Bound Polaron in a Quantum Well Under an Electric Field

We conduct a theoretical study on the properties of a bound polaron in a quantum well under an electric field using linear combination operator and unitary transformation methods, which are valid in the whole range of electron-LO phonon coupling. The changing relations between the ground-state energy of the bound polaron in the quantum well and the Coulomb bound potential, the electric field strength, and the well width are derived. The numerical results show that the ground-state energy increases with the increase of the electric field strength and the Coulomb bound potential and decreases as the well width increases.

Multi-axial strain-stiffening elastic potentials with energy bounds:explicit approach based on uniaxial data

According to the well-known models for rubberlike elasticity with strain- stii^ening effects, the unbounded strain energy is generated with the unlimitedly growing stress when the stretch approaches certain limits. Toward a solution to this issue, an explicit approach is proposed to derive the multi-axial elastic potentials directly from the uniaxial potentials. Then, a new multi-axial potential is presented to characterize the strain-stiffening effect by prescribing suitable forms of uniaxia] potentials so that the strain energy is always bounded as the stress grows to infinity. Numerical examples show good agreement with a number of test data.

Approximate Bound State Solutions for Certain Molecular Potentials

We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number l and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are obtained.

Influence Mechanism of Cerium on the Threshold of Short Fatigue Crack for Aluminum-lithium Alloy 2090

The thresholds of short fatigue cracks for aluminum-lithium alloys 2090 and 2090+Ce are quantitatively evaluated. The essential reason resulting in stronger short crack effect has been ascertained. Influence of cerium on the threshold of short fatigue cracks for aluminum-lithium alloy 2090 was investigated. The results show that, by adding Ce into this alloy, DeltaK(i) and DeltaK(Cl.th) are increased. The influence mechanism of Ce on the threshold of short fatigue crack for alloy 2090 was explored fi om the bound energy, T, phase, the energy of anti-phase boundary, the energy of super-lattice intrinsic stacking fault and the electron bonds. By adding Ce into alloy 2090, the bound energy of Cu atom in this alloy is increased; the effect of thinning and dispersing T, phase is obtained; the effect of increasing the energy of anti-phase boundary and decreasing the energy of super-lattice intrinsic stacking fault for delta ' phase can be achieved.

The top-order energy of quasilinear wave equations in two space dimensions is uniformly bounded

Alinhac solved a long-standing open problem in 2001 and established that quasilinear wave equations in two space dimensions with quadratic null nonlinearities admit global-in-time solutions,provided that the initial data are compactly supported and sufficiently small in Sobolev norm.In this work,Alinhac obtained an upper bound with polynomial growth in time for the top-order energy of the solutions.A natural question then arises whether the time-growth is a true phenomenon,despite the possible conservation of basic energy.In the present paper,we establish that the top-order energy of the solutions in Alinhac theorem remains globally bounded in time.

Energy Bounds for Static Spherically Symmetric Spacetime in f(R, G) Gravity

The main purpose of this paper is to investigate energy bounds in the context of f(R, G) gravity. To meet this aim, we choose static spherically symmetric spacetime in f(R, G) gravity to develop the field equations. We select three different models of f(R, G) gravity, which are thoroughly discussed in the literature. Firstly, the inequalities are formulated using energy bounds and then viability of the considered models are checked respectively. Graphical analysis show that specific f(R, G) gravity models are satisfied under suitable values of model parameters. It is shown that in a certain case energy bounds are satisfied expect SEC, which supports the late time acceleration expansion of unverse.