Velocity correlations in granular materials

A system of inelastic hard disks in a thin pipe capped by hot walls is studied with the aim of investigating velocity correlations between particles. Two effects lead to such correlations: inelastic collisions help to build localized correlations, while momentum conservation and diffusion produce long ranged correlations. In the quasi-elastic limit, the velocity correlation is weak, but it is still important since it is of the same order as the deviation from uniformity. For system with stronger inelasticity, the pipe contains a clump of particles in highly correlated motion. A theory with empirical parameters is developed. This theory is composed of equations similar to the usual hydrodynamic laws of conservation of particles, energy, and momentum. Numerical results show that the theory describes the dynamics satisfactorily in the quasi-elastic limit, however only qualitatively for stronger inelasticity.Comment: 12 pages (REVTeX), 15 figures (Postscript). submitted to Phys. Rev.

Transport coefficients for an inelastic gas around uniform shear flow: Linear stability analysis

The inelastic Boltzmann equation for a granular gas is applied to spatially inhomogeneous states close to the uniform shear flow. A normal solution is obtained via a Chapman-Enskog-like expansion around a local shear flow distribution. The heat and momentum fluxes are determined to first order in the deviations of the hydrodynamic field gradients from their values in the reference state. The corresponding transport coefficients are determined from a set of coupled linear integral equations which are approximately solved by using a kinetic model of the Boltzmann equation. The main new ingredient in this expansion is that the reference state $f^{(0)}$ (zeroth-order approximation) retains all the hydrodynamic orders in the shear rate. In addition, since the collisional cooling cannot be compensated locally for viscous heating, the distribution $f^{(0)}$ depends on time through its dependence on temperature. This means that in general, for a given degree of inelasticity, the complete nonlinear dependence of the transport coefficients on the shear rate requires the analysis of the {\em unsteady} hydrodynamic behavior. To simplify the analysis, the steady state conditions have been considered here in order to perform a linear stability analysis of the hydrodynamic equations with respect to the uniform shear flow state. Conditions for instabilities at long wavelengths are identified and discussed.Comment: 7 figures; previous stability analysis modifie

The second and third Sonine coefficients of a freely cooling granular gas revisited

In its simplest statistical-mechanical description, a granular fluid can be modeled as composed of smooth inelastic hard spheres (with a constant coefficient of normal restitution $\alpha$) whose velocity distribution function obeys the Enskog-Boltzmann equation. The basic state of a granular fluid is the homogeneous cooling state, characterized by a homogeneous, isotropic, and stationary distribution of scaled velocities, $F(\mathbf{c})$. The behavior of $F(\mathbf{c})$ in the domain of thermal velocities ($c\sim 1$) can be characterized by the two first non-trivial coefficients ($a_2$ and $a_3$) of an expansion in Sonine polynomials. The main goals of this paper are to review some of the previous efforts made to estimate (and measure in computer simulations) the $\alpha$-dependence of $a_2$ and $a_3$, to report new computer simulations results of $a_2$ and $a_3$ for two-dimensional systems, and to investigate the possibility of proposing theoretical estimates of $a_2$ and $a_3$ with an optimal compromise between simplicity and accuracy.Comment: 12 pages, 5 figures; v2: minor change

Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases

It is shown that the hydrodynamic modes of a dilute granular gas of inelastic hard spheres can be identified, and calculated in the long wavelength limit. Assuming they dominate at long times, formal expressions for the Navier-Stokes transport coefficients are derived. They can be expressed in a form that generalizes the Green-Kubo relations for molecular systems, and it is shown that they can also be evaluated by means of $N$-particle simulation methods. The form of the hydrodynamic modes to zeroth order in the gradients is used to detect the presence of inherent velocity correlations in the homogeneous cooling state, even in the low density limit. They manifest themselves in the fluctuations of the total energy of the system. The theoretical predictions are shown to be in agreement with molecular dynamics simulations. Relevant related questions deserving further attention are pointed out

Scaling, Multiscaling, and Nontrivial Exponents in Inelastic Collision Processes

We investigate velocity statistics of homogeneous inelastic gases using the Boltzmann equation. Employing an approximate uniform collision rate, we obtain analytic results valid in arbitrary dimension. In the freely evolving case, the velocity distribution is characterized by an algebraic large velocity tail, P(v,t) ~ v^{-sigma}. The exponent sigma(d,epsilon), a nontrivial root of an integral equation, varies continuously with the spatial dimension, d, and the dissipation coefficient, epsilon. Although the velocity distribution follows a scaling form, its moments exhibit multiscaling asymptotic behavior. Furthermore, the velocity autocorrelation function decays algebraically with time, A(t)= ~ t^{-alpha}, with a non-universal dissipation-dependent exponent alpha=1/epsilon. In the forced case, the steady state Fourier transform is obtained via a cumulant expansion. Even in this case, velocity correlations develop and the velocity distribution is non-Maxwellian.Comment: 10 pages, 3 figure

Transport Coefficients for Granular Media from Molecular Dynamics Simulations

Under many conditions, macroscopic grains flow like a fluid; kinetic theory pred icts continuum equations of motion for this granular fluid. In order to test the theory, we perform event driven molecular simulations of a two-dimensional gas of inelastic hard disks, driven by contact with a heat bath. Even for strong dissipation, high densities, and small numbers of particles, we find that continuum theory describes the system well. With a bath that heats the gas homogeneously, strong velocity correlations produce a slightly smaller energy loss due to inelastic collisions than that predicted by kinetic theory. With an inhomogeneous heat bath, thermal or velocity gradients are induced. Determination of the resulting fluxes allows calculation of the thermal conductivity and shear viscosity, which are compared to the predictions of granular kinetic theory, and which can be used in continuum modeling of granular flows. The shear viscosity is close to the prediction of kinetic theory, while the thermal conductivity can be overestimated by a factor of 2; in each case, transport is lowered with increasing inelasticity.Comment: 14 pages, 17 figures, 39 references, submitted to PRE feb 199

Hydrodynamics and transport coefficients for Granular Gases

The hydrodynamics of granular gases of viscoelastic particles, whose collision is described by an impact-velocity dependent coefficient of restitution, is developed using a modified Chapman-Enskog approach. We derive the hydrodynamic equations and the according transport coefficients with the assumption that the shape of the velocity distribution function follows adiabatically the decaying temperature. We show numerically that this approximation is justified up to intermediate dissipation. The transport coefficients and the coefficient of cooling are expressed in terms of the elastic and dissipative parameters of the particle material and by the gas parameters. The dependence of these coefficients on temperature differs qualitatively from that obtained with the simplifying assumption of a constant coefficient of restitution which was used in previous studies. The approach formulated for gases of viscoelastic particles may be applied also for other impact-velocity dependencies of the restitution coefficient.Comment: 16 pages, 4 figure

Описание клинической картины и оценка функциональной активности канала CFTR у пациента с комплексным аллелем [S466X; R1070Q]

The presence of pathogenic variants in the CFTR gene causes cystic fibrosis (CF) through various molecular mechanisms that affect the formation and functional activity of the CFTR chloride channel. An important factor affecting the phenotypic manifestations of CF and the effectiveness of targeted therapy is the presence of complex alleles with > 2 consecutive mutations per 1 allele, or in the cis position. The influence of complex alleles on the manifestations of CF has not been sufficiently studied globally due to the small number of studies.The aim of the study was to investigate the influence of the complex allele [S466X; R1070Q] on the phenotypic manifestations of CF and the effectiveness of targeted therapy in a model of intestinal organoids from a patient with [S466X; R1070Q]/CFTRdele2,3 genotype.Methods. We used medical history data, intestinal current measurement, intestinal organoid method, and forskolin test.Results. The progressive nature of the disease with a clear degradation of lung function was established. The ICM method showed absent chloride channel function. The tests on the culture of organoids obtained from the intestinal tissue indicated a complete loss of the chloride channel function. In addition, the complex allele [S466X; R1070Q] was insensitive to all targeted drugs tested.Conclusion. The complex allele [S466X; R1070Q] causes a complete loss of the functional CFTR protein and is not sensitive to any of the approved targeted drugs.Наличие патогенных вариантов в гене CFTR вызывает муковисцидоз (МВ) посредством различных молекулярных механизмов, оказывающих влияние на образование и функциональную активность хлорного канала CFTR. Важным фактором, влияющим на фенотипические проявления МВ и эффективность таргетной терапии, является наличие комплексных аллелей — > 2 последовательных мутаций на 1-м аллеле, или в цис-положении. Влияние комплексных аллелей на проявления МВ в мире изучено недостаточно из-за небольшого количества проведенных исследований.Целью исследования явилось изучение влияния комплексного аллеля [S466X; R1070Q] на фенотипические проявления МВ и эффективность таргетной терапии на модели кишечных органоидов у пациента с генотипом [S466X; R1070Q]/CFTRdele2,3.Материалы и методы. Использовались данные истории болезни пациента, метод определения разницы кишечных потенциалов (ОРКП), метод кишечных органоидов, форсколиновый тест.Результаты. Установлен прогрессирующий характер заболевания с явной деградацией легочной функции. При использовании метода ОРКП показано отсутствие функции хлорного канала. Проведенные на полученной из ткани кишечника культуре органоидов тесты свидетельствуют о полной утрате функции хлорного канала. Кроме того, комплексный аллель [S466X; R1070Q] оказался нечувствительным ко всем протестированным таргетным препаратам.Заключение. Установлено, что комплексный аллель [S466X; R1070Q] вызывает полную утрату функционального белка CFTR и нечувствителен к действию ни одного из зарегистрированных таргетных препаратов

Interaction of climate change with effects of conspecific and heterospecific density on reproduction

We studied the relationship between temperature and the coexistence of great titParus majorand blue titCyanistes caeruleus, breeding in 75 study plots across Europe and North Africa. We expected an advance in laying date and a reduction in clutch size during warmer springs as a general response to climate warming and a delay in laying date and a reduction in clutch size during warmer winters due to density-dependent effects. As expected, as spring temperature increases laying date advances and as winter temperature increases clutch size is reduced in both species. Density of great tit affected the relationship between winter temperature and laying date in great and blue tit. Specifically, as density of great tit increased and temperature in winter increased both species started to reproduce later. Density of blue tit affected the relationship between spring temperature and blue and great tit laying date. Thus, both species start to reproduce earlier with increasing spring temperature as density of blue tit increases, which was not an expected outcome, since we expected that increasing spring temperature should advance laying date, while increasing density should delay it cancelling each other out. Climate warming and its interaction with density affects clutch size of great tits but not of blue tits. As predicted, great tit clutch size is reduced more with density of blue tits as temperature in winter increases. The relationship between spring temperature and density on clutch size of great tits depends on whether the increase is in density of great tit or blue tit. Therefore, an increase in temperature negatively affected the coexistence of blue and great tits differently in both species. Thus, blue tit clutch size was unaffected by the interaction effect of density with temperature, while great tit clutch size was affected in multiple ways by these interactions terms.Peer reviewe