Penetrative ferroconvection via internal heating in a saturated porous layer with constant heat flux at the lower boundary

A model for penetrative ferroconvection via internal heat generation in a ferrofluid saturated porous layer is explored. The Brinkman-Lapwood extended Darcy equation with fluid viscosity different from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid- paramagnetic and insulated to temperature perturbations, while at upper stress-free boundary a general convective-radiative exchange condition on perturbed temperature is imposed. The resulting eigenvalue problem is solved numerically using the Galerkin method. It is found that increasing in the dimensionless heat source strength N_s, magnetic number M₁ Darcy number Da and the non-linearity of magnetization parameter M₃ is to hasten, while increase in the ratio of viscosities Λ, Biot number Bi and magnetic susceptibility χ is to delay the onset of ferroconvection. Further, increase in Bi, Da⁻¹ and N_s and decrease in Λ, M₁ and M₃ is to diminish the dimension of convection cells.     

Growing networks with preferential deletion and addition of edges

A preferential attachment model for a growing network incorporating the deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t=1,2,…, with probability π₁>0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π₂ a vertex is chosen proportionally to its degree and an edge is added between this vertex and a randomly chosen other vertex, and with probability π₃=1−π₁−π₂<1/2 a vertex is chosen proportionally to its degree and a random edge of this vertex is deleted. The model is intended to capture a situation where high-degree vertices are more dynamic than low-degree vertices in the sense that their connections tend to be changing. A recursion formula is derived for the expected asymptotic fraction p_k of vertices with degree k, and solving this recursion reveals that, for π₃<1/3, we have p_k∼k^{−(3−7π₃)/(1−3π₃)}, while, for π₃>1/3, the fraction p_k decays exponentially at rate (π₁+π₂)/2π₃. There is hence a non-trivial upper bound for how much deletion the network can incorporate without losing the power-law behavior of the degree distribution. The analytical results are supported by simulations.     

Calculation of the binding energy and of the parameters of low-energy scattering in the Λnp system

The cluster-reduction method is used to solve the differential Faddeev equations for S=1/2, T=0 and S=3/2, T=0 spin-isospin states of the Λnp system in the s-wave approximation. The NN interaction is simulated on the basis of the MT I–III potential model, and the ΛN potential is set to V _ΛN =V _NN /2. This simple option makes it possible to reproduce faithfully the binding energy of the hypertriton _Λ ³ H. The doublet and quadruplet Λd scattering lengths and the low-energy phase shifts are calculated. It is shown that the effective-range approximation is applicable to the cases of doublet and quadruplet scattering.     

Dynamic hysteresis of magnetic aggregates with non-integer dimension

We investigate the dynamic hysteresis of nanoscale magnetic aggregates by employing Monte Carlo simulation, based on Ising model in non-integer dimensional space. The diffusion-limited aggregation (DLA) model with adjustable sticking probability is used to generate magnetic aggregates with different fractal dimension D. It is revealed that the exponential scaling law A(H₀, ω)∼H₀^α·ω^β, where A is the hysteresis area, H₀ and ω the amplitude and frequency of external magnetic field, applies to both the low-ω and high-ω regimes, while exponents α and β decrease with increasing D in the low-ω regime and keep invariant in the high-ω regime. A mean-field approach is developed to explain the simulated results.     

Bounded perturbations of the P(ϕ)2 theory

As a perturbation to the P(?)₂ theory we consider interaction densities of the form V(?(x)), where ?(x) is a scalar hermitian boson field and V(α) is a bounded real continuous function. It is proved that the asymptotic fields exist and are equal to the asymptotic fields of the P(?)₂ theory. The connection with non-polynomial theories of rational type is indicated. Furthermore the consequences of a bounded perturbation for the S-matrix and the spectral properties are discussed.     

Liouville dynamics for optimal stochastic phase-space representations of quantum mechanics

It is shown that the space P(Γ_s) of Γ_s-distribution functions ?(q, p) (Husimi transforms) can be described without reference to any conventional representation of the density operator ?. A Liouville-type differential equation governing the free time-evolution of ?_t(q, p) is derived and solved explicitly; the time dependence of this solution supports the thesis that ?(q, p) is a bona fide probability density observable with optimally accurate apparatus for the simultaneous measurement of position and momentum. Liouville-type equations are derived also for the case when local interactions described by analytic potentials are present. Probability currents corresponding to ?(q, p) are defined and it is shown that they obey a continuity equation at space-time points. Reduced Γ_s-distribution functions are defined and it is shown that they obey a BBGKY hierarchy of equations. A Brownian-motion experimental test of the underlying theory of measurement is suggested.     

Compressible effect algebras

We define a special type of additive map J on an effect algebra E called a compression. We call J(1) the focus of J and if p is the focus of a compression then p is called a projection. The set of projections in E is denoted by P(E). A compression J is direct if J(a) ≤ a for all a ε E. We show that direct compressions are equivalent to projections onto components of cartesian products. An effect algebra E is said to be compressible if every compression on E is uniquely determined by its focus and every compression on E has a supplement. We define and characterize the commutant C(p) of a projection p and show that a compression with focus p is direct if and only if C(p) = E. We show that P(E) is an orthomodular poset. It is proved that the cartesian product of effect algebras is compressible if and only if each component is compressible. We then consider compressible sequential effect algebras, Lüders maps and conditional probabilities.     

A dynamical theory for the off-shell continuation of the πNt-matrix

A dynamical theory, based on analyticity and dispersion theory, for the half-off-shell continuation of the on-shell πNt-matrix is proposed and developed. The resulting half-shell t-matrix is covariant, unitary, crossing symmetric, and based on a field-theoretic foundation. The dynamical information required to continue half off shell is obtained from field theory and consists of the off-shell amplitudes corresponding to the exchanges of the nucleon in the s- and u-channels and the ? and σ mesons in the t-channel. A coupled system of integral equations is derived for the partial wave half-shell t-matrix, which is truncated at the S- and P-waves and solved numerically. The results are compared with those obtained from various separable models of the πNt-matrix. The half-shell t-matrix is examined for separability and is found to be approximately separable in the P₃₃ and P₃₁ states. The dynamical content of the half-shell t-matrix is further illustrated by modeling the dynamical equation.     

A-dependence of ΛΛ bond energies in double-Λ hypernuclei

The A-dependence of the bond energy ΔB_ΛΛ of the ΛΛ hypernuclear ground states is calculated in a three-body Λ + Λ + ^A Z model and in the Skyrme-Hartree-Fock approach. Various ΛΛ and Λ-nucleus or ΛN potentials are used and the sensitivity of ΔB_ΛΛ to the interactions is discussed. It is shown that in medium and heavy ΛΛ hypernuclei, ΔB_ΛΛ is a linear function of r _Λ ^{? 3} , where r _Λ is rms radius of the hyperon orbital. It looks unlikely that it will be possible to extract ΛΛ interaction from the double-Λ hypernuclear energies only, the additional information about the Λ- core interaction, in particular, on r _Λ is needed.     

Electronic structure characteristic of carbon nanotubules

Electronic structure near the Fermi energy of single-shell carbon nanotubules has been studied within the framework of the tight-binding approximation. The electronic density of states (DOS) of tubules shows a structure consisting of many spike-like peaks. An analytical expression in a π-electron model is derived which predicts not only the energy gap (E _g ) of semiconducting tubules, but also the energy positions of those spike-like peaks in the π-DOS near the Fermi energy in any tubule. The limitation of the π-electron model in tubules is discussed by investigating the effect of σ-πmixing. The position of σ component edge in the DOS is also investigated as a function of tubule radius (R) and chiral angle (θ). It is found that this edge energy is very sensitive to θ and largely changes with R, because the dominant contribution of θ to its change is given by g(θ)/R in contrast to f(θ)/R ² for E _g .     

Theoretical analysis of the effect of temperature dependence of Auger coefficient on the turn-on time delay of uncooled semiconductor laser diodes

In this paper, a novel interpretation of the effect of Auger recombination coefficient (C) on the turn-on time delay (t_on) of semiconductor laser diodes (SLDs) is presented. To the date, the well-known conclusion is that the main effect of C is to decrease t_on. This is because the earlier studies were based on less physical assumptions. Contrarily, we show that the general effect of C is to increase t_on. This conclusion is supported by including the effect of temperature of operation (T) on t_on of uncooled SLDs. Advanced analytical model is presented to determine t_on analytically and in term of nonradiative (A), radiative (B) and C recombination coefficients. The derived model can be applied to bulk and multiple quantum-well (MQW) long-wavelength SLDs at any value of temperature of operation degree (T) within the range 25-85 °C. The temperature dependence of t_on is calculated according to the temperature dependences of C and threshold carrier density (N_th). The temperature dependence of the latter is calculated according to the temperature dependence of laser cavity parameters and not by the well-known Parkovian relationship. Numerical and analytical results show that t_on increases as T increases due to increasing of N_th and C which its effect dominates at high temperature degrees. In addition, we show that the effect of temperature dependence of t_on in MQW SLD is smaller than the bulk one. Moreover, MQW SLD needs a lower injection current than the bulk one to achieve the same value of t_on.     

Quark fragmentation and trigger side momentum distributions in high-p T processes

It has been widely argued that the experimental evidence concerning the momentum accompanying highp T triggers is a grave problem for models which take the trigger hadron to be a quark fragment. It is claimed that the trigger hadron takes much too large a fraction (z _c ) of the jet momentum for the trigger side jet to be a quark. The jet momentum is not directly measured, but deduced from the derivative of the momentum (p _x ) accompanying the trigger with respect to the trigger transverse momentum-p _T ^t . This argument is shown to be unsafe. Using both an approximate analytic approach to illustrate the physics and subsequently a full numerical computation it is proved that the deduction of the fractional momentum accompanying the trigger, 1/z _c ?1, fromdp _x /dp _T ^t is not correct. Further we show that models—specifically that of Feynman and Field—which do take the trigger to be a quark fragment are essentially in agreement with the data on trigger side momentum distributions. A surprising prediction of our analysis is thatp _x should be approximately constant forp _T ^t ≧6GeV/c.     

Optically pumped quantum magnetometer with combined advantages of M X and M Z devices

A scheme of the magnetometer that simultaneously employs M _X and M _R magnetic resonance signals with the latter signal related to the radial component of the rotating atomic magnetic moment is proposed and tested. With respect to the shape, dynamic characteristics, and metrological parameters, the M _R signal is similar to the M _X signal that is widely used in magnetometry but the former signal can be detected simultaneously with the M _X signal using a common radio optical scheme. The proposed device represents a fast M _X magnetometer with the phase in the feedback loop that is controlled by a slow precise M _R magnetometer implemented using the same atoms. The device that can be based on a conventional M _X sensor simultaneously exhibits a relatively short response time (τ ≤ 0.1 s) and the accuracy that is approximately equal to the resolution of the quantum M _X discriminator at times of 10–100 s. The scheme is experimentally tested, and the statistic estimate of reproducibility is (1.2 ± 1.1) pT.     

On the criterion of the crystal-liquid phase transition

A localization criterion is proposed for the crystal-liquid phase transition (PT). According to this criterion, the PT begins when the E _d/k _b T ratio reaches a boundary value E _d(s)/k _b T _m such that a solid phase is present above it and a liquid phase is present below it in a phase diagram. Here, E _d is the energy of atom delocalization, k _b is the Boltzmann constant, T is the temperature, and E _d(s) is the delocalization energy for a solid phase at melting point T _m. This criterion is shown to generalize the Lindemann criterion of melting to the case of crystallization and the Löven criterion of crystallization to the case of melting. This localization criterion is found to be applicable for both normally melting substances and substances that melt with a decrease in the specific volume upon the transition into a liquid phase. The relation of the localization criterion to the vacancy and diffusional criteria of the crystal-liquid PT has been studied. The inequality T _N < T _m, where T _N is the temperature of the onset of crystallization, is explained using the localization criterion. The calculated values of the T _N /T _m ratio coincide well with the experimental estimates. The maximum value of T _N /T _m is likely to be most probable in crystals with a bcc structure and a small value of the Grüneisen parameter. The T _N /T _m ratio is analyzed at the points in the PT where no change in the specific volume occurs and an entropy jump is nonzero.     

How chaotic is a state of a quantum system?

A concept related to the entropy is studied. Let A and B be two density matrices, with eigenvalues a₁, a₂,… and b₁, b₂,…, arranged in decreasing order and repeated according to multiplicity. Then A is said to be “more mixed”, or “more chaotic”, than B, if a₁?b₁, a₁+a₂?b₁+b₂,…,a₁+…+a_m?b₁+…+b_m,…; It turns out that if A is more mixed than B, then the entropy of A is larger than the entropy of B. However, more generally, let v be an arbitrary concave function, ?0, and vanishing at 0. Then, if A is more mixed than B, trv(A)?trv(B). It is shown that also the converse is true. Furthermore, a variety of other characterizations of the relation “A is more mixed than B” is obtained, and several applications to quantum statistical mechanics are given.     

Measurement of the surface density of states by field ionization

It is shown that recent measurements of field ion energy distributions from clean tungsten surfaces probe the density of metal states in the vicinity of the surface. We find j(ω) = (2π/kh)Σ_m| ∫ d³rψ_m(r)γ_z|²δ(ω??_m), where j(ω) is the ion current a ω, ψ_mand ?_m are electronic metal eigenfunctions and eigenvalues in the presence of the external electric field used in field ionization and γ(z) is a function which is large near the noble gas atom. An explicit expression for γ(z) is given in the text. It is estimated that tungsten metal states with values of k₆ at least as large as 0.5 Å^?1 make an appreciable contribution to j(ω) where k₆ is the electron momentum parallel to the surface.     

Energy fluctuations in multichannel fission and heavy ion collisions

A simple theory for the variance σ_E² of the total kinetic energy distribution of the fission fragments is given and compared with the data. It seems to explain the observed variation of σ_E with the mass number as well as the differences of σ_E for the different fission channels due to shell effects. The physical origin of σ_E is supposed to be the permanent thermal noise along the path from the barrier to scission. The same theory is applied to deep inelastic collisions and leads to much larger σ_E in agreement with measurements.     

Random walks in a simple percolation model with two jump frequencies

We consider transport properties of the system in which the good-conducting bonds lie in parallel planes linked by poor-conducting bonds and the concentration p of good-conducting bonds is close to the two-dimensional percolation threshold p_c. The diffusion coefficient D(τ) which describes the random walking in directions along the planes is calculated as a function of variable τ = p − p_c. For τ → 0 the asymptotic relation D(τ)/D(0) − 1 | ∼ |τ|^α is found w α = 2ν − s. Here s is the superconductivity exponent and ν is the correlation length exponent. It is argued that such behavior is to be expected also for more general models.