Nonlinear void-fraction waves in two-phase bubbly flow

It is shown that nonlinear void-fraction waves constitute exact solutions of the two-fluid equations for bubbly flow, if and only if the virtual-mass coefficientm() is a definite function of the void fraction. In the case of spherical bubbles the functional dependence is given bym()=(1/2)(1–a)(1–3). A similar expression was obtained recently by means of an elaborate linear stability analysis of a uniform two-phase flow. It is remarkable that the greater part of the physical quantities of a nonlinear void-fraction wave depends linearly on. The virtual-mass coefficient may be derived directly from a special form of Hamilton's variational principle.

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Zusammenfassung Es wird gezeigt daß nichtlineare Konzentrationswellen exakte Lösungen der Zweifluiden Gleichungen einer Blasenströmung darstellen dann und nur dann, wenn der Koeffizientm() der virtuellen Masse eine bestimmte Funktion der Volumenkonzentration der Blasen ist. Die funktionelle Abhängigkeit ist im Falle kugelförmiger Blasen gegeben durchm()= (1/2)(1–) (1–3). Ein gleicher Ausdruck wurde neulich mittels einer umständlichen linearen Stabilitätsanalysis einer uniformen Zweiphasen-Strömung erhalten. Es ist bemerkenswert daß der größere Teil der physikalischen Größen einer nichtlinearen Konzentrationswelle in linearer Weise von abhängt. Der Koeffizient der virtuellen Masse kann in direkter Weise von einer speziellen Form des Hamiltonschen Variationsprinzips hergeleitet werden.

     

Supplement to the paper “the averaging operator with respect to a countable partition on a minimal symmetric ideal of the space L1(0, 1)”

Let A be a partition of the segment [0, 1] into a countable number of disjoint subsets of positive measure, let tL₁(0,1), let N_t be the smallest rearrangement-invariant order ideal vector lattice in L₁(0,1), containing t. In the paper one investigates the properties of the image E(N_t¦A) of the averaging operator with respect to A. In particular, one elucidates under what conditions there exists a function g, gL₁(0,1), such that E(N_t¦A)N_g. One formulates a generalization of the known Hardy-Littlewood inequality, namely Theorem E(tA)QE(t*A*), where is the Hardy-Littlewood preorder, t* and A* are the decreasing rearrangements of the function ¦t¦ and (in a special sense) of the partition A, while Q is an absolute constant, 1Q2⁵. One formulates the problem of the smallest value of Q.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 149, pp. 137–141, 1986.     

Singular series of genus 2 for sums of squares

Let f₁, ..., f_h be representatives of classes in the genus of a positive quadratic form f, r_i(k) the number of representations of k by the form f_i, (k) the value of the singular Hardy-Littlewood series, E_i the number of integer automorphisms of f_i. We derive an expression for in terms of the values of singular series of genus 1 and 2. This expression is evaluated for the simplest model f(x)=x ₁ ² +...+x _m ² , m1 (mod 8), k is a prime in-integer, k=1(mod 8).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 151, pp. 26–39, 1986.     

Distribution density of the norm of a stable vector

Let B be a Banach space,X be a stable B -valued random vector with exponentd(0,2), and P(·) be the distribution density of the norm of X. In this paper we study the question of the boundedness of P. In particular, we construct examples of a space B with a symmetric stable vector X with exponentd(1,2) with unbounded P and prove that if X is a nondegenerate strictly stable vector with exponentd(0,1), then P is bounded.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 105–114, 1987.The author is grateful to Yu. A. Davydov, V. I. Paulauskas, V. Yu. Bentkus, and D. Pap for stimulating discussions of the subject of this paper. When the paper was finished the author learned that similar results are found in [9].     

Asymptotic behavior of the spectrum of certain problems,connected with the oscillation of fluids

One obtains the principal term of the asymptotics of the spectrum in a series of problems of the theory of small oscillations of fluids, filling partially a container. First one discusses a certain problem of general character, the nonlocal Steklov type problem. The considered problems are connected with the oscillations of a capillary ideal (or capillary stratified) fluid, of a heavy viscous fluid, of a capillary viscous fluid, and with the oscillations of a fluid in container with an elastic bottom.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 152, pp. 158–164, 1986.The author is deeply grateful to her scientific advisor M. Sh. Birman. The author is grateful also to N. D. Kopachevskii for his interest in the paper.     

A remark on partial linear spaces of girth 5 with an application to strongly regular graphs

We derive a lower bound on the number of points of a partial linear space of girth 5. As an application, certain strongly regular graphs with=2 are ruled out by observing that the first subconstituents are partial linear spaces.     

Influence of crystal-field on the thermal conductivity of PrNi5

The thermal conductivity of PrNi₅ in the temperature range 0·5 to 20 K is investigated. The analysis of crystalline electric field effect on the experimentally obtained temperature dependence of the thermal conductivity indicates that beside the main electronic component also other contributions (phonons, magnetic excitons) can take place in the heat transport in this intermetallic compound.The authors would like to thank Dr. G. Eska for lending the sample and Dr. . Jáno for his interest in the work and stimulating discussions.     

An alternative approach to quantum phenomena

This paper outlines the qualitative foundations of a quasiclassical theory in which particles are pictured as spatially extended periodic excitations of a universal background field, interacting with each other via nonlinearity in the equations of motion for that field, and undergoing collapse to a much smaller volume if and when they are detected. The theory is based as far as possible directly on experiment, rather than on the existing quantum mechanical formalism, and it offers simple physical interpretations of such concepts as mass, 4-momentum, interaction, potentials, and quantization; it may lead directly to the standard equations of quantum theory, such as the multiparticle Schrödinger equation, without going through the conventional process of quantizing a classical theory. The theory also provides an alternative framework in which to discuss wave-particle duality and the quantum measurement problem; in particular, it is suggested that the unpredictability of quantum phenomena may arise from deterministic chaos in the behavior of the background field.     

Effects of small external magnetic fields on the hyperfine field of iron in iron metal above the curie temperature: A new method for studying critical phenomena

By applying magnetic fields up to 2 kG, the equation of state and the critical dynamics of a spin system near its critical point can be studied with the Mössbauer effect. As an example, the equation of state near the Curie temperature of iron is investigated yielding the critical exponent =4.84±0.15.