Equilibrium Distribution Of Electrons Research Articles

Contribution of the triplet component of the supercurrent-carrying density of states to the Josephson current in a nonequilibrium superconductor/ferromagnet/superconductor junction

A weak link of two superconductors with s-type pairing through a ferromagnet has been theoretically investigated in the regime of a nonequilibrium spin-dependent distribution of electrons over energy levels in a ferromagnetic interlayer. It has been shown that, under the given conditions, the triplet component of the supercurrent-carrying density of states, which does not participate in the Josephson current transfer under equilibrium and spin-independent nonequilibrium conditions, is involved in the Josephson current transfer through the junction. In this case, the standard supercurrent transferred by the singlet component of the supercurrent-carrying density of states remains unchanged as compared to the case of the equilibrium distribution of electrons in the interlayer. An additional current transferred by the triplet component is controlled by a voltage that controls the specific shape and the degree of nonequilibrium of the electron distribution function in the interlayer. Depending on this controlling parameter, the additional current can substantially amplify or attenuate the standard supercurrent and also switch the junction between 0 and π states.

Conductivity of composites containing ferromagnetic nanoparticles: The role of a magnetic field

A theory of conductivity is developed for metal-containing nanocomposites. An expression is obtained for the tunneling rate of an electron between nanoparticles. Three regimes of current flow are possible: the cases of weak, strong, and superstrong electric fields. In the weak-field regime, the electrons generated as a result of ionization of neutral nanoparticles are characterized by a nearly equilibrium distribution. The conductivity in this regime is calculated with the use of this nearly equilibrium distribution of electrons and the relationship between the spacing of neighboring particles and their radii. An expression is obtained for the electric conductivity as a function of temperature and a magnetic field (for ferromagnets) with regard to the distribution of nanoparticles with respect to radius and their volume density.

SP154 The role of pharmacogenetics and pharmacogenomics in cancer therapy

A brief survey of modern concepts and principles of the electronic structure and chemical reactivity is presented with an emphasis on the importance of chemical concepts for understanding the molecular behavior. The specificity of the chemical interpretation of molecular processes, in terms of AIM, chemical bonds, functional groups, reactants, etc., is commented upon. The classical structural and reactivity rules are reviewed. The quadratic Taylor expansion of the electronic energy of molecular systems in powers of displacements (perturbations) of the system state-parameters is introduced. It is defined by the generalized response quantities: “potentials”, the first partials of the energy, and charge sensitivities, the second partials of the energy with respect to the system parameters of state. This series constitutes an adequate framework for describing reactant subsystems in a bimolecular reactive system. The role of the electronic density as the source and carrier of the complete information about the system ground-state equilibrium and all its physical and chemical properties is stressed. Basic elements of the electron wave-function and density-functional theories of electronic structure are summarized and the conceptual advantages of DFT over the standard wave-function approach are emphasized. The Euler equation for the ground-state density, the DFT equivalent of the Schrödinger equation of the wave-function theory, is discussed in some detail. It embodies the crucial ground-state relation between the equilibrium distribution of electrons and the external potential due to the system nuclei. This equation is shown to imply the chemical potential (electronegativity) equalization throughout the physical space. A distinction is made between transitions from one ground-state density to another, called here the “horizontal” displacements of the system electronic structure, and those corresponding to flows of electrons between molecular subsystems, for the fixed density of the molecule as a whole, called the “vertical” displacements.

Electron transfer in crystals of the binary and ternary complexes of methylamine dehydrogenase with amicyanin and cytochrome c551i as detected by EPR spectroscopy.

EPR studies of the methylamine dehydrogenase (MADH)-amicyanin and MADH-amicyanin-cytochrome c551i crystalline complexes have been performed on randomly oriented microcrystals before and after exposure to the substrate, methylamine, as a function of pH. The results show that EPR signals from the redox centers present in the various proteins can be observed simultaneously. These results complement and extend earlier studies of the complexes under similar conditions that utilized single-crystal polarized absorption microspectrophotometry. The binary complex shows a blue copper axial signal, characteristic of oxidized amicyanin. After reaction of substrate with the MADH coenzyme tryptophan tryptophylquinone (TTQ), the binary complex exhibits an equilibrium mixture of oxidized copper/reduced TTQ and reduced copper/TTQ. radical, whose ratio is dependent on the pH. In the oxidized ternary complex, the same copper axial signal is observed superimposed on the low-spin ferric heme features characteristic of oxidized cytochrome c551i. After addition of substrate to the ternary complex, a decrease of the copper signal is observed, concomitant with the appearance of the radical signal derived from the semiquinone form of TTQ. The equilibrium distribution of electrons between TTQ and copper as a function of pH is similar to that observed for the binary complex. This result was essential to establish that the copper center retains its function within the crystalline ternary complex. At high pH, with time the low-spin heme EPR features disappear and the spectrum indicates that full reduction of the complex by substrate has occurred.

Enzymatic and Electron Transfer Activities in Crystalline Protein Complexes

Enzymatic and electron transfer activities have been studied by polarized absorption spectroscopy in single crystals of both binary and ternary complexes of methylamine dehydrogenase (MADH) with its redox partners. Within the crystals, MADH oxidizes methylamine, and the electrons are passed from the reduced tryptophan tryptophylquinone (TTQ) cofactor to the copper of amicyanin and to the heme of cytochrome c551i via amicyanin. The equilibrium distribution of electrons among the cofactors, and the rate of heme reduction after reaction with substrate, are both dependent on pH. The presence of copper in the ternary complex is not absolutely required for electron transfer from TTQ to heme, but its presence greatly enhances the rate of electron flow to the heme.

A Current Look at Electron Transport in Organic Liquids

Abstract Recent measurements of the drift mobility (μ D ) of electrons in hydrocarbon liquids at high pressure and of the Hall mobility (μ H ) as a function of temperature are discussed. In some highly branched alkanes μ H ≃ μ D , also high pressure causes μ D to increase at 20°C. These facts are consistent with the tenet that in these liquids electrons remain quasi-free, the observed mobility being a result of scattering due in large part to density fluctuations. For normal and singly branched alkanes the mobility is determined by an equilibrium distribution of electrons between the trapped and quasi-free states. High pressure shifts this equilibrium toward the trapped state because of a volume decrease occurring on trapping. This volume change is attributed to electrostriction of the solvent by the trapped electron.

Far-infrared photothermal ionization spectroscopy of semiconductors in the presence of intrinsic light

The equilibrium distribution of electrons and holes over shallow impurity states and energy bands of an ultrapure semiconductor is studied for the situation where the semiconductor is continuously illuminated with intrinsic light (i.e., radiation with energies of the order of the gap energy of the semiconductor). The response to additional injection of free minority or majority charge carriers into the energy bands—caused by photothermal ionization of minority or majority impurities, respectively—is separately investigated. The equilibrium and the response have theoretically been analyzed by means of a description with a set of rate of change equations. This analysis explains the usually observed behavior that photothermal ionization of minority impurities in ultrapure germanium under continuous illumination with intrinsic light gives rise to a decrease in electrical conductivity. The measured time evolution of the change in conductivity of an ultrapure germanium sample after the start of the photothermal process revealed a slow (∼5 ms) change, connected with minority impurities only, as well as a fast (<0.5 ms) change. The slow response time has been associated with the electron-hole recombination time, yielding a value 5×10−12 cm3 s−1 for the electron-hole recombination constant. It is demonstrated that in photothermal ionization spectroscopy, when using phase-sensitive detection techniques by means of a lock-in amplifier, such a simultaneous presence of a fast and a slow (i.e., of the order of magnitude of the chopping times applied) change in conductivity can cause artefacts in the spectra.

Equilibrium distributions of electrons on smooth plane conductors

It is shown that nth order Fekete points and more general n-tuples of equilibrium points on simple closed curves of class C 3+ ε have very regular distribution as n→∞. The method of proof resembles that of Pommerenke [5] for analytic curves: one introduces explicitly known comparison points such that electrons at those points and constrained to the conducting curve are nearly in equilibrium, and one shows next that the equilibrium points must be close to the comparison points. However, the nonanalytic case requires some new tools: (i) the sharpened Grunsky inequality for quasi-conformal curves; (ii) an initial smoothing of the deviations of the comparison points from the equilibrium points. As a corollary to the regularity of the distribution, one may conclude that the field due to electrons at equilibrium points is not much larger, inside the curve, than the field due to a single electron on the curve (cf. [3]).

Calculations involving ion beam source

A convergent numerical model for the calculation of the optical properties of an ion beam is given. The ion beam is formed by extracting ions from a plasma and subsequently accelerating these ions with an electrode system. The model includes the effects of space-charge of the ions and an equilibrium distribution of electrons. Methods are given for determining the existence of the solution to the nonlinear difference equations, and a convergent iterative numerical procedure is described. Comparisons are made with a procedure that previously has been used to solve such a model.

Mechanism of Polymer Formation in the System Oligoester Aery late—Sodium Naphthalene

Abstract The formation of living soluble and network polymers during anionic polymerization of α, ω-methacrylbis(triethylene glycol) phthalate leads to the two types of the equlibria in the system: the equilibrium distribution of electrons between groups with electron affinity and equilibrium between living soluble and network polymers and oligomer. The equilibrium state can be reached both by direct (polymerization) and reverse (depolym-erization) reactions.

Equilibrium distributions of electrons on roundish plane conductors. I

The paper deals with equilibrium distributions of n electrons (point charges −1) on plane conductors in the shape of a simple closed curve. For Jordan curves γ of class C3+ε and a certain roundness, a precise formula is obtained for the asymptotic behavior of equilibrium sets of n points. The results extend and refine the sophisticated work of Pommerenke on the asymptotic distribution of Fekete points (and other equilibrium points) on “strongly analytic” Jordan curves. They enable one to obtain a close estimate for the field due to n electrons in equilibrium (Faraday cage effect). The basic tool in the paper is a quantitative Tauberian result to the effect that if for a given distribution of n electrons on a smooth, roundish Jordan curve, the tangential forces are small, then the electrons are close to an equilibrium configuration, except possibly for a conformal rotation.

Equilibrium distributions of electrons on roundish plane conductors. II

Summary The paper deals with equilibrium distributions of n electrons (point charges −1) on plane conductors in the shape of a simple closed curve. For Jordan curves γ of class C 3+e and a certain roundness, a precise formula is obtained for the asymptotic behavior of equilibrium sets of n points. The results extend and refine the sophisticated work of Pommerenke on the asymptotic distribution of Fekete points (and other equilibrium points) on “strongly analytic” Jordan curves. They enable one to obtain a close estimate for the field due to n electrons in equilibrium (Faraday cage effect). The basic tool in the paper is a quantitative Tauberian result to the effect that if for a given distribution of n electrons on a smooth, roundish Jordan curve, the tangential forces are small, then the electrons are close to an equilibrium configuration, except possibly for a conformal rotation.

Fields Due to Electrons on an Analytic Curve

Let D be the interior of a simple closed analytic curve C and let $z_{n1} , \cdots ,z_{nn} $, be points on C. Assuming a logarithmic potential, the electrostatic field due to electrons (charges $ - \varepsilon $) at the points $z_{nk} $ may be represented as (the complex conjugate of) \[ \varepsilon E_n (z) = \varepsilon \sum_{k = 1}^n {\frac{1}{{z_{nk} - z}}} .\] The authors give necessary and sufficient conditions under which $E_n (z) \to 0$ as $n \to \infty $ uniformly on the compact subsets of D. For equilibrium distributions of electrons (thinking of C as a conductor) the fields $\varepsilon E_n (z)$ tend to a limit $\varepsilon E(z)$ holomorphic in the closure of D. The limiting field is identically zero if and only if C is a circle. For general analytic C, the limiting field is of the same order of smallness as the field due to a single electron outside D.

Effect of membrane potential on equilibrium poise between cytochrome a and cytochrome c in rat liver mitochondria.

The object of this work was to test the suggestion that the equilibrium poise between cytochromea and cytochromec in mitochondria might be influenced by the membrane potential. 1. The midpoint potentials of cytochromes (c+c1) and cytochromea (CO present) were found to be 250 mV and 245 mV, respectively, by equilibrating rat liver mitochondria with mixtures of ferrocyanide and ferricyanide anaerobically in presence of antimycin A and measuring the redox state of the cytochromes spectrophotometrically. In absence of CO, cytochrome oxidase gave an anomalous redox titration curve with a “midpoint” at about 275 mV. 2. When the mitochondria were equilibrated with ferricyanide/ferrocyanide, the redox poise of cytochromea (CO present) and of cytochromes (a+a3) but not of cytochromes (c+c1) was dependent on the sign and magnitude of the membrane potential developed by treating the mitochondria as follows: by adding ATP, by chaging the composition of the suspension medium so as to vary the Donnan or Nernst potential, by adding valinomycin in a medium of low K+ ion content, or by adding a pulse of acid or alkali when the membrane was made permeable to protons with FCCP. 3. The findings agree with the suggestion that the respiratory chain is arranged across the cristae membrane with cytochromesc1 andc in contact with the outer phase and cytochromesa anda3 plugged through, so that the equilibrium distribution of electrons between thec anda cytochromes is influenced by the electric field across the membrane.

Equilibrium Electron Distributions in Electric and Magnetic Fields†

ABSTRACT In this paper we consider equilibrium distributions of electrons in electric and magnetic fields such that the distribution function only depends on the invariants of the motion of the individual particles. W assume the motion to be collision-free and determine the electric and magnetic fields as functions of the parameters of the distribution function, for which we assume a particularly simple form. The purpose of such a study is to try to obtain information about the reverse procedure, that is, constructing equilibrium distributions for a given field configuration. It seems, from the results obtained in the most simple case discussed here, that the method used in the present paper docs not offer much promise of being able to decide thy equilibrium distribution for a given field configuration, since the number of parameters in the solutions for the field is too largo to enable us to see its behaviour when we vary the distribution function.

Non-Linear Theory of Plasma Oscillations and Waves†

ABSTRACT A non-linear equation for plasma oscillations is derived. Only Coulomb interactions between electrons are considered. From an exact first integration the following properties are found : There is an asymmetry in the oscillations expressed by ρ max = a0+a0 2/3n0 and ρ min = −a0+a0 2/3n0 where ρ is the density of electrons. There is also a dependence of the frequency on the amplitude of the oscillations. The uniform equilibrium distribution of electrons is found to be highly stable. A second approximate integration gives the explicit form of the oscillations and the dependence of the frequency on the amplitude ω = (1 − a0 2/n0 2)1/2 ωp. If collisions between elections are ignored, instead of progressive waves there are stationary plasma waves. The form of these is found for the case of spherical waves in an isotropic plasma. A non-linear approximate equation is found and an exact solution of this equation is obtained. A suitable approximation to this solution is ρ = A cos (B/r). The approximations ...