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Full absorption statistics of diffusing particles with exclusion  [PDF]
Baruch Meerson
Statistics , 2014, DOI: 10.1088/1742-5468/2015/04/P04009
Abstract: Suppose that an infinite lattice gas of constant density $n_0$, whose dynamics are described by the symmetric simple exclusion process, is brought in contact with a spherical absorber of radius $R$. Employing the macroscopic fluctuation theory and assuming the additivity principle, we evaluate the probability distribution ${\mathcal P}(N)$ that $N$ particles are absorbed during a long time $T$. The limit of $N=0$ corresponds to the survival problem, whereas $N\gg \bar{N}$ describes the opposite extreme. Here $\bar{N}=4\pi R D_0 n_0 T$ is the \emph{average} number of absorbed particles (in three dimensions), and $D_0$ is the gas diffusivity. For $n_0\ll 1$ the exclusion effects are negligible, and ${\mathcal P}(N)$ can be approximated, for not too large $N$, by the Poisson distribution with mean $\bar{N}$. For finite $n_0$, ${\mathcal P}(N)$ is non-Poissonian. We show that $-\ln{\mathcal P}(N) \simeq n_0 N^2/\bar{N}$ at $N\gg \bar{N}$. At sufficiently large $N$ and $n_0<1/2$ the most likely density profile of the gas, conditional on the absorption of $N$ particles, is non-monotonic in space. We also establish a close connection between this problem and that of statistics of current in finite open systems.
Temperature and Flow Rate Control of Diffusing Chamber  [PDF]
Yongbo Lai, Guoping Lu, Zhiwei Wang
World Journal of Engineering and Technology (WJET) , 2017, DOI: 10.4236/wjet.2017.51006
Abstract: The temperature and flow rate control of diffusing chamber is one of the key technologies in the production of poly-crystal silicon thin film. As there exist some modeling uncertainties and errors in the actual system, it is difficult to guarantee the chamber variable temperature conditions and the flow rate of diffusion gas being controlled within its targeted range in the rapid thermal processing (RTP). In this paper, the control applies the programmable logic controller (PLC) to configure control hardware system, proposes expert proportional integral derivative (PID) control method to regulate the gas flow rate and H∞ control strategy to attenuate chamber modeling uncertainties and disturbances, respectively, to steer the chamber rapid variable temperature very close to the expected product temperatures. Furthermore, it designs human-machine integrated user control interface (HMI) and achieves rapid and accurately control performances for user operating production. The designed control system are simulated and tested in the application, which demonstrates that the control method has strong robustness when the modeling uncertainties, errors, parameters perturbation and disturbances, the temperature and flow rate meet the requirements of precisely trajectory following.
Multiple reentrant glass transitions in confined hard-sphere glasses  [PDF]
S. Mandal,S. Lang,M. Gross,M. Oettel,D. Raabe,T. Franosch,F. Varnik
Physics , 2014, DOI: 10.1038/ncomms5435
Abstract: Glass forming liquids exhibit a rich phenomenology upon confinement. This is often related to the effects arising from wall-fluid interactions. Here we focus on the interesting limit where the separation of the confining walls becomes of the order of a few particle diameters. For a moderately polydisperse, densely packed hard-sphere fluid confined between two smooth hard walls, we show via event-driven molecular dynamics simulations the emergence of a multiple reentrant glass transition scenario upon a variation of the wall separation. Using thermodynamic relations, this reentrant phenomenon is shown to persist also under constant chemical potential. This allows straightforward experimental investigation and opens the way to a variety of applications in micro- and nanotechnology, where channel dimensions are comparable to the size of the contained particles. The results are in-line with theoretical predictions obtained by a combination of density functional theory and the mode-coupling theory of the glass transition.
Optimal Fourier filtering of a function that is strictly confined within a sphere  [PDF]
Jose M. Soler,Eduardo Anglada
Physics , 2008, DOI: 10.1016/j.cpc.2009.01.017
Abstract: We present an alternative method to filter a distribution, that is strictly confined within a sphere of given radius $r_c$, so that its Fourier transform is optimally confined within another sphere of radius $k_c$. In electronic structure methods, it can be used to generate optimized pseudopotentials, pseudocore charge distributions, and pseudo atomic orbital basis sets.
The Influences of Confined Phonons on the Nonlinear Absorption Coefficient of a Strong Electromagnetic Wave by Confined Electrons in Doping Superlattices
Nguyen Quang Bau;Do Manh Hung;Le Thai Hung
PIER Letters , 2010, DOI: 10.2528/PIERL10030911
Abstract: The influences of confined phonons on the nonlinear absorption coefficient (NAC) by a strong electromagnetic wave for the case of electron-optical phonon scattering in doped superlattices (DSLs) are theoretically studied by using the quantum transport equation for electrons. The dependence of NAC on the energy (), the amplitude () of external strong electromagnetic wave, the temperature (T) of the system, is obtained. Two cases for the absorption: Close to the absorption threshold ∣ - ∣<< and far away from the absorption threshold ∣ - ∣>> (k = 0, 1, 2..., and are the frequency of optical phonon and the average energy of electrons, respectively) are considered. The formula of the NAC contains a quantum number m characterizing confined phonons. The analytic expressions are numerically evaluated, plotted and discussed for a specific of the n-GaAs/p-GaAs DSLs. The computations show that the spectrums of the NAC in case of confined phonon are much different from they are in case of un-confined phonon and strongly depend on a quantum number m characterizing confinement phonon.
Self-adjoint Extensions for Confined Electrons:from a Particle in a Spherical Cavity to the Hydrogen Atom in a Sphere and on a Cone  [PDF]
M. H. Al-Hashimi,U. -J. Wiese
Physics , 2012, DOI: 10.1016/j.aop.2012.06.006
Abstract: In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at the wall of the cavity. In this paper, we study this situation in detail both for a free particle and for a hydrogen atom centered in a spherical cavity. For appropriate values of the self-adjoint extension parameter, the bound states lo calized at the wall resonate with the standard hydrogen bound states. We also examine the accidental symmetry generated by the Runge-Lenz vector, which is explicitly broken in a spherical cavity with general Robin boundary conditions. However, for specific radii of the confining sphere, a remnant of the accidental symmetry persists. The same is true for an electron moving on the surface of a finite circular cone, bound to its tip by a 1/r potential.
Local order variations in confined hard-sphere fluids  [PDF]
Kim Nyg?rd,Sten Sarman,Roland Kjellander
Physics , 2013, DOI: 10.1063/1.4825176
Abstract: Pair distributions of fluids confined between two surfaces at close distance are of fundamental importance for a variety of physical, chemical, and biological phenomena, such as interactions between macromolecules in solution, surface forces, and diffusion in narrow pores. However, in contrast to bulk fluids, properties of inhomogeneous fluids are seldom studied at the pair-distribution level. Motivated by recent experimental advances in determining anisotropic structure factors of confined fluids, we analyze theoretically the underlying anisotropic pair distributions of the archetypical hard-sphere fluid confined between two parallel hard surfaces using first-principles statistical mechanics of inhomogeneous fluids. For this purpose, we introduce an experimentally accessible ensemble-averaged local density correlation function and study its behavior as a function of confining slit width. Upon increasing the distance between the confining surfaces, we observe an alternating sequence of strongly anisotropic versus more isotropic local order. The latter is due to packing frustration of the spherical particles. This observation highlights the importance of studying inhomogeneous fluids at the pair-distribution level.
Effect of polydispersity to specific absorption rate  [PDF]
Zsuzsa Janosfalvi,Jozsef Hakl,Kalman Vad
Physics , 2012,
Abstract: The predictions of a newly developed Bloch-Bloembergen alike analytic magnetization model are compared to experimental results. The effect of size polydipersity on the specific absorption loss is demonstrated for the magnetic nanoparticles containing media. Specific absorption rate shows resonance like behivior as a function of particle size. The obtained results are in excellent agreement with experimental data. The dominace of the Neel relaxation over the Brownian one is demonstrated.
Rate effects on layering of a confined linear alkane  [PDF]
Lionel Bureau
Physics , 2007, DOI: 10.1103/PhysRevLett.99.225503
Abstract: We perform drainage experiments of a linear alkane fluid (n-hexadecane) down to molecular thicknesses, and focus on the role played by the confinement rate. We show that molecular layering is strongly influenced by the velocity at which the confining walls are approached: under high enough shear rates, the confined medium behaves as a structureless liquid of enhanced viscosity for film thickness below $\sim$10 nm. Our results also lead us to conclude that a rapidly confined film can be quenched in a metastable disordered state, which might be related with recent intriguing results on the shear properties of confined films produced at different rates [Zhu and Granick, Phys. Rev. Lett. {\bf 93}, 096101 (2004)].
Effects of inhomogeneous partial absorption and the geometry of the boundary on the population evolution of molecules diffusing in general porous media  [PDF]
Seungoh Ryu
Physics , 2009, DOI: 10.1103/PhysRevE.80.026109
Abstract: We consider aspects of the population dynamics, inside a bound domain, of diffusing agents carrying an attribute which is stochastically destroyed upon contact with the boundary. The normal mode analysis of the relevant Helmholtz equation under the partially absorbing, but uniform, boundary condition provides a starting framework in understanding detailed evolution dynamics of the attribute in the time domain. In particular, the boundary-localized depletion has been widely employed in practical applications that depend on geometry of various porous media such as rocks, cement, bones, and cheese. While direct relationship between the pore geometry and the diffusion-relaxation spectrum forms the basis for such applications and has been extensively studied, relatively less attention has been paid to the spatial variation of the boundary condition. In this work, we focus on the way the pore geometry and the inhomogeneous depletion strength of the boundary become intertwined and thus obscure the direct relationship between the spectrum and the geometry. It is often impossible to gauge experimentally the degree to which such interference occur. We fill this gap by perturbatively incorporating classes of spatially-varying boundary conditions and derive their consequences that are observable through numerical simulations or controlled experiments on glass bead packs and artificially fabricated porous media. We identify features of the spectrum that are most sensitive to the inhomogeneity and apply the method to the spherical pore with a simple hemi-spherical binary distribution of the depletion strength and obtain bounds for the induced change in the slowest relaxation mode.
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