244 research outputs found
Solving the Boltzmann equation in N log N
In [C. Mouhot and L. Pareschi, "Fast algorithms for computing the Boltzmann
collision operator," Math. Comp., to appear; C. Mouhot and L. Pareschi, C. R.
Math. Acad. Sci. Paris, 339 (2004), pp. 71-76], fast deterministic algorithms
based on spectral methods were derived for the Boltzmann collision operator for
a class of interactions including the hard spheres model in dimension three.
These algorithms are implemented for the solution of the Boltzmann equation in
two and three dimension, first for homogeneous solutions, then for general non
homogeneous solutions. The results are compared to explicit solutions, when
available, and to Monte-Carlo methods. In particular, the computational cost
and accuracy are compared to those of Monte-Carlo methods as well as to those
of previous spectral methods. Finally, for inhomogeneous solutions, we take
advantage of the great computational efficiency of the method to show an
oscillation phenomenon of the entropy functional in the trend to equilibrium,
which was suggested in the work [L. Desvillettes and C. Villani, Invent. Math.,
159 (2005), pp. 245-316].Comment: 32 page
Prediction of strong shock structure using the bimodal distribution function
A modified Mott-Smith method for predicting the one-dimensional shock wave
solution at very high Mach numbers is constructed by developing a system of
fluid dynamic equations. The predicted shock solutions in a gas of Maxwell
molecules, a hard sphere gas and in argon using the newly proposed formalism
are compared with the experimental data, direct-simulation Monte Carlo (DSMC)
solution and other solutions computed from some existing theories for Mach
numbers M<50. In the limit of an infinitely large Mach number, the predicted
shock profiles are also compared with the DSMC solution. The density,
temperature and heat flux profiles calculated at different Mach numbers have
been shown to have good agreement with the experimental and DSMC solutionsComment: 22 pages, 9 figures, Accepted for publication in Physical Review
Stability of NbsSn Wires with CuNb Reinforcing Stabilizer on Cryocooled Superconducting Magnet
Investigation of initiation of gigantic jets connecting thunderclouds to the ionosphere
The initiation of giant electrical discharges called as "gigantic jets"
connecting thunderclouds to the ionosphere is investigated by numerical
simulation method in this paper. Using similarity relations, the triggering
conditions of streamer formation in laboratory situations are extended to form
a criterion of initiation of gigantic jets. The energy source causing a
gigantic jet is considered due to the quasi-electrostatic field generated by
thunderclouds. The electron dynamics from ionization threshold to streamer
initiation are simulated by the Monte Carlo technique. It is found that
gigantic jets are initiated at a height of ~18-24 km. This is in agreement with
the observations. The method presented in this paper could be also applied to
the analysis of the initiation of other discharges such as blue jets and red
sprites.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004,
Nice (France
The Moment Guided Monte Carlo method for the Boltzmann equation
In this work we propose a generalization of the Moment Guided Monte Carlo
method developed in [11]. This approach permits to reduce the variance of the
particle methods through a matching with a set of suitable macroscopic moment
equations. In order to guarantee that the moment equations provide the correct
solutions, they are coupled to the kinetic equation through a non equilibrium
term. Here, at the contrary to the previous work in which we considered the
simplified BGK operator, we deal with the full Boltzmann operator. Moreover, we
introduce an hybrid setting which permits to entirely remove the resolution of
the kinetic equation in the limit of infinite number of collisions and to
consider only the solution of the compressible Euler equation. This
modification additionally reduce the statistical error with respect to our
previous work and permits to perform simulations of non equilibrium gases using
only a few number of particles. We show at the end of the paper several
numerical tests which prove the efficiency and the low level of numerical noise
of the method.Comment: arXiv admin note: text overlap with arXiv:0908.026
A Monte Carlo simulation of ion transport at finite temperatures
We have developed a Monte Carlo simulation for ion transport in hot
background gases, which is an alternative way of solving the corresponding
Boltzmann equation that determines the distribution function of ions. We
consider the limit of low ion densities when the distribution function of the
background gas remains unchanged due to collision with ions. A special
attention has been paid to properly treat the thermal motion of the host gas
particles and their influence on ions, which is very important at low electric
fields, when the mean ion energy is comparable to the thermal energy of the
host gas. We found the conditional probability distribution of gas velocities
that correspond to an ion of specific velocity which collides with a gas
particle. Also, we have derived exact analytical formulas for piecewise
calculation of the collision frequency integrals. We address the cases when the
background gas is monocomponent and when it is a mixture of different gases.
The developed techniques described here are required for Monte Carlo
simulations of ion transport and for hybrid models of non-equilibrium plasmas.
The range of energies where it is necessary to apply the technique has been
defined. The results we obtained are in excellent agreement with the existing
ones obtained by complementary methods. Having verified our algorithm, we were
able to produce calculations for Ar ions in Ar and propose them as a new
benchmark for thermal effects. The developed method is widely applicable for
solving the Boltzmann equation that appears in many different contexts in
physics.Comment: 14 page
C-erbB-2 or mutant Ha-ras induced malignant transformation of immortalized human ovarian surface epithelial cells in vitro
Modelling opinion formation by means of kinetic equations
In this chapter, we review some mechanisms of opinion dynamics that can be modelled by kinetic equations. Beside the sociological phenomenon of compromise, naturally linked to collisional operators of Boltzmann kind, many other aspects, already mentioned in the sociophysical literature or no, can enter in this framework. While describing some contributions appeared in the literature, we enlighten some mathematical tools of kinetic theory that can be useful in the context of sociophysics
Heat Shock Protein-27, -60 and -90 expression in gastric cancer: association with clinicopathological variables and patient survival
<p>Abstract</p> <p>Background</p> <p>Heat shock proteins (HSPs) are ubiquitous, highly conserved proteins across all the species and play essential roles in maintaining protein stability within the cells under normal conditions, while preventing stress-induced cellular damage. HSPs were also overexpressed in various types of cancer, being associated with tumor cell proliferation, differentiation and apoptosis. The aim of the present study was to evaluate the clinical significance of HSP -27, -60, and -90 expression in gastric carcinoma.</p> <p>Methods</p> <p>HSP -27, -60, and -90 proteins expression was assessed immunohistochemically in tumoral samples of 66 gastric adenocarcinoma patients and was statistically analyzed in relation to various clinicopathological characteristics, tumor proliferative capacity and patients' survival.</p> <p>Results</p> <p>HSP-27, -60, -90 proteins were abundantly expressed in gastric adenocarcinoma cases examined. HSP-27 expression was significantly associated with tumor size (pT, P = 0.026), the presence of organ metastases (pM, P = 0.046) and pStage (P = 0.041), while HSP-27 staining intensity with nodal status (pN, P = 0.042). HSP-60 expression was significantly associated with patients' sex (P = 0.011), while HSP-60 staining intensity with patients' age (P = 0.027) and tumor histopathological grade (P = 0.031). HSP-90 expression was not associated with any of the clinicopathological parameters examined; however, HSP-90 staining intensity was significantly associated with tumor size (pT, P = 0.020). High HSP-90 expression was significantly associated with longer overall survival times in univariate analysis (log-rank test, P = 0.033), being also identified as an independent prognostic factor in multivariate analysis (P = 0.026).</p> <p>Conclusion</p> <p>HSP-27, -60, and -90 were associated with certain clinicopathological parameters which are crucial for the management of gastric adenocarcinoma patient. HSP-90 expression may also be an independent prognostic indicator in gastric adenocarcinoma patients.</p
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