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The dynamics of a system composed of elastic hard particles confined by an isotropic harmonic potential are studied. In the low-density limit, the Boltzmann equation provides an excellent description, and the system does not reach equilibrium except for highly specific initial conditions: it generically evolves towards and stays in a breathing mode. This state is periodic in time, with a Gaussian velocity distribution, an oscillating temperature and a density profile that oscillates as well. We characterize this breather in terms of initial conditions, and constants of the motion. For low but finite densities, the analysis requires to take into account the finite size of the particles. Under well-controlle approximations, a closed description is provided, which shows how equilibrium is reached at long times. The (weak) dissipation at work erodes the breather's amplitude, while concomitantly shifting its oscillation frequency. An excellent agreement is found between Molecular Dynamics simulation results and the theoretical predictions for the frequency shift. For the damping time, the agreement is not as accurate as for the frequency and the origin of the discrepancies is discussed., Comment: Accepted in Physical Review E

The kinetic theory description of a low density gas of hard spheres or disks, confined between two parallel plates separated a distance smaller than twice the diameter of the particles, is addressed starting from the Liouville equation of the system. The associated BBGKY hierarchy of equations for the reduced distribution functions is expanded in powers of a parameter measuring the density of the system in the appropriate dimensionless units. The Boltzmann level of description is obtained by keeping only the two lowest orders in the parameter. In particular, the one-particle distribution function obeys a couple of equations. Contrary to what happens with a Boltzmann-like kinetic equation that has been proposed for the same system on a heuristic basis, the kinetic theory formulated here admits stationary solutions that are consistent with equilibrium statistical mechanics, both in absence and presence of external fields. In the latter case, the density profile is rather complex due to the coupling between the inhomogeneities generated by the confinement and by the external fields. The general theory formulated provides a solid basis for the study of the properties of strongly confined dilute gases., Comment: Accepted in Physical Review E

Investigating the dynamics of chromatin and the factors that are affecting it, has provided valuable insights into the organization and functionality of the genome in the cell nucleus. We control the expression of Lamin-A, an important organizer protein of the chromatin and nucleus structure. By simultaneously tracking tens of chromosomal loci (telomeres) in each nucleus, we find that the motion of chromosomal loci in Lamin-A depleted cells is both faster and more directed on a scale of a few micrometers, which coincides with the size of chromosome territories. Moreover, in the absence of Lamin-A we reveal the existence of correlations among neighboring telomeres. We show how these pairwise correlations are linked with the intermittent and persistent character of telomere trajectories, underscoring the importance of Lamin-A protein in chromosomal organization.

Self-diffusion along the longitudinal coordinate in a channel of varying cross section is considered. The starting point is the two-dimensional Enskog-Boltzmann-Lorentz kinetic equation with appropriated boundary conditions. It is integrated over the transversal coordinate to get an approximated one-dimensional kinetic equation, keeping the relevant properties of the original one. Then, a macroscopic equation for the time evolution of the longitudinal density is derived, by means of a modified Chapman-Enskog expansion method, that takes into account the inhomogeneity of the equilibrium longitudinal density. This transport equation has the form of the phenomenological Ficks-Jacobs equation, but with an effective diffusion coefficient that contains corrections associated to the variation of the slope of the equilibrium longitudinal density profile.

Boltzmann showed that in spite of momentum and energy redistribution through collisions, a rarefied gas confined in a isotropic harmonic trapping potential does not reach equilibrium; it evolves instead into a breathing mode where density, velocity and temperature oscillate. This counter-intuitive prediction is upheld by cold atoms experiments. Yet, are the breathers eternal solutions of the dynamics even in an idealized and isolated system? We show by a combination of hydrodynamic arguments and Molecular Dynamics simulations that an original dissipative mechanism is at work, where the minute and often neglected bulk viscosity eventually thermalizes the system, that thus reaches equilibrium.

The dynamics of a system composed of inelastic hard spheres or disks that are confined between two parallel vertically vibrating walls is studied (the vertical direction is defined as the direction perpendicular to the walls). The distance between the two walls is supposed to be larger than twice the diameter of the particles so that the particles can pass over each other, but still much smaller than the dimensions of the walls. Hence, the system can be considered to be quasi-two-dimensional (quasi-one-dimensional) in the hard spheres (disks) case. For dilute systems, a closed evolution equation for the one-particle distribution function is formulated that takes into account the effects of the confinement. Assuming the system is spatially homogeneous, the kinetic equation is solved approximating the distribution function by a two-temperatures (horizontal and vertical) gaussian distribution. The obtained evolution equations for the partial temperatures are solved, finding a very good agreement with Molecular Dynamics simulation results for a wide range of the parameters (inelasticity, height and density) for states whose projection over a plane parallel to the walls is homogeneous. In the stationary state, where the energy lost in collisions is compensated by the energy injected by the walls, the pressure tensor in the horizontal direction is analyzed and its relation with an instability of the homogenous state observed in the simulations is discussed., Comment: 36 pages, 14 figures, Accepted in Journal of Statistical Mechanics: Theory and Experiment

The dynamics of a tagged particle immersed in a fluid of particles of the same size but different mass is studied when the system is confined between two hard parallel plates separated a distance smaller than twice the diameter of the particles. The collisions between particles are inelastic while the collisions of the particles with the hard walls inject energy in the direction perpendicular to the wall, so that stationary states can be reached in the long-time limit. The velocity distribution of the tagged particle verifies a Boltzmann-Lorentz-like equation that is solved assuming that it is a spatially homogeneous gaussian distribution with two different temperatures (one associated to the motion parallel to the wall and another associated to the perpendicular direction). It is found that the temperature perpendicular to the wall diverges when the tagged particle mass approaches a critical mass from below, while the parallel temperature remains finite. Molecular Dynamics simulation results agree very well with the theoretical predictions for tagged particle masses below the critical mass. The measurements of the velocity distribution function of the tagged particle confirm that it is gaussian if the mass is not close to the critical mass, while it deviates from gaussianity when approaching the critical mass. Above the critical mass, the velocity distribution function is very far from a gaussian, being the marginal distribution in the perpendicular direction bimodal and with a much larger variance than the one in the parallel direction.

A dilute gas of hard disks confined between two straight parallel lines is considered. The distance between the two boundaries is in between one and two particle diameters, so that the system is quasi-one-dimensional. A Boltzmann-like kinetic equation, that takes into account the limitation in the possible scattering angles, is derived. It is shown that the equation verifies an $H$ theorem implying a monotonic approach to equilibrium. The implications of this result are discussed, and the equilibrium properties are derived. Closed equations describing how the kinetic energy is transferred between the degrees of freedom parallel and perpendicular to the boundaries are derived for states that are homogeneous along the direction of the boundaries. The theoretical predictions agree with results obtained by means of molecular dynamics simulations.

We study a two state ``jumping diffusivity'' model for a Brownian process alternating between two different diffusion constants, $D_{+}>D_{-}$, with random waiting times in both states whose distribution is rather general. In the limit of long measurement times Gaussian behavior with an effective diffusion coefficient is recovered. We show that for equilibrium initial conditions and when the limit of the diffusion coefficient $D_-\to0$ is taken, the short time behavior leads to a cusp, namely a non - analytical behavior, in the distribution of the displacements $P(x,t)$ for $x\longrightarrow 0$. Visually this cusp, or tent-like shape, resembles similar behavior found in many experiments of diffusing particles in disordered environments, such as glassy systems and intracellular media. This general result depends only on the existence of finite mean values of the waiting times at the different states of the model. Gaussian statistics in the long time limit is achieved due to ergodicity and convergence of the distribution of the temporal occupation fraction in state $D_{+}$ to a $\delta$-function. The short time behavior of the same quantity converges to a uniform distribution, which leads to the non - analyticity in $P(x,t)$. We demonstrate how super - statistical framework is a zeroth order short time expansion of $P(x,t)$, in the number of transitions, that does not yield the cusp like shape. The latter, considered as the key feature of experiments in the field, is found with the first correction in perturbation theory.

[Abridged] The measurement of the polarization of the Cosmic Microwave Background radiation is one of the current frontiers in cosmology. In particular, the detection of the primordial B-modes, could reveal the presence of gravitational waves in the early Universe. The detection of such component is at the moment the most promising technique to probe the inflationary theory describing the very early evolution of the Universe. We present the updated performance forecast of the Large Scale Polarization Explorer (LSPE), a program dedicated to the measurement of the CMB polarization. LSPE is composed of two instruments: Strip, a radiometer-based telescope on the ground in Tenerife, and SWIPE (Short-Wavelength Instrument for the Polarization Explorer) a bolometer-based instrument designed to fly on a winter arctic stratospheric long-duration balloon. The program is among the few dedicated to observation of the Northern Hemisphere, while most of the international effort is focused into ground-based observation in the Southern Hemisphere. Measurements are currently scheduled in Winter 2021/22 for SWIPE, with a flight duration up to 15 days, and in Summer 2021 with two years observations for Strip. We describe the main features of the two instruments, identifying the most critical aspects of the design, in terms of impact into performance forecast. We estimate the expected sensitivity of each instrument and propagate their combined observing power to the sensitivity to cosmological parameters, including the effect of scanning strategy, component separation, residual foregrounds and partial sky coverage. We also set requirements on the control of the most critical systematic effects and describe techniques to mitigate their impact. LSPE can reach a sensitivity in tensor-to-scalar ratio of $\sigma_r<0.01$, and improve constrains on other cosmological parameters., Comment: Submitted to JCAP. Abstract abridged for arXiv submission

The Large Scale Polarization Explorer (LSPE) is a cosmology program for the measurement of large scale curl-like features (B-modes) in the polarization of the Cosmic Microwave Background. Its goal is to constrain the background of inflationary gravity waves traveling through the universe at the time of matter-radiation decoupling. The two instruments of LSPE are meant to synergically operate by covering a large portion of the northern microwave sky. LSPE/STRIP is a coherent array of receivers planned to be operated from the Teide Observatory in Tenerife, for the control and characterization of the low-frequency polarized signals of galactic origin; LSPE/SWIPE is a balloon-borne bolometric polarimeter based on 330 large throughput multi-moded detectors, designed to measure the CMB polarization at 150 GHz and to monitor the polarized emission by galactic dust above 200 GHz. The combined performance and the expected level of systematics mitigation will allow LSPE to constrain primordial B-modes down to a tensor/scalar ratio of $10^{-2}$. We here report the status of the STRIP pre-commissioning phase and the progress in the characterization of the key subsystems of the SWIPE payload (namely the cryogenic polarization modulation unit and the multi-moded TES pixels) prior to receiver integration., Comment: 8 pages, 5 figures, Accepted for publication in Journal of Low Temperature Physics

The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic equation, recently derived for this system. As a consequence of the confinement, the pressure tensor and the heat flux contain, in addition to the terms associated to the motion of the particles, collisional transfer contributions, similar to those that appear beyond the dilute limit. The complexity of these terms, and of the kinetic equation itself, compromise the potential of the equation to describe the rich phenomenology observed in this kind of systems. For this reason, a simpler model equation based on the Boltzmann equation is proposed. The model is formulated to keep the main properties of the underlying equation, and it is expected to provide relevant information in more general states than the original equation. As an illustration, the solution describing a macroscopic state with uniform temperature, but a density gradient perpendicular to the plates is considered. This is the equilibrium state for an elastic system, and the inhomogeneous cooling state for the case of inelastic hard spheres. The results are in good agreement with previous results obtained directly from the Boltzmann equation.

A quasi-two-dimensional system of hard spheres strongly confined between two parallel plates is considered. The attention is focussed on the macroscopic self-diffusion process observed when the system is looked from above or from below. The transport equation, and the associated self-diffusion coefficient, are derived from a Boltzmann-Lorentz kinetic equation, valid in the dilute limit. Since the equilibrium state of the system is inhomogeneous, this requires the use of a modified Chapman-Enskog expansion that distinguishes between equilibrium and non-equilibrium gradients of the density of labelled particles. The self-diffusion coefficient is obtained as a function of the separation between the two confining plates. The theoretical predictions are compared with molecular dynamics simulation results and a good agreement is found.

The inhomogeneous cooling state describing the hydrodynamic behavior of a freely evolving granular gas strongly confined between two parallel plates is studied, using a Boltzmann kinetic equation derived recently. By extending the idea of the homogeneous cooling state, we propose a scaling distribution in which all the time dependence occurs through the granular temperature of the system, while there is a dependence on the distance to the confining walls through the density. It is obtained that the velocity distribution is not isotropic, and it has two different granular temperature parameters associated to the motion perpendicular and parallel to the confining plates, respectively, although their cooling rates are the same. Moreover, when approaching the inhomogeneous cooling state, energy is sometimes transferred from degrees of freedom with lower granular temperature to those with a higher one, contrary to what happens in molecular systems. The cooling rate and the two partial granular temperatures are calculated by means of a Gaussian approximation. The theoretical predictions are compared with molecular dynamics simulation results and a good agreement is found.

Aggregation and fragmentation of single molecules in the cell environment lead to a spectrum of diffusivities and to statistical laws of movement very different from typical Brownian motion. Current models of intracellular transport do not explain at a microscopical level the emergence of theses deviations. Employing a many body approach, which we call the Hitchhiker model, we elucidate how the widely observed exponential tails in the particle spreading, i.e. the Laplace distribution and the modulations of the diffusivities, are controlled by size fluctuations of single molecules. By means of numerical simulations Laplace distributions are obtained whether we track one molecule or many molecules in parallel. However, we show that the diffusivity varies significantly depending on which tracking protocol is applied. Using a renewal process in the space of sizes, we quantify to what extent the average diffusivity in the single molecule technique is decreased compared with the ensemble average., Comment: 8 pages, 7 figures

A simple model of a vibrated granular monolayer is studied. It consists of inelastic hard spheres confined between two parallel hard plates separated a distance smaller than twice the diameter of the particles. Both walls are elastic and one of them is vibrating in a sawtooth way. For low densities, a kinetic equation is proposed from which closed evolution equations for the horizontal and vertical temperatures are derived assuming spatial homogeneity and that the system is very thin. An excellent agreement between the theoretical predictions and Molecular Dynamics simulation results is obtained both, for the stationary values and for the dynamics of the temperatures.

In this paper we discuss the latest developments of the STRIP instrument of the "Large Scale Polarization Explorer" (LSPE) experiment. LSPE is a novel project that combines ground-based (STRIP) and balloon-borne (SWIPE) polarization measurements of the microwave sky on large angular scales to attempt a detection of the "B-modes" of the Cosmic Microwave Background polarization. STRIP will observe approximately 25% of the Northern sky from the "Observatorio del Teide" in Tenerife, using an array of forty-nine coherent polarimeters at 43 GHz, coupled to a 1.5 m fully rotating crossed-Dragone telescope. A second frequency channel with six-elements at 95 GHz will be exploited as an atmospheric monitor. At present, most of the hardware of the STRIP instrument has been developed and tested at sub-system level. System-level characterization, starting in July 2018, will lead STRIP to be shipped and installed at the observation site within the end of the year. The on-site verification and calibration of the whole instrument will prepare STRIP for a 2-years campaign for the observation of the CMB polarization., Comment: 17 pages, 15 figures, proceedings of the SPIE Astronomical Telescopes + Instrumentation conference "Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy IX", on June 15th, 2018, Austin (TX)

We investigate the dynamics of an ensemble of inelastic hard spheres confined between two horizontal plates separated a distance smaller than twice the diameter of the particles, in such a way that the system is quasi-two-dimensional. The bottom wall is vibrating and, therefore, it injects energy into the system in the vertical direction and a stationary state is reached. It is found that, if the size of the plates is small enough, the stationary state is homogeneous. Otherwise, a cluster of particles is developed. The instability is understood by using some effective hydrodynamic equations in the horizontal plane. Moreover, the theoretical prediction for the size of the system above which it is unstable agrees very well with Molecular Dynamics simulation results without any fitting parameter.

A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account and it is supposed to be valid up to moderate densities. From the equation, balance equations for the hydrodynamic fields are derived, identifying the collisional transfer contributions to the pressure tensor and heat flux. A Lyapunov functional, $\mathcal{H}[f]$, is identified. For any solution of the kinetic equation, $\mathcal{H}$ decays monotonically in time until the system reaches the inhomogeneous equilibrium distribution, that is a Maxwellian distribution with a the density field consistent with equilibrium statistical mechanics.

A kinetic equation for a dilute gas of hard spheres confined between two parallel plates separated a distance smaller than two particle dimeters is derived. It is a Boltzmann-like equation, which incorporates the effect of the confinement on the particle collisions. A function $S(t)$ is constructed by adding to the Boltzmann expression a confinement contribution. Then it is shown that for the solutions of the kinetic equation, $S(t)$ increases monotonically in time, until the system reaches a stationary inhomogeneous state, when $S$ becomes the equilibrium entropy of the confined system as derived from equilibrium statistical mechanics. From the entropy, other equilibrium properties are obtained, and Molecular Dynamics simulations are used to verify some of the theoretical predictions.

The linear hydrodynamic stability of a model for confined quasi-two-dimensional granular gases is analyzed. The system exhibits homogeneous hydrodynamics, i.e. there are macroscopic evolution equations for homogeneous states. The stability analysis is carried out around all these states and not only the homogeneous steady state reached eventually by the system. It is shown that in some cases the linear analysis is not enough to reach a definite conclusion on the stability, and molecular dynamics simulation results are presented to elucidate these cases. The analysis shows the relevance of nonlinear hydrodynamic contributions to describe the behavior of spontaneous fluctuations occurring in the system, that lead even to the transitory formation of clusters of particles. The conclusion is that the system is always stable. The relevance of the results for describing the instabilities of confined granular gases observed experimentally is discussed.

We introduce a simple model of deterministic particles in weakly disordered media which exhibits a transition from normal to anomalous diffusion. The model consists of a set of non-interacting overdamped particles moving on a disordered potential. The disordered potential can be thought as a substrate having some "defects" scattered along a one-dimensional line. The distance between two contiguous defects is assumed to have a heavy-tailed distribution with a given exponent $\alpha$, which means that the defects along the substrate are scarce if $\alpha$ is small. We prove that this system exhibits a transition from normal to anomalous diffusion when the distribution exponent $\alpha$ decreases, i.e., when the defects become scarcer. Thus we identify three distinct scenarios: a normal diffusive phase for $\alpha>2$, a superdiffusive phase for $1/2<\alpha\leq 2$, and a subdiffusive phase for $\alpha \leq 1/2$. We also prove that the particle current is finite for all the values of $\alpha$, which means that the transport is normal independently of the diffusion regime (normal, subdiffusive, or superdiffusive). We give analytical expressions for the effective diffusion coefficient for the normal diffusive phase and analytical expressions for the diffusion exponent in the case of anomalous diffusion. We test all these predictions by means of numerical simulations., Comment: 9 pages, 6 figures

The $H$-theorem, originally derived at the level of Boltzmann non-linear kinetic equation for a dilute gas undergoing elastic collisions, strongly constrains the velocity distribution of the gas to evolve irreversibly towards equilibrium. As such, the theorem could not be generalized to account for dissipative systems: the conservative nature of collisions is an essential ingredient in the standard derivation. For a dissipative gas of grains, we construct here a simple functional $\mathcal H$ related to the original $H$, that can be qualified as a Lyapunov functional. It is positive, and results backed by three independent simulation approaches (a deterministic spectral method, the stochastic Direct Simulation Monte Carlo technique, and Molecular Dynamics) indicate that it is also non-increasing. Both driven and unforced cases are investigated.

Irreversible thermodynamics of single-molecule experiments subject to external constraining forces of a mechanical nature is presented. Extending Onsager's formalism to the non-linear case of systems under non-equilibrium external constraints, we are able to calculate the entropy production and the general non-linear kinetic equations for the variables involved. In particular, we analyze the case of RNA stretching protocols obtaining critical oscillations between different configurational states when forced by external means to remain in the unstable region of its free-energy landscape, as observed in experiments. We also calculate the entropy produced during these hopping events, and show how resonant phenomena in stretching experiments of single RNA macromolecules may arise. We also calculate the hopping rates using Kramer's approach obtaining a good comparison with experiments.

The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and momentum fluxes are calculated to Navier-Stokes order, and the associated transport coefficients are explicitly determined as functions of the coefficient of normal restitution and the velocity parameter involved in the definition of the model. Also an Euler transport term contributing to the energy transport equation is considered. This term arises from the gradient expansion of the rate of change of the temperature due to the inelasticity of collisions, and vanishes for elastic systems. The hydrodynamic equations are particularized for the relevant case of a system in the homogeneous steady state. The relationship with previous works is analyzed.

We study the fluctuations of the total internal energy of a granular gas under stationary uniform shear flow by means of kinetic theory methods. We find that these fluctuations are coupled to the fluctuations of the different components of the total pressure tensor. Explicit expressions for all the possible cross and auto correlations of the fluctuations at one and two times are obtained in the two dimensional case. The theoretical predictions are compared with Molecular Dynamics simulation and a good agreement is found for the range of inelasticity considered.

The accuracy of a model to describe the horizontal dynamics of a confined quasi-two-dimensional system of inelastic hard spheres is discussed by comparing its predictions for the relaxation of the temperature in an homogenous system with molecular dynamics simulation results for the original system. A reasonably good agreement is found. Next, the model is used to investigate the peculiarities of the nonlinear evolution of the temperature when the parameter controlling the energy injection is instantaneously changed while the system was relaxing. This can be considered as a non-equilibrium generalization of the Kovacs effect. It is shown that, in the low density limit, the effect can be accurately described by using a simple kinetic theory based on the first Sonine approximation for the one-particle distribution function. Some possible experimental implications are indicated.

The hydrodynamic equation governing the homogeneous time evolution of the temperature in a model of confined granular gas is studied by means of the Enskog equation. The existence of a normal solution of the kinetic equation is assumed as a condition for hydrodynamics. Dimensional analysis implies a scaling of the distribution function that is used to determine it in the first Sonine approximation, with a coefficient that evolves in time through its dependence on the temperature. The theoretical predictions are compared with numerical results obtained by the direct simulation Monte Carlo method, and a good agreement is found. The relevance of the normal homogeneous distribution function to derive inhomogeneous hydrodynamic equations, for instance using the Champan-Enskog algorithm, is indicated., Comment: Accepted in Phys. Rev. E

The non-equilibrium statistical mechanics and kinetic theory for a model of a confined quasi-two-dimensional gas of inelastic hard spheres is presented. The dynamics of the particles includes an effective mechanism to transfer the energy injected in the vertical direction to the horizontal degrees of freedom. The Enskog approximation is formulated and used as the basis to investigate the temperature and the distribution function of the steady state eventually reached by the system. An exact scaling of the distribution function of the system having implications on the form of its moments is pointed out. The theoretical predictions are compared with numerical results obtained by a particle simulation method, and a good agreement is found.

The decay of a small homogeneous perturbation of the temperature of a dilute granular gas in the steady uniform shear flow state is investigated. Using kinetic theory based on the inelastic Boltzmann equation, a closed equation for the decay of the perturbation is derived. The equation involves the generalized shear viscosity of the gas in the time-dependent shear flow state, and therefore it predicts relevant rheological effects beyond the quasi-elastic limit. A good agreement is found when comparing the theory with molecular dynamics simulation results. Moreover, the Onsager postulate on the regression of fluctuations is fulfilled.

We study the dynamics of a granular gas heated by the stochastic thermostat. From a Boltzmann description, we derive the hydrodynamic equations for small perturbations around the stationary state that is reached in the long time limit. Transport coefficients are identified as Green-Kubo formulas obtaining explicit expressions as a function of the inelasticity and the spacial dimension.