We investigate poly($N$-isopropylacrylamide) (pNIPAM) microgels randomly copolymerized with large mol % of protonated acrylic acid (AAc), finding that above the lower critical solution temperature the presence of the acid strongly disrupts pNIPAM's collapse, leading to unexpected new behavior at high temperatures. Specifically, we see a dramatic increase in the ratio between the radius of gyration and the hydrodynamic radius above the theoretical value for homogeneous spheres, and a corresponding increase of the network length scale, which we attribute to the presence of a heterogeneous polymer distribution that forms due to frustration of pNIPAM's coil-to-globule transition by the AAc. We analyze this phenomenon using a Debye-Bueche-like scattering contribution as opposed to the Lorentzian term often used, interpreting the results in terms of mass segregation at the particle periphery.

A method for computing the thermopower in interacting systems is proposed. This approach, which relies on Monte Carlo simulations, is illustrated first for a diatomic chain of hard-point elastically colliding particles and then in the case of a one-dimensional gas with (screened) Coulomb interparticle interaction. Numerical simulations up to $N>{10}^4$ particles confirm the general theoretical arguments for momentum-conserving systems and show that the thermoelectric figure of merit increases linearly with the system size.

The mean-square displacement (MSD) is widely utilized to study the dynamical properties of stochastic processes. The time-averaged MSD (TAMSD) provides some information on the dynamics which cannot be extracted from the ensemble-averaged MSD. In particular, the relative standard deviation (RSD) of the TAMSD can be utilized to study the long-time relaxation behavior. In this work, we consider a class of Langevin equations which are multiplicatively coupled to time-dependent and fluctuating diffusivities. Various interesting dynamics models such as entangled polymers and supercooled liquids can be interpreted as the Langevin equations with time-dependent and fluctuating diffusivities. We derive a general formula for the RSD of the TAMSD for the Langevin equation with the time-dependent and fluctuating diffusivity. We show that the RSD can be expressed in terms of the correlation function of the diffusivity. The RSD exhibits the crossover at the long time region. The crossover time is related to a weighted average relaxation time for the diffusivity. Thus the crossover time gives some information on the relaxation time of fluctuating diffusivity which cannot be extracted from the ensemble-averaged MSD. We discuss the universality and possible applications of the formula via some simple examples.

We investigate stochastic models of particles entering a channel with a random time distribution. When the number of particles present in the channel exceeds a critical value $N$, a blockage occurs and the particle flux is definitively interrupted. By introducing an integral representation of the $n$-particle survival probabilities, we obtain exact expressions for the survival probability, the distribution of the number of particles that pass before failure, the instantaneous flux of exiting particles, and their time correlation. We generalize previous results for $N=2$ to an arbitrary distribution of entry times and obtain exact solutions for $N=3$ for a Poisson distribution and partial results for $N\ge 4$.

We derive exact analytic expressions for the average work done and work fluctuations in instantaneous quenches of the ground and thermal states of a one-dimensional anisotropic XY model. The average work and a quantum fluctuation relation is used to determine the amount of irreversible entropy produced during the quench, eventually revealing how the closing of the excitation gap leads to increased dissipated work. The work fluctuation is calculated and shown to exhibit nonanalytic behavior as the prequench anisotropy parameter and transverse field are tuned across quantum critical points. Exact compact formulas for the average work and work fluctuation in ground state quenches of the transverse field Ising model allow us to calculate the first singular field derivative at the critical field values.

We consider stochastic energy balance and entropy production (EP) in a generalized Langevin dynamics of macrospins, allowing for both amplitude and direction fluctuations, under external magnetic field. EP is calculated using a Fokker-Planck equation, distinguishing between reversible and irreversible parts of probability currents. The system entropy increases due to irreversible non-equilibrium processes, and reduces as heat dissipates to the surrounding environment. Using path probability distributions of time-forward trajectories and conjugate trajectories under time reversal, we obtain fluctuation theorems (FT) for total stochastic EP. We show that the choice of conjugate trajectories is crucial in obtaining entropy-like quantities that obey FTs.

We examine the ordering properties of rectangular hard rods with length $L$ and diameter $D$ at a single planar wall and between two parallel hard walls using the second virial density-functional theory. The theory is implemented in the three-state Zwanzig approximation, where only three mutually perpendicular directions are allowed for the orientations of hard rods. The effect of varying shape anisotropy is examined at $L/D=10,15,\mathrm{and}20$. In contact with a single hard wall, the density profiles show planar ordering, damped oscillatory behavior, and a wall-induced surface ordering transition below the coexisting isotropic density of a bulk isotropic-nematic $\left(I\text{−}N\right)$ phase transition. Upon approaching the coexisting isotropic density, the thickness of the nematic film diverges logarithmically, i.e., the nematic wetting is complete for any shape anisotropy. In the case of confinement between two parallel hard walls, it is found that the continuous surface ordering transition depends strongly on the distance between confining walls $H$ for $H<L$, while it depends weakly on $H$ for $H>L$. The minimal density at which a surface ordering transition can be realized is located at around $H\sim 2D$ for all studied shape anisotropies due to the strong interference effect between the two hard walls. The first-order $I\text{−}N$ phase transition of the bulk system becomes a surface ordered isotropic $I_B$ to capillary nematic $N_B$ phase transition in the slit pore. This first-order $I_B\text{−}{N}_B$ transition weakens with decreasing pore width and terminates in a critical point for all studied shape anisotropies.

Using a recently developed bead-spring model for semiflexible polymers that takes into account their natural extensibility, we report an efficient algorithm to simulate the dynamics for polymers like double-stranded DNA (dsDNA) in the absence of hydrodynamic interactions. The dsDNA is modeled with one bead-spring element per base pair, and the polymer dynamics is described by the Langevin equation. The key to efficiency is that we describe the equations of motion for the polymer in terms of the amplitudes of the polymer's fluctuation modes, as opposed to the use of the physical positions of the beads. We show that, within an accuracy tolerance level of $5\%$ of several key observables, the model allows for single Langevin time steps of $\approx 1.6$, 8, 16, and 16 ps for a dsDNA model chain consisting of 64, 128, 256, and 512 base pairs (i.e., chains of 0.55, 1.11, 2.24, and 4.48 persistence lengths), respectively. Correspondingly, in 1 h, a standard desktop computer can simulate 0.23, 0.56, 0.56, and 0.26 ms of these dsDNA chains, respectively. We compare our results to those obtained from other methods, in particular, the (inextensible discretized) wormlike chain (WLC) model. Importantly, we demonstrate that at the same level of discretization, i.e., when each discretization element is one base pair long, our algorithm gains about five to six orders of magnitude in the size of time steps over the inextensible WLC model. Further, we show that our model can be mapped one on one to a discretized version of the extensible WLC model, implying that the speed-up we achieve in our model must hold equally well for the latter. We also demonstrate the use of the method by simulating efficiently the tumbling behavior of a dsDNA segment in a shear flow.

We present a model of biopolymer gels that includes two types of elastic nonlinearities, stiffening under extension and softening (due to buckling) under compression, to predict the elastic anisotropy induced by both external as well as internal (e.g., due to cell contractility) stresses in biopolymer gels. We show how the stretch-induced anisotropy and the strain-stiffening nonlinearity increase both the amplitude and power-law range of transmission of internal, contractile, cellular forces, and relate this to recent experiments.

In this work, we analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. We provide two improvements in our understanding of this quantity: first of all, in our interpretation, a hyperbolic network is “aristocratic”, since few elements “connect” the system, while a non-hyperbolic network has a more “democratic” structure with a larger number of crucial elements. The second contribution is the introduction of the average hyperbolicity of the neighbors of a given node. Through this definition, we outline an “influence area” for the vertices in the graph. We show that in real networks the influence area of the highest degree vertex is small in what we define “local” networks (i.e., social or peer-to-peer networks), and large in “global” networks (i.e., power grid, metabolic networks, or autonomous system networks).

We present an experimental study on the statistical properties of the injected power needed to maintain an inelastic ball bouncing constantly on a randomly accelerating piston in the presence of gravity. We compute the injected power at each collision of the ball with the moving piston by measuring the velocity of the piston and the force exerted on the piston by the ball. The probability density function of the injected power has its most probable value close to zero and displays two asymmetric exponential tails, depending on the restitution coefficient, the piston acceleration, and its frequency content. This distribution can be deduced from a simple model assuming quasi-Gaussian statistics for the force and velocity of the piston.

The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool—nonlinear mode decomposition (NMD)—which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques—which, together with the adaptive choice of their parameters, make it extremely noise robust—and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.

Using high-resolution particle tracking velocimetry and filter-space techniques, we study the links between the scale-to-scale transfer of energy and enstrophy and instantaneously rotational and straining regions as determined by the classic Okubo-Weiss parameter in a quasi-two-dimensional laboratory flow. Although the Okubo-Weiss parameter has shortcomings, we find that, when suitably conditioned, it is surprisingly a good predictor for the future evolution of the spectral fluxes. By studying Lagrangian correlation functions, we explain our findings by showing that both the spectral fluxes and the Okubo-Weiss parameter are independently correlated for long times along fluid-element trajectories and thus that any predictive capacity of the Okubo-Weiss parameter arises because it is coupled to fluid advection. Our results suggest potential strategies for forecasting in complex flows by looking for quantities with long Lagrangian correlation times.

We describe the impact of heating and ionization on emission from the target of $K\alpha$ and $K\beta$ radiation induced by the propagation of hot electrons generated by laser-matter interaction. We consider copper as a test case and, starting from basic principles, we calculate the changes in emission wavelength, ionization cross section, and fluorescence yield as Cu is progressively ionized. We have finally considered the more realistic case when hot electrons have a distribution of energies with average energies of 50 and 500 keV (representative respectively of “shock ignition” and of “fast ignition” experiments) and in which the ions are distributed according to ionization equilibrium. In addition, by confronting our theoretical calculations with existing data, we demonstrate that this study offers a generic theoretical background for temperature diagnostics in laser-plasma interactions.

The emission of x rays from warm dense matter is of great interest for both spectroscopic diagnostics and development of intense x-ray sources. We report the results from the collisional-radiative steady-state (CRSS) modeling of atomic and optical properties of copper plasmas at near-solid and solid-state density for a range of temperatures. The CRSS model is validated against the available data on the average charge state and shifts of energy levels in aluminum and the opacity and emissivity spectra of carbon and aluminum plasmas. The average charge states, number density of ion species, and free electrons as a function of temperature are investigated for the solid-density copper plasma. Due to the dense plasma environment the four outer electrons are found to be unbounded even in the low-temperature limit $\sim 1\mathrm{eV}$. As the temperature changes from 1 to 100 eV, the predominant species vary from fivefold- to twelvefold-ionized copper ions. The opacity and emissivity spectra of dense copper plasmas are studied using the local thermodynamic equilibrium (LTE) and non-LTE approaches. It is found that the non-LTE effects are important in the spectral region of soft x rays emitted from the $K$ shell. The emissivity in spectral lines is completely suppressed, indicating the importance of the energy-dissipating radiative processes in this soft x-ray region. Line broadening and redshifts of the $K$- and $L$-shell spectral lines toward higher wavelengths are observed with the increase of plasma density. These results have important implications for understanding the radiative properties of warm dense copper and can be useful for future experimental studies.

Evaluating the concentration dependence of static and dynamic properties of macromolecules in semidilute polymer solutions requires accurate calculation of long-range hydrodynamic interactions (HI) and short range excluded volume (EV) forces. In conventional Brownian dynamics simulations (BDS), computation of HI necessitates construction of a dense diffusion tensor commonly performed via Ewald summation. Krylov subspace techniques allow efficient decomposition of this tensor [computational cost scales as $O\left(N^2\right)$, where $N$ is the total number of beads in bead-spring representation of macromolecules in a simulation box] and computation of Brownian displacements in the box. In this paper, a matrix-free approach for calculation of HI is implemented which leads to $O\left(NlogN\right)$ scaling of computational expense. The fidelity of the algorithm is demonstrated by evaluating the asymptotic value of center-of-mass diffusivity of polymer molecules at very low concentrations and their radius of gyration scaling as a function of number of beads for dilute and semidilute solutions (with concentrations up to 5 times the overlap concentration). In turn, a favorable comparison between our results and the blob theory is shown.

We solve the Navier-Stokes equations with two simultaneous forcings. One forcing is applied at a given large scale and it injects energy. The other forcing is applied at all scales belonging to the inertial range and it injects helicity. In this way we can vary the degree of turbulence helicity from nonhelical to maximally helical. We find that increasing the rate of helicity injection does not change the energy flux. On the other hand, the level of total energy is strongly increased and the energy spectrum gets steeper. The energy spectrum spans from a Kolmogorov scaling law $k^{-5/3}$ for a nonhelical turbulence, to a non-Kolmogorov scaling law $k^{-7/3}$ for a maximally helical turbulence. In the latter case we find that the characteristic time of the turbulence is not the turnover time but a time based on the helicity injection rate. We also analyze the results in terms of helical modes decomposition. For a maximally helical turbulence one type of helical mode is found to be much more energetic than the other one, by several orders of magnitude. The energy cascade of the most energetic type of helical mode results from the sum of two fluxes. One flux is negative and can be understood in terms of a decimated model. This negative flux, however, is not sufficient to lead an inverse energy cascade. Indeed, the other flux involving the least energetic type of helical mode is positive and the largest. The least energetic type of helical mode is then essential and cannot be neglected.

The direction of the steady-state heat currents across a generic quantum system connected to multiple baths may be engineered to realize virtually any thermodynamic cycle. In spite of their versatility, such continuous energy-conversion systems are generally unable to operate at maximum efficiency due to non-negligible sources of irreversible entropy production. In this paper we introduce a minimal model of irreversible absorption chiller. We identify and characterize the different mechanisms responsible for its irreversibility, namely heat leaks and internal dissipation, and gauge their relative impact in the overall cooling performance. We also propose reservoir engineering techniques to minimize these detrimental effects. Finally, by looking into a known three-qubit embodiment of the absorption cooling cycle, we illustrate how our simple model may help to pinpoint the different sources of irreversibility naturally arising in more complex practical heat devices.

The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the conceptual framework we solve a pedagogical, yet experimentally relevant, system analytically. As a main result we obtain the exact quantum work distributions for charged particles traveling through a time-dependent vector potential evolving under Schrödinger as well as under Dirac dynamics, and for which the Jarzynski equality is verified. Special emphasis is put on the conceptual and technical subtleties arising from relativistic quantum mechanics.