Proportional toT Research Articles

Randomized approximate nearest neighbors algorithm

We present a randomized algorithm for the approximate nearest neighbor problem in d -dimensional Euclidean space. Given N points { x j } in , the algorithm attempts to find k nearest neighbors for each of x j , where k is a user-specified integer parameter. The algorithm is iterative, and its running time requirements are proportional to T · N ·( d ·(log d ) + k ·( d + log k )·(log N )) + N · k 2 ·( d + log k ), with T the number of iterations performed. The memory requirements of the procedure are of the order N ·( d + k ). A by-product of the scheme is a data structure, permitting a rapid search for the k nearest neighbors among { x j } for an arbitrary point . The cost of each such query is proportional to T ·( d ·(log d ) + log( N / k )· k ·( d + log k )), and the memory requirements for the requisite data structure are of the order N ·( d + k ) + T ·( d + N ). The algorithm utilizes random rotations and a basic divide-and-conquer scheme, followed by a local graph search. We analyze the scheme’s behavior for certain types of distributions of { x j } and illustrate its performance via several numerical examples.

A SPATIAL DYNAMIC PANEL DATA MODEL WITH BOTH TIME AND INDIVIDUAL FIXED EFFECTS

This paper establishes asymptotic properties of quasi-maximum likelihood estimators for spatial dynamic panel data with both time and individual fixed effects when the number of individualsnand the number of time periodsTcan be large. We propose a data transformation approach to eliminate the time effects. Whenn / T→ 0, the estimators are$\root \of {nT}$consistent and asymptotically centered normal; whennis asymptotically proportional toT, they are$\root \of {nT}$consistent and asymptotically normal, but the limit distribution is not centered around 0; whenn / T→ ∞, the estimators are consistent with rateTand have a degenerate limit distribution. We also propose a bias correction for our estimators. When n1/3/T→ 0, the correction will asymptotically eliminate the bias and yield a centered confidence interval. The estimates from the transformation approach can be consistent whennis a fixed finite number.

Cementation of gold by magnesium in cyanide solutions

Contact deposition of gold by a magnesium powder in a hydrodynamic mode in 0.001–0.005 M solutions of the system [Au(CN)2]−-CN− is investigated. It is found that the cementation rate of gold (V c ) is directly proportional tot he concentration of the [Au(CN)2]− complex and the area of the cementing agent. As the temperature is increased in the ranges 20–30 and 30–40°C, the increase in V c is 20–25 and 8–10%, respectively. The time dependence of degree of gold extraction on magnesium has an extreme character due to the increasing rate of the inverse process of leaching. In an ultrasonic field, the cementation rate and degree of gold extraction increase. This phenomenon is conditioned by destruction of the hydroxide film on the magnesium surface. The deposited gold has a film nature.

Low-temperature transport properties ofnon-stoichiometric La0.95-xSrxMnO3 manganites

The low-temperature specific heat and electrical resistivity of the polycrystalline non-stoichiometric manganites La0.95-xSrxMnO3 have been investigated in the doping regionx = 0.00-0.30. The specific heat has terms proportional toT and T3. The resistivity of the samples decreases asT1/2 with increasing temperature, goes through aminimum and then increases proportionally to T3. Thetemperature Tmin , corresponding to the minimum of the resistivity, shifts with Sr content as Tmin ~x-2/5.

The evolution of a beamed gamma-ray-burst afterglow: the non-relativistic case

There has been increasing evidence that at least some gamma-ray bursts (GRBs) are emission beamed. The beamed GRB-afterglow evolution has been discussed by several authors in the ultrarelativistic case. It has been shown that the dynamics of the blast wave will be significantly modified by the sideways expansion, and there may be a sharp break in the afterglow light curves under certain circumstances. However, this is only true when the fireball is still relativistic. Here we present an analytical approach to the evolution of the beamed GRB blast wave expanding in the surrounding medium (density n proportional tor(-s)) in the non-relativistic case, our purpose is to explore whether the sideways expansion will strongly affect the blast-wave evolution as in the relativistic case. We find that the blast-wave evolution is strongly dependent on the speed of the sideways expansion. If it expands with the sound speed, then the jet angle theta increases with time as theta proportional to ln t, which means that the sideways expansion has little effect on the afterglow light curves, the flux F proportional tot(-3(5 alpha -1)/5) for s=0 and F proportional tot(-7 alpha +1/3) for s=2. It is clear that the light curve of s=2 is not always steeper than that of s=0, as in the relativistic case. We also show that if the expansion speed is a constant, then the jet angle theta proportional tot and the radius r proportional tot(0), in this case the sideways expansion has the most significant effect on the blast-wave evolution, the flux F proportional tot(-(5 alpha -1)), independent of s, and we expect that there should be a smooth and gradual break in the light curve.

Anomalous raman scattering in the normal state of uederdoped crystals of YBA2Cu3O7-x

The integrated intensity of the electronic background between 200 and 700 cm-1 observed in the Raman spectra of the YBa2Cu3O7-x 1-2-3 system exciting at 1.16 eV shows three changes with temperature. This electronic background is due to the scattering between quasi-degenerate bands at the Fermi level with apical oxygen character which have neither CuO2 nor chain character. One of these transitions coincides with the appearance of superconductivity in the system. This indicates that even if the opening of the gap in the apical oxygen electronic levels is not clearly observed, the interband transition between these two levels is coupled to the superconducting order parameter. The other two changes of the background intensity occur at temperatures greater thanT c . The one at lower temperature is proportional toT c and coincides probably with the appearance of self-organized electronic nanostructures already observed by EXAFS measurements in other HTc material systems (La-Sr-Cu-O, Ba-Sr-Ca-Cu-O). The latter transition is observed at TD>- Tc (where TD decreases as Tc increases). This temperature coincides with the opening of a pseudogap that has been detected by several experimental techniques in underdoped High-T,. systems. The possibility to observe the opening of a pseudogap in the density of states by means of Raman scattering is analyzed in terms of different theoretical models that have been postulated to explain superconductivity in cuprates.

Absence of renormalization group pathologies near the critical temperature. Two examples

We consider real-space renormalization group transformations for Ising-type systems which are formally defined by $$\exp \left[ { - H'(\sigma ')} \right] = \sum\limits_\sigma {T(\sigma ,\sigma ')} \exp \left[ { - H(\sigma )} \right]$$ whereT(σ, σ′) is a probability kernel, i.e., ∑σ′T(σ,σ′) = 1 for every configuration σ. For each choice of the block spin configuration σ′, let σ′, let μσ′ be the measure on spin configurations σ which is formally given by taking the probability of σ to be proportional toT(σ, σ′) exp[−H(σ)]. We give a condition which is sufficient to imply that the renormalized HamiltonianH′ is defined. Roughly speaking, the condition is that the collection of measures μσ′ is in the high-temperature phase uniformly in the block spin configuration σ′. The proof of this result uses methods of Olivieri and Picco. We use our theorem to prove that the first iteration of the renormalization group transformation is defined in the following two examples: decimation with spacingb = 2 on the square lattice with β < 1.36βc and the Kadanoff transformation with parameterp on the trian gular lattice in a subset of the β,p plane that includes values of β greater than βc.

Thermal boundary resistance between liquid helium and silver sinter at low temperatures

We present measurements of the thermal coupling between Ag sinter (nominal grain size ≈ 700 Å) and superfluid3He-B atp = 0.3, 10, and 20 bar as well as a phase-separated3He4-He mixture atp = 0.5 bar in the submillikelvin regime. In order to analyze the data of the pure3He-B sample with respect to different contributions to the thermal resistance, a one-dimensional model for the heat flow in the sinter is presented. As a result it is shown that the thermal conductivity of the liquid in the sinter has to be taken into account to extract the temperature and pressure dependence of the boundary resistance in the confining geometry of the sinter. Depending on the value of this thermal conductivity, a boundary resistance proportional toT −2 orT −3 is found. Moreover, it is shown that a pressure dependence of the boundary resistance might be explained by a pressure dependence of the thermal conductivity of the liquid in the sinter. The data on the phase-separated mixture are equally well described by aT −2- and aT −3-dependence of the boundary resistance. We point out that a common problem in most measurements of the Kapitza resistance performed so far is the small temperature interval investigated, which usually does not allow a definite conclusion concerning the temperature dependence.

A dynamical approach to anomalous conductivity

We study a process of anomalous diffusion of a variable resulting from the fluctuations of a dichotomous velocity whose two states, in the absence of perturbation, have the same waiting time distribution ψ(t). In the long-time limit the function ψ(t) is proportional tot−μ with 2 1/e, where e is proportional to the intensity of the weak perturbation. We show that the resulting transport process is characterized by a succession of two regimes: the first still satisfies the prescriptions of the Green-Kubo approach to conductivity, and, in accordance with the nature of the anomalous diffusion studied here, corresponds to a state of increasing conductivity (IC); the second regime is characterized by a constant conductivity (CC). The transition from the IC to the CC regime takes place in a time of the order oft∼1/e and consequently the transition occurs at longer and longer times, as the perturbation intensity decreases. The final stationary regime corresponds to an asymmetric Levy process of diffusion.

Meissner effect in Au induced by the proximity effect in the clean limit

The Meissner effect in Au induced by the proximity effect of Nb has been investigated for Au-clad Nb wire and Au/Nb/Au sandwich over a wide range of Au thicknessdN and the electronic mean free path lN in Au. The Meissner screening length ϱ in Au increases in proportion toT−1 with a decrease in temperature and becomes nearly constant as it approachesdN. Within the temperature range where ϱ is proportional toT−1, ϱ is independent of lN anddN. The typical temperature dependence of ϱ expected in the clean-limit theory has not been observed.

Longitudinal spin relaxation in a dilute, degenerate Fermi gas at arbitrary polarization

We calculate the longitudinal magnetic relaxation timeT1−1 for a dilute, polarized Fermi gas with short range interactions at low temperatures. In the limit of small polarizationsT1−1 is proportional toT−2 in agreement with earlier predictions, while in the opposite caseT1−1 is strongly affected by polarization, and in the limit of large polarizations becomes proportional to the square of the energy separation between the Fermi surfaces for up and down spins. The possibility of measuringT1 in dilute solutions of3He in superfluid4He is investigated.

Shock fluctuations in the asymmetric simple exclusion process

We consider the one dimensional nearest neighbors asymmetric simple exclusion process with ratesq andp for left and right jumps respectively;q<p. Ferrari et al. (1991) have shown that if the initial measure isv ρ,λ , a product measure with densities ρ and λ to the left and right of the origin respectively, ρ<λ, then there exists a (microscopic) shock for the system. A shock is a random positionX t such that the system as seen from this position at timet has asymptotic product distributions with densities ρ and λ to the left and right of the origin respectively, uniformly int. We compute the diffusion coefficient of the shockD=lim t→∞ t −1(E(X t )2−(EX t )2) and findD=(p−q)(λ−ρ)−1(ρ(1−ρ)+λ(1−λ)) as conjectured by Spohn (1991). We show that in the scale $$\sqrt t$$ the position ofX t is determined by the initial distribution of particles in a region of length proportional tot. We prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities ρ and λ. This is the so called dynamical phase transition. Under shock initial conditions we show how the density fluctuation fields depend on the initial configuration.

Variable gravitational coupling, mass creation and celestial mechanics

The Einstein-Hilbert action is extended to include the time-dependent gravitational couplingG∞t−1. The resulting field equation requires a matter creation process inside the source; the creation rate in a homogeneous ball of perfect fluid is evaluated and the massM of the ball is found proportional tot. It is suggested that such a process could explain the well-known discrepancy betweenG∞t−1 and the Viking-lander-range data on the orbit of Planet Mars.

Theoretical analysis of the acoustic phonon limited energy loss rate and relaxation time of hot 2D-excitons in a GaAs-square quantum well (SQW)

The average energy loss rate and relaxation time of non-degenerate 2D-excitons interacting with the deformation- and piezoelectric potential of 3D acoustic bulk phonons are calculated perturbation theoretically as a function of the exciton temperature using the matrix elements previously derived in [1]. The energy loss rate limited by the acoustic deformation potential increases proportional toT 3 7/2 (T 3 3/2 ) if the phonon energy is much larger (smaller) than the thermal energy of the excitons having the temperatureT e . It is shown, that the phonon wavevector componentq z perpendicular to the interface of the QW must be taken into account in the calculation of the total excitonic loss rate in order to obtain the energy relaxation time value of 30 ps recently estimated in [2] from photoluminescence intensity measurements.

Some possible consequences of Zel’dovich’s cosmological term

According to Zel’dovich, the energy tensor of the polarized vacuum of quantum field theory implies the existence of a non-zero cosmological A term in i Einstein’s gravitational equation. I investigate the consequences of Zel’dovich’s λ in a spatially flat isotropic universe with the Hubble parameterH proportional tot−1 (t = the cosmic time); I find:tH > 2/3, -1 <q < 1/2, λt2= constant,Gt = constant, whereq is the deceleration parameter andG the gravitational coupling; another result is a mass creation process throughout the universe at the rate 10−47gs−3 cm−3. This approach explains two well-known empirical relations connecting microphysics to cosmology.

Specific immunosuppression of human anti-murine antibody responses in hu-PBL-SCID mice

Severe combined immunodeficient (SCID) mice were reconstituted with normal human peripheral blood leukocytes (PBLs) and were shown to produce a human anti-mouse immunoglobulin antibody response on immunization with heat-treated murine monoclonal IgG1 antibody to ovalbumin, referred to as ha-Mab-2. The human anti-mouse antibody response was proportional tot the number of B cells and mononuclear cells transferred from a given batch of PBL. However, pretreatment of hu-PBL-SCID mice with a tolerogenic covalent conjugate of monomethoxypolyethylene glycol (mPEG) and Mab-2 suppressed this response on subsequent injections of ha-Mab-2, and this suppression was shown to be antigen-specific, i.e., it did not suppress the antibody response to ovalbumin and did not affect the level of production of human immunoglobulin of hu-PBL-SCID mice. The suppression was due to the generation of human suppressor CD8+ T (Ts) cells, which down regulated CD4+ helper T cells in an antigen and HLA class I specific manner, i.e., these findings were in accord with the previously shown immunosuppressive effect of tolerogenic mPEG conjugates in normal mice.

Effects of an oscillating field on a diffusion process in the presence of a trap

Consider a diffusion process on an infinite line terminated by a trap and modulated by a periodic field. When the frequency is equal to zero the mean time to trapping will be finite or infinite, depending on the sign of the field. We ask whether this behavior can be changed by an oscillatory field, and show that it cannot for pure Brownian motion. We suggest that transition can appear when the signal propagation velocity is finite as for the telegrapher's equation. We further suggest that the asymptotic time dependence of the survival probability is proportional tot−1/2 just as in the case of ordinary diffusion. The same conclusion is shown to hold for a system whose dynamics is governed by the equation\(\dot x = xv(t)/^\cdot L\), whereL is a constant.

Longitudinal relaxation time for dilute quantum gases

We calculate the longitudinal relaxation timeT 1 for a polarized spin-1/2 Fermi gas, in zero magnetic field, for conditions of temperatureT and densityn such that Boltzmann statistics are valid. Our results show generally thatT 1 is independent of polarization of the gas. At highT, where the thermal wavelength λ is small compared to the scattering lengtha, T 1 is proportionalT 1/2, while at lowT, such that λ is greater thana, T 1 is proportional toT −1/2.T 1 thus has a minimum at some intermediate temperature confirming the numerical results of Shizgal. Physical arguments show that the existence of the minimum does not depend on the presence of an attractive part of the potential. As an example of the expected temperature dependence we calculateT 1 numerically, via the distorted-wave Born approximation, for the case of a gas interacting via a hard core. We also computeT 1 for a spin-1/2 Bose gas, which also shows a minimum.

Thermoelectric power of heavy-fermion compounds

We calculate the diffusion thermopower of the Anderson lattice as a model for heavyfermion compounds in a semi-phenomenological theory. In this theory, the thermopower is expressed by the dynamical susceptibility which describes spin fluctuations and can be measured by neutron scattering. The Kondo effect is taken into account for a singlef-electron spin which is coupled to all other spins and to the conduction electrons. This approach neglects multiple intesite-scattering of the conduction electrons. We obtain a “Kondo” termS (1) (T) (in which the thermopower of non-interacting spins is multiplied by a factor which describes the spin dynamics) and a “resonance” termS (2) (T) of opposite sign which vanishes for vanishing interactions. The superposition of both terms leads to a broad maximum of the thermopower roughly at the Kondo temperatureT K and to an additional minimum belowT K . ForT→0 the termS (1) vanishes asT 2 and the termS (2) becomes proportional toT. We also show that the Sommerfeld expansion leads to an incorrect result for the low temperature resistivity of the Anderson lattice and that the Gorter-Nordheim relation does not hold at low temperatures.

Specific heat of the high-T c oxide superconductors

We review the specific heat measurements on La2CuO4, La2−xMxCuO4 (M = Ca, Sr, and Ba), YBa2Cu3O7, and the Bi-Ca-Sr-Cu-O and Tl-Ca-Ba-Cu-O systems. Tables of properties derived from the data are presented. Results on RBa2Cu3O7 (R=rare earth elements other than Y) are summarized, as are results on YBa2(Cu3−xMx)O7 (M=Zn, Cr, Fe, or Ni). The difficulties of analyzing the specific heat data, and specifically the separation of the contributions associated with magnetic impurities, are discussed. It is tentatively concluded that the data nearT c are consistent with BCS theory, although they show evidence of fluctuation effects. It is also concluded that the low-temperature zero-field data on a majority of the high-T c oxide superconductors provide evidence of anintrinsic term that is proportional toT, a result that is inconsistent with a gap in the electronic density of states.