We study dynamic cooling, where an externally driven two-level system is cooled via reservoir, a quantum system with initial canonical equilibrium state. We obtain explicitly the minimal possible temperature $T_{\min }>0$ reachable for the two-level system. The minimization goes over all unitary dynamic processes operating on the system and reservoir and over the reservoir energy spectrum. The minimal work needed to reach $T_{\min }$ grows as $1/T_{\min }$. This work cost can be significantly reduced, though, if one is satisfied by temperatures slightly above $T_{\min }$. Our results on $T_{\min }>0$ prove unattainability of the absolute zero temperature without ambiguities that surround its derivation from the entropic version of the third law. We also study cooling via a reservoir consisting of $N\gg 1$ identical spins. Here we show that $T_{\min }\propto \frac{1}{N}$ and find the maximal cooling compatible with the minimal work determined by the free energy. Finally we discuss cooling by reservoir with an initially microcanonic state and show that although a purely microcanonic state can yield the zero temperature, the unattainability is recovered when taking into account imperfections in preparing the microcanonic state.

Low-dimensional systems with long-range couplings usually present phase transitions which are absent in the short-ranged counterpart model. In this work, we show that a harmonic chain with long-range couplings restricted by a cost function proportional to the chain length $N$ exhibits two distinct phase transitions. In the present model, two sites at a distance $r>1$ are connected by a spring with probability $1/r^{\alpha }$ with the constraint that the total length of the non-nearest-neighbor couplings is limited to $\lambda N$, where $\lambda$ is a cost parameter. A geometrical phase transition is found at $\alpha =1.5$ between a phase with a finite number of long-range couplings and a phase on which the number of long-range couplings is proportional to the system size. Further, the normal vibrational modes of this chain display a phase transition from delocalized to localized modes at a smaller value of $\alpha$. Maximum effective disorder is reached at $\alpha =2$ for which the frequency of the lowest vibrational mode exhibits a pronounced peak.

The late-time distribution function $P(x,t)$ of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is given by two distinct scaling forms, corresponding to a diffusive ($x\sim t^{1/2}$) and a subdiffusive ($x\sim t^{\gamma }$ with a given $\gamma <1/2$) length scale, respectively, (ii) the overall scaling function is selected by the initial condition, and (iii) depending on the tail of the initial condition, the scaling exponent that characterizes the scaling function is found to exhibit a transition from a continuously varying to a fixed value.

A new theorem shows that noise can speed convergence to equilibrium in discrete finite-state Markov chains. The noise applies to the state density and helps the Markov chain explore improbable regions of the state space. The theorem ensures that a stochastic-resonance noise benefit exists for states that obey a vector-norm inequality. Such noise leads to faster convergence because the noise reduces the norm components. A corollary shows that a noise benefit still occurs if the system states obey an alternate norm inequality. This leads to a noise-benefit algorithm that requires knowledge of the steady state. An alternative blind algorithm uses only past state information to achieve a weaker noise benefit. Simulations illustrate the predicted noise benefits in three well-known Markov models. The first model is a two-parameter Ehrenfest diffusion model that shows how noise benefits can occur in the class of birth-death processes. The second model is a Wright-Fisher model of genotype drift in population genetics. The third model is a chemical reaction network of zeolite crystallization. A fourth simulation shows a convergence rate increase of 64% for states that satisfy the theorem and an increase of 53% for states that satisfy the corollary. A final simulation shows that even suboptimal noise can speed convergence if the noise applies over successive time cycles. Noise benefits tend to be sharpest in Markov models that do not converge quickly and that do not have strong absorbing states.

By means of contact dynamics simulations, we investigate the shear strength and internal structure of granular materials composed of two-dimensional nonconvex aggregates. We find that the packing fraction first grows as the nonconvexity is increased but declines at higher nonconvexity. This unmonotonic dependence reflects the competing effects of pore size reduction between convex borders of aggregates and gain in porosity at the nonconvex borders that are captured in a simple model fitting nicely the simulation data both in the isotropic and sheared packings. On the other hand, the internal angle of friction increases linearly with nonconvexity and saturates to a value independent of nonconvexity. We show that fabric anisotropy, force anisotropy, and friction mobilization, all enhanced by multiple contacts between aggregates, govern the observed increase of shear strength and its saturation with increasing nonconvexity. The main effect of interlocking is to dislocate frictional dissipation from the locked double and triple contacts between aggregates to the simple contacts between clusters of aggregates. This self-organization of particle motions allows the packing to keep a constant shear strength at high nonconvexity.

We present a new analytical approach to the strong electrostatic coupling regime (SC) that can be achieved equivalently at low temperatures, high charges, low dielectric permittivity, etc. Two geometries are analyzed in detail: one charged wall first, and then two parallel walls at small distances that can be likely or oppositely charged. In all cases, only one type of mobile counterions is present, and ensures electroneutrality (salt-free case). The method is based on a systematic expansion around the ground state formed by the two-dimensional Wigner crystal(s) of counterions at the plate(s). The leading SC order stems from a single-particle theory, and coincides with the virial SC approach that has been much studied in the last 10 years. The first correction has the functional form of the virial SC prediction, but the prefactor is different. The present theory is free of divergences and the obtained results, both for symmetrically and asymmetrically charged plates, are in excellent agreement with available data of Monte Carlo simulations under strong and intermediate Coulombic couplings. All results obtained represent relevant improvements over the virial SC estimates. The present SC theory starting from the Wigner crystal and therefore coined Wigner SC, sheds light on anomalous phenomena like the counterion mediated like-charge attraction, and the opposite-charge repulsion.

The current-source density (CSD) analysis is a widely used method in brain electrophysiology, but this method rests on a series of assumptions, namely that the surrounding extracellular medium is resistive and uniform, and in some versions of the theory, that the current sources are exclusively made by dipoles. Because of these assumptions, this standard model does not correctly describe the contributions of monopolar sources or of nonresistive aspects of the extracellular medium. We propose here a general framework to model electric fields and potentials resulting from current source densities, without relying on the above assumptions. We develop a mean-field formalism that is a generalization of the standard model and that can directly incorporate nonresistive (nonohmic) properties of the extracellular medium, such as ionic diffusion effects. This formalism recovers the classic results of the standard model such as the CSD analysis, but in addition, we provide expressions to generalize the CSD approach to situations with nonresistive media and arbitrarily complex multipolar configurations of current sources. We found that the power spectrum of the signal contains the signature of the nature of current sources and extracellular medium, which provides a direct way to estimate those properties from experimental data and, in particular, estimate the possible contribution of electric monopoles.

Bursting is one of the primary activity regimes of neurons. Our study is focused on determining a generic biophysical mechanism underlying the coexistence of the bursting and silent regimes observed in a neuron model. We show that the main ingredient for this mechanism is a saddle periodic orbit. The stable manifold of the orbit sets a threshold between the regimes of activity. Thus, the range of the controlling parameters, where the coexistence is observed, is limited by the bifurcations' values at which the saddle orbit appears and disappears. We show that it appears through the subcritical Andronov-Hopf bifurcation, where the equilibrium representing the silent regime loses stability, and disappears at the homoclinic bifurcation. Correspondingly, the bursting regime disappears in close proximity to the homoclinic bifurcation.

The flow of polymer solutions is examined in a flow geometry where a jet is used to inject the viscoelastic solution into a cylindrical tube. We show that this geometry allows for the generation of a “turbulentlike” flow at very low Reynolds numbers with a fluctuation level which can be as high as 30%. The fluctuations increase with an increase in solution polymer concentration and flow velocity. The turbulent fluctuations decay downstream for small flow velocities but persist for high velocities. The statistical properties of the generated fluctuations indicate that this turbulentlike flow is different from previously studied flows displaying elastic turbulence and shows a direct cascade of energy to small scales with practically no intermittency.

Self-organization of hydrogen bubbles is reported under etching of metallic Aluminum in a weakly basic solution. The ascending gas bubbles drift to the areas with higher density of bubbles. As a result, ascending bubbles form various stationary structures whose symmetry is determined by the symmetry of the etched area. Bubbles are aligned along the bisectors of the contour of the etched area. The special laser-assisted profiling of the etched area in shape of a vortex induces a torque in the fluid above the etched area. The process is interpreted on the basis of Bernoulli equation.

The shape that a liquid drop will assume when resting statically on a solid surface inclined to the horizontal is studied here in two dimensions. Earlier experimental and numerical studies yield multiple solutions primarily because of inherent differences in surface characteristics. On a solid surface capable of sustaining any amount of hysteresis, we obtain the global, and hence unique, minimum energy shape as a function of equilibrium contact angle, drop volume, and plate inclination. It is shown, in the energy minimization procedure, how the potential energy of this system is dependent on the basis chosen to measure it from, and two realistic bases, front-pinned and back-pinned, are chosen for consideration. This is at variance with previous numerical investigations where both ends of the contact line are pinned. It is found that the free end always assumes Young's equilibrium angle. Using this, simple equations that describe the angles and the maximum volume are then derived. The range of parameters where static drops are possible is presented. We introduce a detailed force balance for this problem and study the role of the wall in supporting the drop. We show that a portion of the wall reaction can oppose gravity while the other portion aids it. This determines the maximum drop volume that can be supported at a given plate inclination. This maximum volume is the least for a vertical wall, and is higher for all other wall inclinations. This study can be extended to three-dimensional drops in a straightforward manner and, even without this, lends itself to experimental verification of several of its predictions.

Transport of emulsions in porous media is relevant to several subsurface applications. Many enhanced oil recovery (EOR) processes lead to emulsion formation and as a result conformance originating in the flow of a dispersed phase may arise. In some EOR processes, emulsion is injected directly as a mobility control agent. Modeling the flow of emulsion in porous media is extremely challenging due to the complex nature of the associated flows and numerous interfaces. The descriptions based on effective viscosity are not valid when the drop size is of the same order of magnitude as the pore-throat characteristic length scale. An accurate model of emulsion flow through porous media should describe this local change in mobility. The available filtration models do not take into account the variation of the straining and capturing rates with the local capillary number. In this work, we present experiments of emulsion flow through sandstone cores of different permeability and a first step on a capillary network model that uses experimentally determined pore-level constitutive relationships between flow rate and pressure drop in constricted capillaries to obtain representative macroscopic flow behavior emerging from microscopic emulsion flow at the pore level. A parametric analysis is conducted to study the effect of the permeability and dispersed phase droplet size on the flow response to emulsion flooding in porous media. The network model predictions qualitatively describe the oil-water emulsion flow behavior observed in the experiments.

The generation of ultrastrong attosecond pulses through laser-plasma interactions offers the opportunity to surpass the intensity of any known laboratory radiation source, giving rise to new experimental possibilities, such as quantum electrodynamical tests and matter probing at extremely short scales. Here we demonstrate that a laser irradiated plasma surface can act as an efficient converter from the femto- to the attosecond range, giving a dramatic rise in pulse intensity. Although seemingly similar schemes have been described in the literature, the present setup differs significantly from the previous attempts. We present a model describing the nonlinear process of relativistic laser-plasma interaction. This model, which is applicable to a multitude of phenomena, is shown to be in excellent agreement with particle-in-cell simulations. The model makes it possible to determine a parameter region where the energy conversion from the femto- to the attosecond regime is maximal. Based on the study we propose a concept of laser pulse interaction with a target having a groove-shaped surface, which opens up the potential to exceed an intensity level of ${10}^{26}$ W/cm${}^2$ and observe effects due to nonlinear quantum electrodynamics with upcoming laser sources.

We investigate both analytically and numerically the ensemble of minimum-weight loops in the negative-weight percolation model on random graphs with fixed connectivity and bimodal weight distribution. This allows us to study the mean-field behavior of this model. The analytical study is based on a conjectured equivalence with the problem of self-avoiding walks in a random medium. The numerical study is based on a mapping to a standard minimum-weight matching problem for which fast algorithms exist. Both approaches yield results that are in agreement on the location of the phase transition, on the value of critical exponents, and on the absence of any sizable indications of a glass phase. By these results, the previously conjectured upper critical dimension of $d_u=6$ is confirmed.

In this paper, we investigate relationships between the volumes of cells of three-dimensional Voronoi tessellations and the lengths and areas of sections obtained by intersecting the tessellation with a randomly oriented plane. Here, in order to obtain analytical results, Voronoi cells are approximated to spheres. First, the probability density function for the lengths of the radii of the sections is derived and it is shown that it is related to the Meijer $G$ function; its properties are discussed and comparisons are made with the numerical results. Next, the probability density function for the areas of cross sections is computed and compared with the results of numerical simulations.

The discrete element method has been used to examine axial dispersion within rotating cylinders containing two sizes of particle. Two bed configurations are considered: initially segregated, which consists of a pulse (narrow axial band) of small particles within a bed of large particles, and initially mixed, in which the cylinder is loaded with a homogeneous mixture of the two particle sizes. The dispersion of the small particles within initially segregated beds is found to depend strongly on the initial length of the pulse of small particles. Initially mixed beds are found to undergo a transient period in which the small particles disperse rapidly. Following this transient, axial dispersion of both particles sizes is found to follow Fick's second law, in that the mean squared deviation of the axial position of the particles is proportional to time. Axial dispersion coefficients have been calculated for initially mixed beds that have reached steady state; the axial dispersion coefficients of both particle sizes decrease as the volume fraction of small particles is increased.

The molecular mean-field theory for the nematic-isotropic (N-Iso) phase transition in the vicinity of the surface is derived. We have shown that the nematic order parameter in liquid crystal near the surface is generally different from that in the bulk. It is never equal to zero if the anisotropic interaction with the surface is present. At the same time, transition from the phase with large nematic order parameter at the surface to the phase with small nematic order parameter at the surface is possible on heating. This surface transition always happens at higher temperatures than N-Iso phase transition related to the bulk. The theoretical prediction was well reproduced experimentally.

In the intracytoplasmic sperm injection (ICSI) process, a piezoelectric actuator is commonly used to assist the piercing of cell membrane. The longitudinal pulses that are performed by the piezo actuator, however, cause undesired lateral vibrations at the drawn tip of the injection micropipette. This mechanism is not well understood, despite its critical role in piezo-assisted cellular microinjection. We provide an analytical model to characterize the micropipette tip vibrations under assumed base excitation arising from the piezoelectric pulses. The resulting dynamic response is determined by using the Duhamel integral method. This study quantifies the effect of fluid damping, embedded mercury, and the apparent cell membrane elasticity. We found that, in practice, a small mercury droplet filled in pipette essentially creates higher shear forces at the membrane-pipette interface. The increased shear due to underdamped eigenmodes is conceived to assist the piercing of the cell membrane.

The occurrence of persistence in climatic systems has been investigated by analyzing 1167 surface temperature records, covering 110 years, in the whole United States. Due to the nonlinear and nonstationary character of temperature time series, the seasonal cycle suffers from both phase and amplitude modulations, which are not properly removed by the classical definition of the temperature anomaly. In order to properly filter out the seasonal component and the monotonic trends, we define the temperature anomaly in a different way by using the empirical mode decomposition (EMD). The essence of this method is to empirically identify the intrinsic oscillatory modes from the temperature records according to their characteristic time scale. The original signal is thus decomposed into a collection of a finite small number of intrinsic mode functions (IMFs), having its own time scale and representing oscillations experiencing amplitude and phase modulations, and a residue, describing the mean trend. The sum of all the IMF components as well as the residue reconstructs the original signal. Partial reconstruction can be achieved by selectively choosing IMFs in order to remove trivial trends and noise. The EMD description in terms of time-dependent amplitude and phase functions overcomes one of the major limitation of the Fourier analysis, namely, a correct description of nonlinearities and nonstationarities. By using the EMD definition of temperature anomalies we found persistence of fluctuations with a different degree according to the geographical location, on time scales in the range 3–15 years. The spatial distribution of the detrended fluctuation analysis exponent, used to quantify the degree of memory, indicates that the long-term persistence could be related to to the presence of climatic regions, which are more sensitive to climatic phenomena such as the El Niño southern oscillation.