The relationship between the transition voltage of the I–V curve of the ferroelectrics and the coercive field of the P–V hysteretic curve

The relationship between the transition voltage of the I–V curve of the ferroelectrics and the coercive field of the P–V hysteretic curve is calculated. The first mathematical analysis to explain the relation between the transition voltage V_t and the coercive voltage V_c is obtained. The origin of the interrelation between the transition voltage of the I–V curve and the coercive field is that the height of the boundary barrier is inversely proportional to the effective dielectric constant of the near-boundary region, which is dependent on a derivative of polarization on the electric field, ∂P/∂E. The term ξ(eV_t) plus the term (en_b²δ/dN_dP_s)(eV_c) equals a constant. V_t is the function of E_g, P_s, V_c, and E. There is a linear relation between V_c and V_t. This relationship will induce the matchable relations between the I–V curve and the E–P loop. As long as the V_c of the V–P loop exists, the correspondent V_t of I–V curve will certainly exist. It will be the foundation of a new ferroelectric memory, which operates by the I–V characteristics. These relations are the conditions that can enable nonvolatile memory and nondestructive readout.     

The length and the relative length of tangent vectors of finsler spaces

We consider the length of a vector in a Finsler space with the fundamental function L(x,y). The length of a vector X is usually defined as the value L(x,X) of L. On the other hand, we have an essential tensor g_ij(x,y), called the fundamental tensor, and the concept of relative length |X_y| of X may be introduced by |X|_y^y = g_ij(x,y)XⁱX^j with re spect to a supporting element y. The question arises whether is L(x,X) the minimum of |X|_y or not? If there exists a supporting element y satisfying |X|_y < L(x,X), then a curve x(t) in the Finsler space will be measured shorter than the usual length, by integrating |dx/dt|_y with the field of such supporting element y(t) along the curve.     

Stochastic dynamics and Parrondo’s paradox

The Spanish physicist Juan Parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game. If a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures.The appropriate abstract setting is as follows. There is given a compact metric space (M,d), and M is written as the union of certain closed subsets A₁,…,A_r. For every ρ=1,…,r there is prescribed a strict contraction Γ_ρ:A_ρ→M. A random walk (X_m)_m∈N0 on M is then defined as follows. The starting position is X₀=x₀, where x₀∈M is fixed, and if the walk at the m’th step is at position X_m∈M, then one chooses a ρ among the ρ with X_m∈A_ρ (with equal probability, say) and defines X_m+1 as Γ_ρ(X_m). Associated with the walk is a gainφ(X_m) in every round, where φ:M→R is a continuous function.The aim of the present investigations is the study of the expectation G_m of φ(X_m) as a function of m. Our main result states that the sequence (G_m) is “eventually approximately periodic” provided that all A_ρ are not only closed but also open in M: for every ε there is an l₀∈N such that (G_m) is l₀-periodic up to an error of at most ε for sufficiently large m. In fact it turns out that the behaviour of our process can be described well with a finite Markov chain.In the general case, however, the process might behave rather chaotically. We give an example where M is the unit interval. M is written as the union of two closed subsets A₁,A₂, the contractions Γ₁,Γ₂ are rather simple, but the expectations of the gains are not even Cesáro convergent.     

Lower bounds on the slope parameter

A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t₀ where A(s, t) is the absorptive part of the elastic scattering amplitude and t₀ is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like s^α(t)ln^η(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t₀, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.     

Measurement of the spin parameters A and Ann in pp elastic scattering in the 1–3 GeV/c region

We have measured the asymmetry parameter A and the spin correlation parameter A_nn in pp elastic scattering, using the Argonne ZGS polarized proton beam and a polarized proton target. Angular distributions of A and A_nn for |t| ? 0.2 (GeV/c)²wereobtainedateightmomentabetween 1.10 and 2if2.75 GeV/c. We find significant structure in both the energy and t-dependence of A_nn at these energies. At p_lab ≈ 1.34 GeV/cA_nn reaches a very large value of about 0.8–0.9 near θ_cm = 90°.     

Scaling form of zero-field-cooled and field-cooled susceptibility in superparamagnet

The scaling form of the normalized ZFC and FC susceptibility of superparamagnets (SPMs) is presented as a function of the normalized temperature y(=k_BT/K_u〈V〉), normalized magnetic field h (=H/H_K), and the width σ of the log-normal distribution of the volumes of nanoparticles, based on the superparamagnetic blocking model with no interaction between the nanoparticles. Here 〈V〉 is the average volume, K_u is the anisotropy energy, and H_K is the anisotropy field. Main features of the experimental results reported in many SPMs can be well explained in terms of the present model. The normalized FC susceptibility monotonically increases as the normalized temperature y decreases. The normalized ZFC susceptibility exhibits a peak at the normalized blocking temperature y_b(=k_BT_b/K_u〈V〉), forming the y_b vs h diagram. For large , y_b starts to increase with increasing h, showing a peak at h=h_b, and decreases with further increasing h. The maximum of y_b at h=h_b is due to the nonlinearity of the Langevin function. For small σ, y_b monotonically decreases with increasing h. The derivative of the normalized FC magnetization with respect to h shows a peak at h=0 for small y. This is closely related to the pinched form of M_FC vs H curve around H=0 observed in SPMs.     

New features of a smectic-A-crystal-B phase transition in a homologous series of liquid crystals

The components L _j of the Lorentz tensor and the polarizability density of molecules G in the smectic-A and crystalline-B phases have been determined for homologues of the series of alkyl-p-(4-alkoxybenzylideneamino-)cinnamates. The quantity L _j (G) in both phases is a linear (quadratic) function of the orientational order parameter of molecules S, which is invariant (noninvariant) with respect to the A-B transition, which is manifested in the form of jumps δL _j and δG and enhancement of the G(S) dependence. An increase in the length of terminal molecular chains and weakening of interlayer correlation of molecules are accompanied by strengthening of the A-B transition of the first order and G(S) dependences in both phases together with an increase in δL _j and δG. Change δG and dependence G(S) in the B phase are related to change in the conformation (flattening) of aromatic molecular cores.     

CriticalZ N spin systems andφ 4 theory

The continuum limit ofZ _N (N≧4) spin systems at the critical point is identified with a two-component massless scalar field with quartic self-interactionf _αβγδ φ _α φ _β φ _γ φ _δ , withf _αβγδ = 1/3 (δ _αβ δ _γδ +δ _αγ δ _βδ +δ _αδ δ _βγ ) ≡S _αβγδ forN≧5 andf _αβγδ =S _αβγδ ? 2/3δ _αβ δ _αγ δ _αδ forN=4. The result is based on the study of the two and four-point irreducible correlation functions in the one-loop approximation.     

Magnetic properties of transition metal substituted MnP

The magnetic properties of polycrystalline samples of Mn_1?tT_tP (T = V, Cr, Fe and Co for 0.00 ≦ t ≦ 0.50) are studied by magnetic susceptibility, magnetization and neutron diffraction measurements. The magnetic phase diagrams of the Mn_1?tT_tP phases exhibit paramagnetic, ferromagnetic, helimagnetic and spin glass regions depending on temperature and substitution (T, t). The concentrated spin glass regions observed in Mn_1?tV_tP and Mn_1?tCo_tP (0.30 ≦ t ≦ 0.50) are believed to result from the disorder in the metal sublattice. The variation of the magnetic moment of the ordered Mn_1?tT_tP phases with the substitution (T, t) is discussed.     

Pseudoscalar quarkonium exclusive decays to vector meson pair

The pseudoscalar quarkonia exclusive decays to light mesons still poses a challenge to the theoretical understanding of quarkonium properties in decay. In this work, we evaluate the processes of pseudoscalar heavy quarkonium decays into vector meson pairs, especially the helicity suppressed processes of ηb→J/ψJ/ψ and ηc→VV. In the framework of NRQCD, the branching fraction of Br[ηb→J/ψJ/ψ] are evaluated at the next-to-leading order of perturbative QCD; and within the light-cone distribution formalism, we calculate also the higher twist effects in these processes. Numerical results show that the higher twist terms contribute more than what from the NLO QCD corrections in the process of ηb→J/ψJ/ψ. It is found that the experimental results on ηc→VV are hard to be understood by merely the quark model and perturbative QCD calculation.     

Eigenvalue comparisons for quantum systems in a box

Comparison theorems are obtained for the first even and odd solutions of Schrödinger's equation −v″ + Q(t)v = λv, −l ≤ t ≤ l with boundary conditions v(−l) = v(l) = 0. The comparison functions Q_i(t), i = 1, 2, may intersect at a finite number of points within [−l,l]. Immediate extensions are possible for a more general class of Sturm-Liouville problems, and for problems in unbounded regions.     

The combined effect of temperature of operation and external optical feedback on the turn-on time delay of semiconductor laser diodes

In this paper, the combined effect of temperature of operation (T) and external optical feedback (EOF) on the turn-on time delay (t_on) of semiconductor laser (SLD) is investigated theoretically. General and exact analytical model of t_on in term nonradiative (A), radiative (B) and Auger (C) recombination coefficients, carrier density, injection current (I_inj) and T is derived for the first time. In addition, EOF parameters, i.e. external reflectivity (r_ext) and phase of reflected light (?) is also included. The combined effect of T and EOF on t_on is calculated according to its effect on threshold carrier density (N_th). We show that when SLD operates under the effect of coherent (incoherent) EOF, t_on decreases (increases) as r_ext increases due to decreasing (increasing) of N_th at coherent (incoherent) EOF. Moreover, t_on increases as T increases due to increasing of N_th. Moreover, we identified in operable regions of SLD where the latter fails to operate due to very long t_on.     

A Sublinear Variance Bound for Solutions of a Random Hamilton–Jacobi Equation

We estimate the variance of the value function for a random optimal control problem. The value function is the solution w ^? of a Hamilton?CJacobi equation with random Hamiltonian H(p,x,??)=K(p)?V(x/?,??) in dimension d??2. It is known that homogenization occurs as ???0, but little is known about the statistical fluctuations of w ^? . Our main result shows that the variance of the solution w ^? is bounded by O(?/|log?|). The proof relies on a modified Poincaré inequality of Talagrand.     

Kinetic Limit of N-Body Description of Wave–Particle Self-Consistent Interaction

A system of N particles $\xi ^N = x_1 ,\upsilon_1,...,x_N ,\upsilon _N )$ interacting self-consistently with one wave Z = A exp(iφ) is considered. Given initial data (Z ^(N)(0), ξ ^N (0)), it evolves according to Hamiltonian dynamics to (Z ^(N)(t), ξ ^N (t)). In the limit N → ∞, this generates a Vlasov-like kinetic equation for the distribution function f(x, v, t), abbreviated as f(t), coupled to the envelope equation for Z: initial data (Z ^(∞)(0), f(0)) evolve to (Z ^(∞)(t), f(t)). The solution (Z, f) exists and is unique for any initial data with finite energy. Moreover, for any time T>0, given a sequence of initial data with N particles distributed so that the particle distribution f ^N(0) → f(0) weakly and with Z ^(N)(0) → Z(0) as N → ∞, the states generated by the Hamiltonian dynamics at all times 0 ≤ t ≤ T are such that (Z ^(N)(t), f ^N(t)) converges weakly to (Z ^(∞)(t), f(t)).     

Logistic equation of arbitrary order

The paper is concerned with the new logistic equation of arbitrary order which describes the performance of complex executive systems X vs. number of tasks N, operating at limited resources K, at non-extensive, heterogeneous self-organization processes characterized by parameter f. In contrast to the classical logistic equation which exclusively relates to the special case of sub-extensive homogeneous self-organization processes at f=1, the proposed model concerns both homogeneous and heterogeneous processes in sub-extensive and super-extensive areas. The parameter of arbitrary order f, where −∞<f<+∞, depends on both the coefficient of external resource utilization u=N/K, where 0<u<1, and the internal microscopic character of realized processes related to the depth of feedback β. The coefficient β directly influences self-organization of processes by the change of microscopic parameters V_i, S_i, i and Z, where V_i is the number of references (visit) to the ith component of the system during the service of each task, S_i is the time of serving the task by the ith component, and Z is the think time of a given process. In the general case of complex system, parameters V_i, S_i, i and Z can have values in the range from 0 to +∞. In this way the new equation includes all possible cases of a complex executive system’s operation. Furthermore, it allows us to define the optimal matching point between X and N with f as the parameter. It also helps to balance the load in complex systems and to equip artificial systems with self-optimization mechanisms similar to those observed in natural systems.     

The muon spectra from decays ofW- andZ-bosons produced ine + e −-collisions

The muon spectra from the decays ofW-andZ-bosons, produced ine ⁺ e ^?→W ⁺ W ^?,e ⁺ e ^?→Zγ,e ⁺ e ^?→ZZ ande ⁺ e ^?→ZH reactions have been obtained (H is the Higgs boson). It has been shown (in terms of Glashow-Weinberg-Salam theory) that the main source of muons are thee ⁺ e ^?→Zγ ande ⁺ e ^?→W ⁺ W ^? processes (over theW-boson production threshold). The contribution of thee ⁺ e ^?→ZZ ande ⁺ e ^?→ZH reactions to the inclusive muon spectra is small. It has been also shown, that it is possible to distinguish contributions of thee ⁺ e ^?→Zγ ande ⁺ e ^?→W ⁺ W ^? reactions if the decay muons move at a small angle to the initial electron momentum.     

Analysis of the lattice,strong coupling series for g0φ4 field theory in d dimensions

We analyze the renormalized strong coupling series for lattice g₀φ⁴ field theory which is a double series in x = M⁴a⁴/g₀a_4?dandy = 1/M²a², where M is the renormalized mass, a the lattice spacing, g₀ the bare coupling constant and d the dimension of space-time. We extrapolate to large y for fixed x by using a Padé-like extrapolation technique. We study the dimensionless renormalized coupling constant G/M^4?d and find that as we approach the continuum(x → 0, y → ∞) the entire spectrum of g₀ from zero to infinity can be studied. Our results for d = 1,2,3,4 based on a series in y up to y⁵ and in x up to x³ show that for fixed lattice spacing a, G/M^4?d is a monotonic function of g₀ ranging from zero at g₀ = 0 to a maximum at g₀ = ∞. Using the high temperature expansion results, we have also derived 9 terms in y on 8 lattices of dimension 1,2,3 and 4 for the linear term in x, and studied this series to see if one can see a breakdown in this monotonic behavior of G for large y. The analysis of this latter series is inconclusive.     

The single-particle potential of nuclear matter in the LOCV framework

The density and momentum dependence of single-particle potential (SPP) and effective mass of symmetric nuclear matter are studied in the framework of lowest order constrained variational (LOCV) method. The Reid68, the Reid68-Δ and the ₁₈Av interactions are considered as the input nucleon-nucleon potentials. It is shown that the SPP of nuclear matter, at fixed density, is an increasing function of nucleon momentum, and it has different behavior for the Reid type potentials with respect to ₁₈Av interaction. We find good agreements between our LOCV SPP and those coming from others many-body techniques such as the (Dirac-)Brueckner-Hartree-Foch ((D)BHF), the fermion hypernetted chain (FHNC), mean field (MF), etc. On the other hand SPP dramatically depends on the density at low and high nucleon momentums. While the effective mass of nuclear matter increases as we increase the nucleon momentum, it decreases at the Fermi surface. Again, good agreements are observed between our calculated effective mass and those coming from the methods mentioned above.