviscous wave equation. For simplicity, we focus on the case of one relaxation process. We derive an exact formula for the time reversal image $\mathcal{I}$, which depends on the relaxation time ${\tau }_1$ and the compressibility ${\kappa }_1$ of the dissipative medium, and show $\mathcal{I}({\tau }_1,{\kappa }_1)\to \phi$ for ${\kappa }_1\to 0$. This implies that $\mathcal{I}=\phi$ holds in the dissipation-free case and that $\mathcal{I}$ is similar to $\phi$ for sufficiently small compressibility ${\kappa }_1$. Moreover, we show for tissue similar to water that the small wave number approximation ${\mathcal{I}}_0$ of the time reversal image satisfies ${\mathcal{I}}_0={\eta }_0{*}_{\mathbf{x}}\phi$ with ${\widehat{\eta }}_0\left(\right|\mathbf{k}\left|\right)\approx \text{const}.$ for $\left|\mathbf{k}\right|\ll \frac{1}{c_0{\tau }_1}$, where $\phi$ denotes the initial pressure function. For such tissue, our theoretical analysis and numerical simulations show that the time reversal image $\mathcal{I}$ is very similar to the initial pressure function $\phi$ and that a resolution of $\sigma \approx 0.036\text{mm}$ is feasible (for exact measurement data).

We present numerical evidence for an extended order parameter and conjugate field for the dynamic phase transition in a Ginzburg-Landau mean-field model driven by an oscillating field. The order parameter, previously taken to be the time-averaged magnetization, comprises the deviations of the Fourier components of the magnetization from their values at the critical period. The conjugate field, previously taken to be the time-averaged magnetic field, comprises the even Fourier components of the field. The scaling exponents $\beta$ and $\delta$ associated with the extended order parameter and conjugate field are shown numerically to be consistent with their values in the equilibrium mean-field model.

We discuss statics and dynamics of condensation in a zero-range process with compartments of limited sizes. For the symmetric dynamics the stationary state has a factorized form. For the asymmetric dynamics the steady state factorizes only for special hopping rules which allow for overjumps of fully occupied compartments. In the limit of large system size the grand canonical analysis is exact also in a condensed phase, and for a broader class of hopping rates as compared to the previously studied systems with infinite compartments. The dynamics of condensation exhibits dynamical self-blocking, which significantly prolongs relaxation times. These general features are illustrated with a concrete example: an inhomogeneous system with hopping rates that result in Bose-Einstein-like condensations.

We present and analyze a model for the combination of bulk and surface electroclinic effects in the smectic-$A^{*}$ (Sm-$A^{*}$) phase near a Sm-$A^{*}$–Sm-$C^{*}$ transition. As part of our analysis we calculate the dependence of the surface tilt on external electric field and show that it can be eliminated, or even reversed from its zero-field value, as demonstrated in previous experimental work on a system (W415) with a continuous Sm-$A^{*}$–Sm-$C^{*}$ transition. We also analyze, for the first time, the combination of bulk and surface electroclinic effects in systems with a first-order Sm-$A^{*}$–Sm-$C^{*}$ transition. The variation of surface tilt with electric field in this case is much more dramatic, with discontinuities and hysteresis. With regard to technological, e.g., display, applications, this could be a feature to be avoided or potentially exploited. Near each type of Sm-$A^{*}$–Sm-$C^{*}$ transition we obtain the temperature dependence of the field required to eliminate surface tilt. Additionally, we analyze the effect of varying the system's enantiomeric excess, showing that it strongly affects the field dependence of surface tilt, in particular, near a first-order Sm-$A^{*}$–Sm-$C^{*}$ transition. In this case, increasing enantiomeric excess can change the field dependence of surface tilt from continuous to discontinuous. Our model also allows us to calculate the variation of layer spacing in going from surface to bulk, which in turn allows us to estimate the strain resulting from the difference between the surface and bulk layer spacing. We show that for certain ranges of applied electric field, this strain can result in layer buckling, which reduces the overall quality of the liquid crystal cell. For de Vries materials, with small tilt-induced change in layer spacing, the induced strain for a given surface tilt should be smaller. However, we argue that this may be offset by the fact that de Vries materials, which typically have Sm-$A^{*}$–Sm-$C^{*}$ transitions near a tricritical point, will generally have larger surface tilt.

The formation of a macroscopic cholesteric spiral in a nematic liquid crystal (LC) doped with chiral molecules is studied. Measurements of the orientation of the disclination line formed in a LC θ-cell manufactured with one substrate having linear in-plane alignment and the opposing substrate having circular alignment showed the formation of a uniform macroscopic cholesteric spiral with a pitch length of centimeters. We found a linear dependence of the reciprocal pitch $p^{-1}$ on the concentration $c$ in a wide range of $p$, extending from micrometers up to several centimeters. It suggests that the pitch of a spiral in a nematic LC doped with chiral dopants results from a long-range orientation owing to short-range chiral interactions in the vicinity of the chiral additive.

Experimentally resonant modes are commonly presumed to correspond to eigenmodes in the same bounded domain. However, the one-to-one correspondence between theoretical eigenmodes and experimental observations is never reached. Theoretically, eigenmodes in numerous classical and quantum systems are the solutions of the homogeneous Helmholtz equation, whereas resonant modes should be solved from the inhomogeneous Helmholtz equation. In the present paper we employ the eigenmode expansion method to derive the wave functions for manifesting the distinction between eigenmodes and resonant modes. The derived wave functions are successfully used to reconstruct a variety of experimental results including Chladni figures generated from the vibrating plate, resonant patterns excited from microwave cavities, and lasing modes emitted from the vertical cavity.

We study theoretically and numerically the velocity dynamics of fully chaotic time-dependent shape-preserving billiards. The average velocity of an ensemble of initial conditions generally asymptotically follows the power law $\langle v\rangle =n^{\beta }$ with respect to the number of collisions $n$. If a shape of a fully chaotic time-dependent billiard is not preserved it is well known that the acceleration exponent is $\beta =1/2$. We show, on the other hand, that if a shape of a fully chaotic time-dependent billiard is preserved then there are only three possible values of $\beta$ depending solely on the rotational properties of the billiard. In a special case in which the only transformation is a uniform rotation there is no acceleration, $\beta =0$. Excluding this special case, we show that if a time-dependent transformation of a billiard is such that the angular momentum of the billiard is preserved then $\beta =1/6$, while $\beta =1/4$ otherwise. Our theory is centered around the detailed study of the energy fluctuations in the adiabatic limit. We show that three quantities, two scalars and one tensor, completely determine the energy fluctuations of the billiard for arbitrary time-dependent shape-preserving transformations. Finally, we provide several interesting numerical examples, all in a perfect agreement with the theory.

We study the synchronization of dissipatively coupled van der Pol oscillators in the quantum limit, when each oscillator is near its quantum ground state. Two quantum oscillators with different frequencies exhibit an entanglement tongue, which is the quantum analog of an Arnold tongue. It means that the oscillators are entangled in steady state when the coupling strength is greater than a critical value, and the critical coupling increases with detuning. An ensemble of many oscillators with random frequencies still exhibits a synchronization phase transition in the quantum limit, and we analytically calculate how the critical coupling depends on the frequency disorder. Our results can be experimentally observed with trapped ions or neutral atoms.

In stably stratified turbulent flows, the mixing efficiency associated with eddy diffusivity for heat, or equivalently the turbulent Prandtl number (${\text{Pr}}_t$), is fraught with complex dynamics originating from the scalewise interplay between shear generation of turbulence and its dissipation by density gradients. A large corpus of data and numerical simulations agree on a near-universal relation between ${\text{Pr}}_t$ and the Richardson number ($R_i$), which encodes the relative importance of buoyancy dissipation to mechanical production of turbulent kinetic energy. The ${\text{Pr}}_t–R_i$ relation is shown to be derivable solely from the cospectral budgets for momentum and heat fluxes if a Rotta-like return to isotropy closure for the pressure-strain effects and Kolmogorov's theory for turbulent cascade are invoked. The ratio of the Kolmogorov to the Kolmogorov-Obukhov-Corrsin phenomenological constants, and a constant associated with isotropization of the production whose value ($=3/5$) has been predicted from Rapid Distortion Theory, explain all the macroscopic nonlinearities.

The observation is presented of naturally occurring pairing of particles and their cooperative drift in a two-dimensional plasma crystal. A single layer of plastic microspheres was suspended in the plasma sheath of a capacitively coupled radio-frequency discharge in argon at a low pressure of 1 Pa. The particle dynamics were studied by combining the top-view and side-view imaging of the suspension. Cross-analysis of the particle trajectories allowed us to identify naturally occurring metastable pairs of particles. The lifetime of pairs was long enough for their reliable identification.

Hierarchical and fractal designs have been shown to yield high mechanical efficiency under a variety of loading conditions. Here a fractal frame is optimized for compressive loading in a two-dimensional space. We obtain the dependence of volume required for stability against loading for which the structure is optimized and a set of scaling relationships is found. We evaluate the dependence of the Hausdorff dimension of the optimal structure on the applied loading and establish the limit to which it tends under gentle loading. We then investigate the effect of a single imperfection in the structure through both analytical and simulational techniques. We find that a single asymmetric perturbation of beam thickness, increasing or decreasing the failure load of the individual beam, causes the same decrease in overall stability of the structure. A scaling relationship between imperfection magnitude and decrease in failure loading is obtained. We calculate theoretically the limit to which the single perturbation can effect the overall stability of higher generation frames.

We study the wave breaking mechanism for the weakly dispersive defocusing nonlinear Schrödinger equation with a constant phase dark initial datum that contains a vacuum point at the origin. We prove by means of the exact solution to the initial value problem that, in the dispersionless limit, the vacuum point is preserved by the dynamics until breaking occurs at a finite critical time. In particular, both Riemann invariants experience a simultaneous breaking at the origin. Although the initial vacuum point is no longer preserved in the presence of a finite dispersion, the critical behavior manifests itself through an abrupt transition occurring around the breaking time.