On the Bardeen-Cooper-Schrieffer integral equation in the theory of superconductivity

The Bardeen-Cooper-Schrieffer integral equation with a positive kernel is studied in full generality. It is shown that, there exists a unique finite transition temperature, T _c so that, if T _c ,the equation possesses a positive solution, representing the onset of the superconducting phase, while if T>T _c ,the only solution of the equation is the trivial one, indicating the occurrence of the normal phase. Moreover, it is demonstrated that such a positive solution may be approximated by a sequence of solutions of the equation restricted on bounded domains. This latter result provides a useful computational scheme for the problem.     

Electron paramagnetic relaxation in aqueous solutions of manganese (II) ions

The processes of the electron paramagnetic relaxation, molecular motions and structural changes in aqueous solutions of manganese nitrate have been investigated by direct measurement of spin-lattice (T ₁) and spin-spin (T ₂) relaxation times for a wide range of concentrations, temperatures and viscosities. T ₁ and T ₂ were measured by a non-resonance absorption method.

It was discovered that some structural regions exist at the different concentrations of Mn(II) ions in solution. So, the structure of highly concentrated solutions may be considered as one of the corresponding crystallohydrate. The structural microinhomogeneities were observed also in the intermediate concentration range at definite temperatures. It is shown that the relaxation mechanism proposed by Bloembergen and Morgan is not effective in the concentration range studied by us.

The analysis of relaxation times and E.P.R. spectra has shown the formation of ‘liquid microphases’ at the freezing point of the solution. Such microphases can exist at temperatures a few tenths of a degree below the solvent freezing point, and its composition considerably differs from the initial solution.

The correlation times for intramolecular and intermolecular electron relaxation mechanisms are evaluated and their nature is discussed.     

On the mathematical structure of Einstein's equations in mixed initial and boundary value problems

It is shown that, also in the mixed initial and boundary value problem, Einstein's equations may be replaced by the two subsystemsT _l ^m /m=0 and, provided that the initial data verify the consistency conditions and that the analogous relations are imposed on the boundaries of the given domain.     

Diffusion on the torus for Hamiltonian maps

For a mapping of the torusT ² we propose a definition of the diffusion coefficientD suggested by the solution of the diffusion equation ofT ². The definition ofD, based on the limit of moments of the invariant measure, depends on the set where an initial uniform distribution is assigned. For the algebraic automorphism of the torus the limit is proved to exist and to have the same value for almost all initial sets in the subfamily of parallelograms. Numerical results show that it has the same value for arbitrary polygons and for arbitrary moments.     

The Non-Perturbative Approach to the Infrared Problem in QCD at Finite Temperature

A non-perturbative approach is developed for investigation of the infrared problem in QCD at T ≠ 0 in the ghost-free axial gauge. The problem is solved by using a 3-dimensional theory within the exact Slavnov-Taylor identities and Schwinger-Dyson equations. The system of two non-linear integral equations for the structural functions of the gluon polarization tensor is obtained whose solution determines the infrared behavior of the temperature Green functions in the 4-dimensional QCD. The simplest solution of these equations which is the same as the first term of the perturbation expansion shows the presence of singularities in the gluon propagator at momenta p ∼ g²T, that cannot be eliminated by any choice of the gauge. The infrared instability of QCD at T ≠ 0 caused by these singularities is discussed.     

Rigorous Results on Spontaneous Symmetry Breaking in a One-Dimensional Driven Particle System

We study spontaneous symmetry breaking in a one-dimensional driven two-species stochastic cellular automaton with parallel sublattice update and open boundaries. The dynamics are symmetric with respect to interchange of particles. Starting from an empty initial lattice, the system enters a symmetry broken state after some time T ₁ through an amplification loop of initial fluctuations. It remains in the symmetry broken state for a time T ₂ through a traffic jam effect. Applying a simple martingale argument, we obtain rigorous asymptotic estimates for the expected times 〈 T ₁〉 ∝ Lln L and ln 〈 T ₂〉 ∝ L, where L is the system size. The actual value of T ₁ depends strongly on the initial fluctuation in the amplification loop. Numerical simulations suggest that T ₂ is exponentially distributed with a mean that grows exponentially in system size. For the phase transition line we argue and confirm by simulations that the flipping time between sign changes of the difference of particle numbers approaches an algebraic distribution as the system size tends to infinity.     

Ordering behaviour of the mineral lawsonite

Lawsonite crystals have been investigated by dilatometry and dynamic mechanical analysis as well as by measurements of the optical birefringence and the dielectric constant in the temperature range 90K ≤T ≤ 633K. Two successive phase transitions have been found at low temperatures. The analysis of the spontaneous strain and the excess birefringence data reveals that the transition around 273 K (T ₁) is tricritical. The other transition around 120K. (T ₂) is of second order and proper ferroelectric. The mineral shows remarkable pretransitional effects in a temperature range up to 200 K. above T ₁. The data below T ₂ are interpreted in terms of a mutual interference of the two different ordering processes associated with T ₁ and T ₂, respectively.     

T1Effects in Sequential Dynamic Susceptibility Contrast Experiments

Residual effects of an initial bolus of gadolinium contrast agent have been previously demonstrated in sequential dynamic susceptibility contrast MR experiments. While these residual effects quickly reach a saturation steady state, their etiology is uncertain, and they can lead to spurious estimates of hemodynamic parameters in activation experiments. The possible influence ofT₁effects is now investigated with experiments in whichT₁weighting is varied as well as with serial regionalT₁measurements. Little evidence for significant residualT₁effects is found, suggesting instead that susceptibility effects underlie these observations. An initial saturation dose of contrast agent minimizes this effect.     

Bipartite Matching and Van der Waerden Conjecture

In this paper I show that the free energy F and the cost C associated to a bipartite matching problem can be explicitly estimated in term of the solution of a suitable system of equations (cavity equations in the following). The proof of these results relies on a well known result in combinatorics: the Van der Waerden conjecture (Egorychev–Falikman Theorem). Cavity equations, derived by a mean field argument by Mèzard and Parisi, can be considered as a smoothed form of the dual formulation for the bipartite matching problem. Moreover cavity equation are the Euler–Lagrange equations of a convex functional G parameterized by the temperature T. In term of their unique solution it is possible to define a free-energy-like function of the temperature g(T). g is a strictly decreasing concave function of T and C=g(0). The convexity of G allows to define an explicit algorithm to find the solution of the cavity equations at a given temperature T. Moreover, once the solution of the cavity equations at a given temperature T is known, the properties of g allow to find exact estimates from below and from above of the cost C.     

Transmission of an X‐ray beam through a two‐dimensional photonic crystal and the Talbot effect

Results of computer simulations of the transmission of an X‐ray beam through a two‐dimensional photonic crystal as well as the propagation of an X‐ray beam in free space behind the photonic crystal are reported. The photonic crystal consists of a square lattice of silicon cylinders of diameter 0.5 µm. The amount of matter in the path of the X‐ray beam rapidly decreases at the sides of the cylinder projections. Therefore the transmission is localized near the boundaries, and appears like a channeling effect. The iterative method of computer simulations is applied. This method is similar to the multi‐slice method that is widely used in electron microscopy. It allows a solution to be obtained with acceptable accuracy. A peculiarity in the intensity distribution inside the Talbot period z_T in free space was found when the intensity is approximately equal to the initial value at a distance 0.46z_T, and it is shifted by half a period at distance 0.5z_T. The reason for this effect is the existence of a periodic phase of the wavefunction of radiation inside the intensity peaks. Simulations with zero phase do not show this effect. Symmetry rules for the Talbot effect are discussed.     

Transfer-matrix for the two-channel scattering problem

The transfer-matrix for the two-channel scattering problem is obtained. The elements of this matrix are expressed in terms of transmission T ₁, T ₂ and reflection R ₁, R ₂ amplitudes. The transfer-matrix for N localized and nonoverlapping scattering centers is presented. Recurrent equations for matrix elements are derived and initial conditions for them are defined.     

Ultimate gravitational mass defect

We present a new type of gravitational mass defect in which an infinite amount of matter may be bounded in a zero ADM mass. This interpolates between effects typical of closed worlds and T-spheres. We consider the Tolman model of dust distribution and show that this phenomenon reveals itself for a solution that has no origin on one side but is closed on the other side. The second class of examples corresponds to smooth gluing T-spheres to the portion of the Friedmann-Robertson-Walker solution. The procedure is generalized to combinations of smoothly connected T-spheres, FRW and Schwarzschild metrics. In particular, in this approach a finite T-sphere is obtained that looks for observers in two R-regions as the Schwarzschild metric with two different masses one of which may vanish.     

Double-diaphragm shock tube at the Ioffe Physicotechnical Institute

Results of numerical calculations of the flow in a double-diaphragm shock tube with a tailored contact surface are reported. The calculations were carried out using a model of an ideal shock tube allowing for the real properties of the driver gas at high pressures and equilibrium thermodynamics of the processes behind the shock waves at Mach numbers M _s1 of the shock wave in the working gas varying in the range 5–25. Flow regimes with a tailored contact surface were obtained for Mach numbers M _s1=6.3, 11, and 15 using the double-diaphragm shock tube at the Ioffe Physicotechnical Institute. Under these conditions, the parameters of the working gas were kept constant for more than 1 ms. The calculated data were compared with the experimental results and it was shown that the calculated data may be used to determine the section lengths in a double-diaphragm shock tube and to estimate its operating time. The calculated values of the initial pressure in the sections of the tube were substantially lower than those achieved experimentally. Measurements were made of the static pressure along the axis of a conical nozzle during the expansion of hydrogen (initial temperature T ₀=293 K) and shock-heated nitrogen (T ₀=4000 K). It is found that the expansion of hydrogen is accompanied by deactivation of the rotational degrees of freedom, and that partial freezing of the vibrational degrees of freedom takes place in the nitrogen stream. Zh. Tekh. Fiz. 67, 88–95 (November 1997)     

A new technique for determination of melting temperature of poly(ethylene glycol) by ultrasonic velocimetry

Ultrasonic velocity and density of poly(ethylene glycol) (PEG) (mol. wt. 2000 and 8000) solutions in water and benzene have been studied as a function of temperature from which respective isentropic compressibility has also been calculated. The velocity (as well as isentropic compressibility) undergoes a sudden change near melting temperature, T _m, of the solute polymer. Normally, we expect only one peak in viscoelastic properties at the T _m of PEG. However, we see two peaks (T _m1 and T _m2) in the case of the aqueous solution of PEG while there is only one peak for the case of benzene solution. This has been interpreted on the basis that one of the peaks (T _m1) is for unsolvated PEG and the other peak (T _m2) is that of PEG with water solvation shell. Such solvation shell is not formed with the aprotic solvent (benzene).     

<Emphasis Type="Italic">T</Emphasis>-solutions of different types and their relations to <Emphasis Type="Italic">R</Emphasis>-solutions

Different types of T-solutions are investigated. The conditions at which one region of space-time can be described only by a statistic R-solution and another region can be described only by a T-solution are obtained. The common metric for R- and T-solutions is obtained where the spatial and temporal variables are interchanged. The T-solution which has the same mass function as for the internal static Schwarzschild solution is obtained.     

Determining NMR flow propagator moments in porous rocks without the influence of relaxation

Flow propagators, used for the study of advective motion of brine solution in porous carbonate and sandstone rocks, have been obtained without the influence of Nuclear Magnetic Resonance (NMR) relaxation times, T₁ and T₂. These spin relaxation mechanisms normally result in a loss of signal that varies depending on the displacement ζ of the flowing spins, thereby preventing the acquisition of quantitative propagator data. The full relaxation behaviour of the system under flow needs to be characterised to enable the implementation of a true quantitative measurement. Two-dimensional NMR correlations of ζ − T₂ and T₁ − T₂ are used in combination to provide the flow propagators without relaxation weighting. T₁ − ζ correlations cannot be used due to the loss of T₁ information during the displacement observation time Δ. Here the moments of the propagators are extracted by statistical analysis of the full propagator shape. The measured displacements (first moments) are seen to correlate with the expected mean displacements for long observation times Δ. The higher order moments of the propagators determined by this method indicate those obtained previously using a correction were overestimated.     

Transverse energy measurement in Au+Au collisions by the STAR experiment

Transverse energy (E _T ) has been measured with both of its components, namely hadronic (E _T ^had ) and electromagnetic (E _T ^em ) in a common phase space at mid-rapidity for 62.4 GeV Au+Au collisions by the STAR experiment. E _T production with centrality and ?{s_NN }\sqrt {s_{NN} } is studied with similar measurements from SPS to RHIC and is compared with a final state gluon saturation model (EKRT). The most striking feature is the observation of a nearly constant value of E _T /N _ch ∼ 0.8 GeV from AGS, SPS to RHIC. The initial energy density estimated by the boost-invariant Bjorken hydrodynamic model, is well above the critical density for a deconfined matter of quarks and gluons predicted by lattice QCD calculations.     

Electron-electron bremsstrahlung in a non-equilibrium plasma

Electron-electron bremsstrahlung in a weakly ionized uniform non-stationary plasma is investigated. The respective problem is solved analytically for two initial electron-distributions: maxwellian with the temperatureT ₀, and the delta distribution. In the case of initial maxwellian distribution the radiation intensity is proportional to ^3/2, where=T+(T ₀–T) exp (–s),s=2mv ₁ t/M,v ₁ is the momentum transfer frequency, and the other symbols are standard. In the case of initial delta distribution the radiation intensity is proportional to [1 -exp (–s)]^3/2. The proportionality factors are known, and are expressed in terms of mathematical and physical constants.     

Time-dependent paths,fictive temperatures and residual entropy of glass

After describing the Clausius limits of entropy, determined from the C _pd ln T integral, and its current use in determining the entropy of metastable (atomic) crystals, we determine two fictive temperature T _f values of four glasses – one from the integral of C _pdT and the other from C _pd ln T. The C _p data of the two metal–alloy glasses are from this calorimetric study; the C _p data of (i) quenched basalt composition glass fibers before and after partial annealing, and (ii) quenched NBS-710 composition glass fibers are taken from the literature. The C _pd ln T integral, which is not the entropy change, and the C _pdT integral yield the same T _f values. Therefore, the effect of the difference between the cooling and heating paths in the liquid–glass transformation range is too small to indicate whether the residual entropy, S _res, is a result of using the C _pd ln T integral. This questions the notion that S _res stems from use of the C _pd ln T integral. Extrapolation of the C _p values of the liquid and glass to high temperatures lead to erroneous T _f values, as do permanent (irreversible) loss of the strain and surface energies of glass on initial heating.