ON A MODEL FOR THE PROPAGATION OF ISOTOPIC DISEQUILIBRIUM BY DIFFUSION

2009 ◽  
Vol 19 (08) ◽  
pp. 1277-1294 ◽  
Author(s):  
E. COMPARINI ◽  
R. DAL PASSO ◽  
C. PESCATORE ◽  
M. UGHI
Keyword(s):  
Parabolic Equation ◽  
Chemical Element ◽  
Chemical Potential ◽  
Hyperbolic Equations ◽  
Total Concentration ◽  
The Other ◽  
Qualitative Properties ◽  
Used Nuclear Fuel ◽  
Solvent Molecules ◽  
Isotopic Disequilibrium

We consider a model for the distribution of radionuclides in the ground water around a deep repository for used nuclear fuel, based on the assumption that different isotopes of the same chemical element A contribute jointly to the chemical potential of A. In this hypothesis, the total flux Ji of a particular isotope Ai of an element A has two components, one due to the interaction of Ai with the solvent molecules B, the other with the kin isotopes. We study some qualitative properties of the solution in the physically relevant assumption that the first of these components is negligible. In this assumption the problem reduces to a parabolic equation for the total concentration of the element A, possibly coupled with hyperbolic equations for the concentrations of the single isotopes.

scholarly journals Decachlorocyclopentasilanes coordinated by pairs of chloride anions, with different cations, but the same solvent molecules

2017 ◽  
Vol 73 (12) ◽  
pp. 1903-1907 ◽  
Author(s):  
Maximilian Moxter ◽  
Julian Teichmann ◽  
Hans-Wolfram Lerner ◽  
Michael Bolte ◽  
Matthias Wagner
Keyword(s):  
Crystal Structures ◽  
General Position ◽  
Rotation Axis ◽  
Chloride Ion ◽  
The Other ◽  
Structural Motif ◽  
Solvent Molecules

We have determined the crystal structures of two decachlorocyclopentasilanes, namely bis(tetra-n-butylammonium) dichloride decachlorocyclopentasilane dichloromethane disolvate, 2C16H36N+·2Cl−·Si5Cl10·2CH2Cl2, (I), and bis(tetraethylammonium) dichloride decachlorocyclopentasilane dichloromethane disolvate, 2C8H20N+·2Cl−·Si5Cl10·2CH2Cl2, (II), both of which crystallize with discrete cations, anions, and solvent molecules. In (I), the complete decachlorocyclopentasilane ring is generated by a crystallographic twofold rotation axis. In (II), one cation is located on a general position and the other two are disordered about centres of inversion. These are the first structures featuring the structural motif of a five-membered cyclopentasilane ring coordinated from both sides by a chloride ion. The extended structures of (I) and (II) feature numerous C—H...Cl interactions. In (II), the N atoms are located on centres of inversion and as a result, the ethylene chains are disordered over equally occupied orientations.

Thermodynamic properties of light mesons and phase transition in an extended SU(2) NJL model

2019 ◽  
Vol 34 (13) ◽  
pp. 1950070
Author(s):  
J. R. Morones Ibarra ◽  
A. J. Garza Aguirre ◽  
Francisco V. Flores-Baez
Keyword(s):  
Chemical Potential ◽  
Pion Mass ◽  
Quark Condensate ◽  
The Other ◽  
Chiral Symmetry Restoration ◽  
Chiral Phase ◽  
Potential Dependence ◽  
Njl Model ◽  
The Masses ◽  
Sigma Meson

In this work, we study the temperature and chemical potential dependence of the masses of sigma and pion mesons as well as the quark condensate by using a SU(2) flavor version of the Nambu–Jona–Lassino model, introducing a prescription that mimics confinement. We have found that as the temperature increases, the mass of sigma shifts down, while the pion mass remains almost constant. On the other hand, the quark condensate decreases as the temperature and chemical potential increases. We have also analyzed the temperature and chemical potential dependence of the spectral function of the sigma meson, from which we observe at low values of T and [Formula: see text] an absence of a peak. Furthermore, as the Mott temperature is reached, its value increases abruptly and a distinct peak emerges, which is related with the dissociation of the sigma. For the case of [Formula: see text], the Mott dissociation is exhibited about the temperature of 189 MeV. We have also obtained the chiral phase diagram and the meson dissociation for different values of [Formula: see text]. From these results, we can state a relation between chiral symmetry restoration and Mott dissociation.

ON THE CONTINUITY OF THE RESPONSE MAP AND AN ALTERNATIVE SHOOTING METHOD FOR THE HALF-SPACE GINZBURG–LANDAU MODEL

2006 ◽  
Vol 16 (09) ◽  
pp. 1527-1558
Author(s):  
CATHERINE BOLLEY ◽  
BERNARD HELFFER
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Shooting Method ◽  
The Other ◽  
Complete Analysis ◽  
Qualitative Properties ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Ginzburg Landau Equations ◽  
Physical Literature

As a consequence of a rather complete analysis of the qualitative properties of the solutions of the Ginzburg–Landau equations, we prove, in this paper, both the continuity of a fundamental map σ, called response map in the physical literature on superconductors, and the convergence of an efficient algorithm for the computation of the graph of σ. The response map σ gives the intensity h of the external magnetic field for which the Ginzburg–Landau equations (in a half-space) have a solution such that the parameter order has a prescribed value at the boundary of the sample. Our study involves a shooting method on either one or the other unknown of the system; our algorithm has been introduced in Bolley–Helffer for small values of the Ginzburg–Landau parameter κ and extended in Bolley to any value of κ. Our preceding mathematical studies were not sufficient to prove the convergence, but a recent result (in Ref. 3) on the monotonicity of the solutions with respect to h, combined with a more extensive use of the properties of the solutions of the Ginzburg–Landau system, allow us to complete the proof and to get, as a by-product, the continuity of σ.

scholarly journals (η6-Benzene)(carbonato-κ2O,O′)[dicyclohexyl(naphthalen-1-ylmethyl)phosphane-κP]ruthenium(II) chloroform trisolvate

2014 ◽  
Vol 70 (7) ◽  
pp. m272-m273
Author(s):  
Saravanan Gowrisankar ◽  
Helfried Neumann ◽  
Anke Spannenberg ◽  
Matthias Beller
Keyword(s):  
Hydrogen Bonding ◽  
Metal Complex ◽  
Room Temperature ◽  
Crystal Packing ◽  
The Other ◽  
Asymmetric Unit ◽  
Carbonate Group ◽  
Acta Cryst ◽  
Hydrogen Bonding Interactions ◽  
Solvent Molecules

The title compound, [Ru(CO3)(η6-C6H6){(C6H11)2P(CH2C10H7)}]·3CHCl3, was synthesized by carbonation of [RuCl2(η6-C6H6){(C6H11)2P(CH2C10H7)}] with NaHCO3in methanol at room temperature. The RuIIatom is surrounded by a benzene ligand, a chelating carbonate group and a phosphane ligand in a piano-stool configuration. The crystal packing is consolidated by C—H...O and C—H...Cl hydrogen-bonding interactions between adjacent metal complexes and between the complexes and the solvent molecules. The asymmetric unit contains one metal complex and three chloroform solvent molecules of which only one was modelled. The estimated diffraction contributions of the other two strongly disordered chloroform solvent molecules were substracted from the observed diffraction data using the SQUEEZE procedure inPLATON[Spek (2009).Acta Cryst.D65, 148–155].

Time-dependent singularities in a semilinear parabolic equation with absorption

2016 ◽  
Vol 18 (05) ◽  
pp. 1550077 ◽  
Author(s):  
Jin Takahashi ◽  
Eiji Yanagida
Keyword(s):  
Parabolic Equation ◽  
Singular Point ◽  
Fundamental Solution ◽  
Laplace Equation ◽  
Space Variable ◽  
The Other ◽  
Time Dependent ◽  
Singular Solutions ◽  
Semilinear Parabolic Equation ◽  
Semilinear Parabolic

This paper concerns solutions with time-dependent singularities for a semilinear parabolic equation with a superlinear absorption term. Here, by time-dependent singularity, we mean a singularity with respect to the space variable whose position depends on time. It is shown that if the power of the nonlinearity is in some range, then any singularity is removable. On the other hand, in other range, two types of time-dependent singular solutions exist: One resembles the fundamental solution of the Laplace equation near the singular point, and the other has a stronger singularity.

Isentropic compressibilities of electrolytes in acetonitrile at 25 °C

1981 ◽  
Vol 59 (14) ◽  
pp. 2212-2217 ◽  
Author(s):  
Isobel Davidson ◽  
Gérald Perron ◽  
Jacques E. Desnoyers
Keyword(s):  
General Formula ◽  
Free Space ◽  
Infinite Dilution ◽  
Inorganic Ions ◽  
The Other ◽  
Square Root ◽  
Isentropic Compressibilities ◽  
Ionic Size ◽  
Acetonitrile Solutions ◽  
Solvent Molecules

The sound velocities of some 1:1 electrolytes in acetonitrile were measured by the "sing around" method. Apparent molal isentropic compressibilities [Formula: see text] of the electrolytes were derived from these data and from previously determined densities. Infinite dilution partial molal compressibilities [Formula: see text] were obtained by extrapolation from the plot [Formula: see text] against the square-root of the molality. Approximate ionic values are obtained on the assumption that [Formula: see text] In general, [Formula: see text] of inorganic ions are much more negative in acetonitrile than in water and, except for Li+, show little dependence on ionic size. On the other hand, [Formula: see text] of tetraalkylammonium bromides become increasingly positive as the size of the cations increases. This is again in contrast with [Formula: see text] of these electrolytes in water which remain negative. These large positive values arise from the free space between the ions and the solvent molecules, which is large in acetonitrile solutions.

scholarly journals Distribution of Polycyclic Aromatic Hydrocarbons (PAHs) in Surface Sediments Collected From Selected Estuaries of Kerala, West Coast of India

2021 ◽  
Author(s):  
Krishnamoorthy Radhakrishnan ◽  
Anandarao Rajkumar ◽  
Nazeerkhan Akramkhan ◽  
Prakasheswar P. ◽  
Subbiah Krishnakumar ◽  
...  
Keyword(s):  
Grain Size ◽  
Polycyclic Aromatic Hydrocarbons ◽  
Aromatic Hydrocarbons ◽  
Surface Sediments ◽  
Total Concentration ◽  
The Other ◽  
Estuarine Sediments ◽  
Sampling Point ◽  
Sediment Grain Size ◽  
Polycyclic Aromatic

Abstract The investigation aims to study the source and concentration of polycyclic aromatic hydrocarbon (PAHs) fractions in the surface sediments of selected estuaries of the southwest coast of Kerala India. The concentration of PAHs ranged from 0.47 to 126.64 ng/g. The estuarine sediments were enriched by HMW-PAHs and they are occupied nearly 93.76 % of the total concentration, followed by LMW-PAHs (LMW-PAH – 6.23%). The sum of surface sediment-associated PAH distribution was higher in the inner part of the estuary, especially at Anjuthengu and Kadinamkulam estuaries. The sediment grain size and distance of the sampling point from the coast are significantly playing an important role in the distribution of the PAHs. The ratio of LMW/HMW PAHs in this study indicating that the pyrolytic process is the chief source of PAHs in the estuarine sediments. The calculated total TEQ value ranged from 0.20 to 54.80 ng/g. A comparative study suggests that the obtained TEQ value was less than the other locations of India and worldwide.

scholarly journals The maximum norm analysis of a nonmatching grids method for a class of parabolic equation with nonlinear source terms

2019 ◽  
Vol 38 (4) ◽  
pp. 157-174 ◽  
Author(s):  
Salah Boulaaras ◽  
Mohammed Cherif Bahi ◽  
Mohamed Haiour ◽  
Abderrahman Zarai
Keyword(s):  
Parabolic Equation ◽  
The Other ◽  
Maximum Norm ◽  
Euler Scheme ◽  
Source Terms ◽  
Parabolic Differential Equations ◽  
Schwarz Alternating Method ◽  
Nonlinear Source ◽  
Nonmatching Grids ◽  
Mutually Independent

Motivated by the idea which has been introduced by M. Haiour and S.Boulaaras (Proc. Indian Acad. Sci. (Math. Sci.) Vol. 121,No. 4, November 2011,pp.481--493), We provide a maximum norm analysis of Euler scheme combined with finite element Schwarz alternating method for a class of parabolic equation with nonlinear source terms on two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a stability analysis on the theta scheme which given by our work in (App. Math. Comp., 217, 6443--6450 (2011).), we establish, on each subdomain, an optimal asymptotic behavior between the discrete Schwarz sequence and the asymptotic solution of parabolic differential equations.

Atomic Understanding of the Swelling and Phase Transition of Polyacrylamide Hydrogel

2016 ◽  
Vol 08 (07) ◽  
pp. 1640002 ◽  
Author(s):  
Shuai Xu ◽  
Ying Wang ◽  
Jianying Hu ◽  
Zishun Liu
Keyword(s):  
Phase Transition ◽  
Continuum Mechanics ◽  
Chemical Potential ◽  
Polymer Network ◽  
Point Of View ◽  
Dynamics Simulation ◽  
Mechanics Model ◽  
Basic Parameters ◽  
Solvent Molecules ◽  
And Diffusion

A polymer network can imbibe copious amounts of solvent (water) and swell, and the resulting state is known as a hydrogel. In this study, we have made the modification for the all-atom consistent valence force field (CVFF) to investigate the swelling property of polyacrylamide (PAM) hydrogel by molecular dynamics simulation. We have built 21 hydrogel models with different solvent contents and calculate the average chemical potential and diffusion coefficient of solvent molecules in PAM hydrogel. We find that when the mass fraction of solvent is about 90%, PAM hydrogel reaches its free swelling limitation and loses the motivation of absorbing solvent. Furthermore, it is also found that PAM hydrogel has a phase transition phenomenon when the values of solvent chemical potential are between [Formula: see text][Formula: see text]kcal/mol and [Formula: see text][Formula: see text]kcal/mol. This study will provide insight into the basic parameters which are widely used in continuum mechanics analysis of hydrogels from atomic point of view and help researchers to improve the continuum mechanics model for neutral hydrogel.

Sign in / Sign up

Export Citation Format

Share Document