Octahedral spherical hohlraums with a single laser ring at an injection angle of ${55}^{\circ }$ are attractive concepts for laser indirect drive due to the potential for achieving the x-ray drive symmetry required for high convergence implosions. Laser-plasma instabilities, however, are a concern given the long laser propagation path in such hohlraums. Significant stimulated Raman scattering has been observed in cylindrical hohlraums with similar laser propagation paths during the ignition campaign on the National Ignition Facility (NIF). In this Rapid Communication, experiments demonstrating low levels of laser-driven plasma instability (LPI) in spherical hohlraums with a laser injection angle of ${55}^{\circ }$ are reported and compared to that observed with cylindrical hohlraums with injection angles of $28.5^{\circ }$ and ${55}^{\circ }$, similar to that of the NIF. Significant LPI is observed with the laser injection of $28.5^{\circ }$ in the cylindrical hohlraum where the propagation path is similar to the ${55}^{\circ }$ injection angle for the spherical hohlraum. The experiments are performed on the SGIII laser facility with a total $0.35\text{−}\mu \mathrm{m}$ incident energy of 93 kJ in a 3 nsec pulse. These experiments demonstrate the role of hohlraum geometry in LPI and demonstrate the need for systematic experiments for choosing the optimal configuration for ignition studies with indirect drive inertial confinement fusion.

We show that uncorrelated Gaussian noise can drive a system out of equilibrium and can serve as a resource from which work can be extracted. We consider an overdamped particle in a periodic potential with an internal degree of freedom and a state-dependent friction, coupled to an equilibrium bath. Applying additional Gaussian white noise drives the system into a nonequilibrium steady state and causes a finite current if the potential is spatially asymmetric. The model thus operates as a Brownian ratchet, whose current we calculate explicitly in three complementary limits. Since the particle current is driven solely by additive Gaussian white noise, this shows that the latter can potentially perform work against an external load. By comparing the extracted power to the energy injection due to the noise, we discuss the efficiency of such a ratchet.

We introduce a two-component one-dimensional system, which is based on two nonlinear Schrödinger or Gross-Pitaevskii equations (GPEs) with spatially periodic modulation of linear coupling (“Rabi lattice”) and self-repulsive nonlinearity. The system may be realized in a binary Bose-Einstein condensate, whose components are resonantly coupled by a standing optical wave, as well as in terms of the bimodal light propagation in periodically twisted waveguides. The system supports various types of gap solitons (GSs), which are constructed, and their stability is investigated, in the first two finite bandgaps of the underlying spectrum. These include on- and off-site-centered solitons (the GSs of the off-site type are additionally categorized as spatially even and odd ones), which may be symmetric or antisymmetric, with respect to the coupled components. The GSs are chiefly stable in the first finite bandgap and unstable in the second one. In addition to that, there are narrow regions near the right edge of the first bandgap, and in the second one, which feature intricate alternation of stability and instability. Unstable solitons evolve into robust breathers or spatially confined turbulent modes. On-site-centered GSs are also considered in a version of the system that is made asymmetric by the Zeeman effect, or by birefringence of the optical waveguide. A region of alternate stability is found in the latter case too. In the limit of strong asymmetry, GSs are obtained in a semianalytical approximation, which reduces two coupled GPEs to a single one with an effective lattice potential.

Nonparametric detrending or noise reduction methods are often employed to separate trends from noisy time series when no satisfactory models exist to fit the data. However, conventional noise reduction methods depend on subjective choices of smoothing parameters. Here we present a simple multivariate noise reduction method based on available nonlinear forecasting techniques. These are in turn based on state-space reconstruction for which a strong theoretical justification exists for their use in nonparametric forecasting. The noise reduction method presented here is conceptually similar to Schreiber's noise reduction method using state-space reconstruction. However, we show that Schreiber's method has a minor flaw that can be overcome with forecasting. Furthermore, our method contains a simple but nontrivial extension to multivariate time series. We apply the method to multivariate time series generated from the Van der Pol oscillator, the Lorenz equations, the Hindmarsh-Rose model of neuronal spiking activity, and to two other univariate real-world data sets. It is demonstrated that noise reduction heuristics can be objectively optimized with in-sample forecasting errors that correlate well with actual noise reduction errors.

We consider a cyclically competing species model on a ring with global mixing at finite rate, which corresponds to the well-known Lotka-Volterra equation in the limit of infinite mixing rate. Within a perturbation analysis of the model from the infinite mixing rate, we provide analytical evidence that extinction occurs deterministically at sufficiently large but finite values of the mixing rate for any species number $N\ge 3$. Further, by focusing on the cases of rather small species numbers, we discuss numerical results concerning the trajectories toward such deterministic extinction, including global bifurcations caused by changing the mixing rate.

Low-frequency Raman spectra of multilamellar vesicles made either of 1-palmitoyl-2-oleoyl-$sn$-glycero-3-phosphocholine (POPC) or 1,2-dipalmitoyl-$sn$-glycero-3-phosphocholine (DPPC) have been studied in a wide temperature range. Below $0{}^{\circ }\mathrm{C}$ two peaks are found at frequencies around 8–9 and $14-17\mathrm{c}{\mathrm{m}}^{-1}$ and attributed to the normal vibrational modes of the phospholipid bilayer, which are determined by the bilayer thickness and stiffness (elastic modulus). The spectral positions of the peaks depend on the temperature and the bilayer composition. It is suggested that the ratio of the intensities of the first and second peaks can serve as a measure of the interleaflet elastic coupling. The addition of cholesterol to the phospholipid bilayer leads to peak shift and broadening, which may be assigned to the composition heterogeneities commonly attributed to the lipid raft formation.

The microstructural organization of a granular system is the most important determinant of its macroscopic behavior. Here we identify the fundamental factors that determine the statistics of such microstructures, using numerical experiments to gain a general understanding. The experiments consist of preparing and compacting isotropically two-dimensional granular assemblies of polydisperse frictional disks and analyzing the emergent statistical properties of quadrons—the basic structural elements of granular solids. The focus on quadrons is because the statistics of their volumes have been found to display intriguing universal-like features [T. Matsushima and R. Blumenfeld, Phys. Rev. Lett. 112, 098003 (2014)]. The dependence of the structures and of the packing fraction on the intergranular friction and the initial state is analyzed, and a number of significant results are found. (i) An analytical formula is derived for the mean quadron volume in terms of three macroscopic quantities: the mean coordination number, the packing fraction, and the rattlers fraction. (ii) We derive a unique, initial-state-independent relation between the mean coordination number and the rattler-free packing fraction. The relation is supported numerically for a range of different systems. (iii) We collapse the quadron volume distributions from all systems onto one curve, and we verify that they all have an exponential tail. (iv) The nature of the quadron volume distribution is investigated by decomposition into conditional distributions of volumes given the cell order, and we find that each of these also collapses onto a single curve. (v) We find that the mean quadron volume decreases with increasing intergranular friction coefficients, an effect that is prominent in high-order cells. We argue that this phenomenon is due to an increased probability of stable irregularly shaped cells, and we test this using a herewith developed free cell analytical model. We conclude that, in principle, the microstructural characteristics are governed mainly by the packing procedure, while the effects of intergranular friction and initial states are details that can be scaled away. However, mechanical stability constraints suppress slightly the occurrence of small quadron volumes in cells of order $\ge 6$, and the magnitude of this effect does depend on friction. We quantify in detail this dependence and the deviation it causes from an exact collapse for these cells. (vi) We argue that our results support strongly the view that ensemble granular statistical mechanics does not satisfy the uniform measure assumption of conventional statistical mechanics. Results (i)–(iv) have been reported in the aforementioned reference, and they are reviewed and elaborated on here.

Dynamics of Langmuir solitons in the presence of a background density gradient is investigated numerically, including cases with steep gradients to the extent the solitons can disintegrate. The disintegration threshold is explained by regarding the electric field part of the soliton as a point mass moving along the self-generated potential well corresponding to the density cavity. On the other hand, it is demonstrated that the Langmuir solitons are robust when the density gradient is below the threshold. During the acceleration phase toward low density regions, Langmuir solitons adjust themselves to balance the electric field pressure and the negative plasma pressure by expelling the imbalanced portion as density cavities at the sound velocity. When the density gradient is below the disintegration threshold, the electric field part of the soliton bounces back and forth within the potential well suggesting the solitons have internal structures.

The self-energy term used in transport calculations, which describes the coupling between electrode and transition regions, is able to be evaluated only from a limited number of the propagating and evanescent waves of a bulk electrode. This obviously contributes toward the reduction of the computational expenses in transport calculations. In this paper, we present a mathematical formula for reducing the computational expenses further without using any approximation and without losing accuracy. So far, the self-energy term has been handled as a matrix with the same dimension as the Hamiltonian submatrix representing the interaction between an electrode and a transition region. In this work, through the singular-value decomposition of the submatrix, the self-energy matrix is handled as a smaller matrix, whose dimension is the rank number of the Hamiltonian submatrix. This procedure is practical in the case of using the pseudopotentials in a separable form, and the computational expenses for determining the self-energy matrix are reduced by 90% when employing a code based on the real-space finite-difference formalism and projector-augmented wave method. In addition, this technique is applicable to the transport calculations using atomic or localized basis sets. Adopting the self-energy matrices obtained from this procedure, we present the calculation of the electron transport properties of ${\mathrm{C}}_{20}$ molecular junctions. The application demonstrates that the electron transmissions are sensitive to the orientation of the molecule with respect to the electrode surface. In addition, channel decomposition of the scattering wave functions reveals that some unoccupied ${\mathrm{C}}_{20}$ molecular orbitals mainly contribute to the electron conduction through the molecular junction.

The deformation and fragmentation of liquid metal microdroplets by intense subpicosecond Ti:sapphire laser pulses is experimentally studied with stroboscopic shadow photography. The experiments are performed at a peak intensity of ${10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ at the target's surface, which produces shock waves with pressures in the Mbar range. As a result of such a strong impact, the droplet is transformed into a complex-shaped hollow structure that undergoes asymmetrical expansion and eventually fragments. The hollow structure of the expanding target is explained by the effects of cavitation and spallation that follow the propagation of the laser-induced shock wave.

For stationary, homogeneous Markov processes (viz., Lévy processes, including Brownian motion) in dimension $d\ge 3$, we establish an exact formula for the average number of $(d-1)$-dimensional facets that can be defined by $d$ points on the process's path. This formula defines a universality class in that it is independent of the increments' distribution, and it admits a closed form when $d=3$, a case which is of particular interest for applications in biophysics, chemistry, and polymer science. We also show that the asymptotical average number of facets behaves as $\langle {\mathcal{F}}_T^{\left(d\right)}\rangle \sim 2{\left[ln\left(T/\mathrm{\Delta }t\right)\right]}^{d-1}$, where $T$ is the total duration of the motion and $\mathrm{\Delta }t$ is the minimum time lapse separating points that define a facet.

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast-growing complex systems. In order to model such phenomena we apply both a discrete and a continuous master equation. The derivation of elementary rates from known stationary distributions is a generalization of the fluctuation-dissipation theorem. Entropic distance evolution is given for such systems. We reconstruct distributions obtained for growing networks, particle production, scientific citations, and income distribution.

A perturbative renormalization group method is used to obtain steady-state density profiles of a totally asymmetric simple exclusion process with particle adsorption and evaporation. This method allows us to obtain a globally valid solution for the density profile without the asymptotic matching of bulk and boundary layer solutions. In addition, we show a nontrivial scaling of the boundary layer width with the system size close to specific phase boundaries.

We numerically investigate spherically symmetric collapses in the Gross–Pitaevskii equation with attractive nonlinearity in a harmonic potential. Even below threshold for direct collapse, the wave function bounces off from the origin and may eventually become singular after a number of oscillations in the trapping potential. This is reminiscent of the evolution of Einstein gravity sourced by a scalar field in anti de Sitter space where collapse corresponds to black-hole formation. We carefully examine the long time evolution of the wave function for continuous families of initial states in order to sharpen out this qualitative coincidence which may bring new insights in both directions. On the one hand, we comment on possible implications for the so-called Bosenova collapses in cold atom Bose–Einstein condensates. On the other hand, Gross–Pitaevskii provides a toy model to study the relevance of either the resonance conditions or the nonlinearity for the problem of anti de Sitter instability.

A recent burst of dynamic single-cell data makes it possible to characterize the stochastic dynamics of cell division control in bacteria. Different models were used to propose specific mechanisms, but the links between them are poorly explored. The lack of comparative studies makes it difficult to appreciate how well any particular mechanism is supported by the data. Here, we describe a simple and generic framework in which two common formalisms can be used interchangeably: (i) a continuous-time division process described by a hazard function and (ii) a discrete-time equation describing cell size across generations (where the unit of time is a cell cycle). In our framework, this second process is a discrete-time Langevin equation with simple physical analogues. By perturbative expansion around the mean initial size (or interdivision time), we show how this framework describes a wide range of division control mechanisms, including combinations of time and size control, as well as the constant added size mechanism recently found to capture several aspects of the cell division behavior of different bacteria. As we show by analytical estimates and numerical simulations, the available data are described precisely by the first-order approximation of this expansion, i.e., by a “linear response” regime for the correction of size fluctuations. Hence, a single dimensionless parameter defines the strength and action of the division control against cell-to-cell variability (quantified by a single “noise” parameter). However, the same strength of linear response may emerge from several mechanisms, which are distinguished only by higher-order terms in the perturbative expansion. Our analytical estimate of the sample size needed to distinguish between second-order effects shows that this value is close to but larger than the values of the current datasets. These results provide a unified framework for future studies and clarify the relevant parameters at play in the control of cell division.

Polycrystals of thin colloidal deposits, with thickness controlled by spin-coating speed, exhibit axial symmetry with local 4-fold and 6-fold symmetric structures, termed orientationally correlated polycrystals (OCPs). While spin-coating is a very facile technique for producing large-area colloidal deposits, the axial symmetry prevents us from achieving true long-range order. To obtain true long-range order, we break this axial symmetry by introducing a patterned surface topography and thus eliminate the OCP character. We then examine symmetry-independent methods to quantify order in these disordered colloidal deposits. We find that all the information in the bond-orientational order parameters is well captured by persistent homology analysis methods that only use the centers of the particles as input data. It is expected that these methods will prove useful in characterizing other disordered structures.

We carry out phase field simulations to study properties of the comblike step patterns induced by an adatom source. When an adatom source advances right in front of a step, step wandering is caused by the asymmetry of the surface diffusion field and small protrusions are formed. If the velocity of the source $V_{\mathrm{p}}$ is smaller than a critical value $V_{\mathrm{p}}^{\mathrm{c}}$, the protrusions follow the adatom source with coarsening of the step pattern, and a regular comblike pattern with finger-like protrusions is formed. With a sufficiently small $V_{\mathrm{p}}$, the gap of the supersaturation is large at the adatom source. Since the period of protrusions, $\mathrm{\Lambda }$, decreases with increasing $V_{\mathrm{p}}$, the coarsening of step pattern is irrelevant for the protrusions to catch up with the adatom source. Near $V_{\mathrm{p}}^{\mathrm{c}}$, the gap of the supersaturation at the adatom source is small. Taking account of the increase in $\mathrm{\Lambda }$ with increasing $V_{\mathrm{p}}$, the coarsening of the step pattern is essential for the protrusions to follow the adatom source.

We consider the acousto-optic effect in a random medium. We derive the radiative transport equations that describe the propagation of multiply scattered light in a medium whose dielectric permittivity is modulated by an acoustic wave. Using this result, we present an analysis of the sensitivity of an acousto-optic measurement to the presence of a small absorbing inhomogeneity.

We present a self-contained engine, which is made of one or more two-level systems, each of which is coupled to a single bath, as well as to a common load composed of a particle on a tilted lattice. We show that an increase in time of energy and entropy in the system composed of the spins and the particle, due to the interaction with the bath, can set the particle into upward motion at an average constant speed, even when driven by a single spin connected to a single bath. When considering an ensemble of different spins, the velocity of the particle is larger when the tilt is on resonance with any of the spins' energy splitting. Interestingly, we find regimes where the spins' polarization enters periodic cycles with the oscillation period being determined by the tilt of the lattice.

Using the algebraic Bethe Ansatz, we derive a matrix product representation of the exact Bethe-Ansatz states of the six-vertex Heisenberg chain (either $XXX$ or $XXZ$ and spin-$\frac{1}{2}$) with open boundary conditions. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices that act on a tensor product of auxiliary spaces. As compared to the matrix product states of the same Heisenberg chain but with periodic boundary conditions, the dimension of the exact auxiliary matrices is enlarged as if the conserved number of spin-flips considered would have been doubled. This result is generic for any non-nested integrable model, as is clear from our derivation, and we further show this by providing an additional example of the same matrix product state construction for a well-known model of a gas of interacting bosons. Counterintuitively, the matrices do not depend on the spatial coordinate despite the open boundaries, and thus they suggest generic ways of exploiting (emergent) translational invariance both for finite size and in the thermodynamic limit.