Two-soliton interaction in the vicinity of a defect inside a fiber Bragg grating and its application for obtaining an all-optical memory

We study the interaction between two Bragg solitons in the vicinity of a defect inside a fiber Bragg grating. A soliton that is trapped in the defect can be released by launching a second soliton. The effect can be used to obtain an all-optical memory that is not strongly sensitive to the phase and the timing arrival of the solitons.     

A boundary value problem of thermal convection

The two-dimensional thermal convection of a viscous fluid in a rectangular region is analyzed using the Boussinesq theory, and the Rayleigh boundary conditions. The existence of a unique convention state bifurcating from each eigenvalue of the linearized theory is established by using the Morse lemma. This establishes the validity of the formal perturbation method for determining the convection states. The effects of imperfections on the transition from the conduction to the convection states are studied. A theorem of Thom is used to justify a previous asymptotic expansion method near the critical Rayleigh number.     

Thickness dependence of the work function in double-layer metallic films

The work function of metallic thin films limited by symmetric surfaces is expected to be thickness dependent at a level of 0.1 eV and a thickness range of about 5 nm. Recent experiments, however, demonstrated that Cu films on glass or Ni substrates show a long ranging (10–20 nm) increase of the work function with increasing film thickness [1]. This effect was attributed to a violation of local charge neutrality in films with unlike surfaces. In this paper we show that the barrier height of thin film diodes like metal-insulator-metal (MIM)-, metal-semiconductor (Schottky contacts)-and metal-vacuum-metal (Kelvin capacitors) structures decreases with increasing thickness of one metal electrode. This metal electrode consists of a double layer whose single layer thicknesses are of the order of few tens of nm. The observed effect can be attributed to a decrease of the work function at the counter limiting interface not exposed to the evaporation beam. A possible explanation can be found again in the violation of the local charge neutrality in films with unlike surfaces.     

Upper bound on the characters of the symmetric groups

Let C be a conjugacy class in the symmetric group S _n , and λ be a partition of n. Let f ^λ be the degree of the irreducible representation S ^λ , χ ^λ (C)– the character of S ^λ at C, and r ^λ (C)– the normalized character χ ^λ (C) f ^λ . We prove that there exist constants b > 0 and 1 > q > 0 such that for n > 4, for every conjugacy class C in S _n and every irreducible representation S ^λ of S _n ∣r ^λ (C)∣≦ ( max {q,λ ₁ n, λ ₁ ′ n}) ^{b ⋅ supp(C)} where supp (C) is the number of non-fixed digits under the action of a permutation in C, λ ₁ is the size of the largest part in λ, and λ ₁ ′ is the number of parts in λ. The proof is obtained by enumeration of rim hook tableaux, the Hook formula and probabilistic arguments. Combinatorial, algebraic and statistical applications follow this result. In particular, we estimate the rate of mixing of random walks on the alternating groups with respect to conjugacy classes. Oblatum 14-III-1995 & 30-X-1995     

The spectrum-generating groups program and the string

Schrödinger's approach was analytical, but it is equivalent to an algebraic treatment. We review the evolution of group theory as a physical tool and its application to the Hilbert space of Schrödinger's eigenstates. Special emphasis is put on recent results relating to the relativistic quantized string.Dedicated to the 100th anniversary of the birth of Erwin Schrödinger. Invited Lecture at the 1987 Washington APS Meeting, Symposium on Dynamical Symmetries.Also on leave from the Center for Particle Theory, University of Texas, Austin.     

Approximations to the distributions of ordered distance random variables

Summary In the present note we give short proofs of asymptotic theorems for the distributions of extreme and intermediate ordered distance random variables. Moreover, a quick goodness-of-fit test is proposed which is based on a single intermediate ordered distance random variable.     

Optimization of Adiabatic Selective Pulses

Adiabatic RF pulses play an important role in spin inversion due to their robust behavior in presence of inhomogeneous RF fields. These pulses are characterized by the trajectory swept by the tip of theB_effvector and the rate of motion upon it. In this paper, a method is described for optimizing adiabatic inversion pulses to achieve a frequency-selective magnetization inversion over a given bandwidth in a shorter time and to improve slice profile. An efficient adiabatic pulse is used as an initial condition. This pulse allows for flexibility in choosing its parameters; in particular, the transition sharpness may be traded off against the inverted bandwidth. The considerations for selecting the parameters of the pulse according to the requirements of the design are discussed. The optimization process then improves the slice profile by optimizing the rate of motion along the trajectory of the pulse while preserving the trajectory itself. The adiabatic behavior of the optimized pulses is fully preserved over a twofold range of variation in the RF amplitude which is sufficient for imaging applications in commercial high-field MRI machines. Design examples demonstrate the superiority of the optimized pulses over the conventional sech/tanh pulse.