Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries

We extend the definition of generalized parity $P$, charge-conjugation $C$ and time-reversal $T$ operators to nondiagonalizable pseudo-Hermitian Hamiltonians, and we use these generalized operators to describe the full set of symmetries of a pseudo-Hermitian Hamiltonian according to a fourfold classification. In particular we show that $TP$ and $CTP$ are the generators of the antiunitary symmetries; moreover, a necessary and sufficient condition is provided for a pseudo-Hermitian Hamiltonian $H$ to admit a $P$-reflecting symmetry which generates the $P$-pseudounitary and the $P$-pseudoantiunitary symmetries. Finally, a physical example is considered and some hints on the $P$-unitary evolution of a physical system are also given.Comment: 20 page

Lithographically and electrically controlled strain effects on anisotropic magnetoresistance in (Ga,Mn)As

It has been demonstrated that magnetocrystalline anisotropies in (Ga,Mn)As are sensitive to lattice strains as small as 10^-4 and that strain can be controlled by lattice parameter engineering during growth, through post growth lithography, and electrically by bonding the (Ga,Mn)As sample to a piezoelectric transducer. In this work we show that analogous effects are observed in crystalline components of the anisotropic magnetoresistance (AMR). Lithographically or electrically induced strain variations can produce crystalline AMR components which are larger than the crystalline AMR and a significant fraction of the total AMR of the unprocessed (Ga,Mn)As material. In these experiments we also observe new higher order terms in the phenomenological AMR expressions and find that strain variation effects can play important role in the micromagnetic and magnetotransport characteristics of (Ga,Mn)As lateral nanoconstrictions.Comment: 11 pages, 4 figures, references fixe

The Wilson renormalization group for low x physics: towards the high density regime

We continue the study of the effective action for low $x$ physics based on a Wilson renormalization group approach. We express the full nonlinear renormalization group equation in terms of the average value and the average fluctuation of extra color charge density generated by integrating out gluons with intermediate values of $x$. This form clearly exhibits the nature of the phenomena driving the evolution and should serve as the basis of the analysis of saturation effects at high gluon density at small $x$.Comment: 14 pages, late

A Homogenization Approach for Turbulent Channel Flows over Porous Substrates: Formulation and Implementation of Effective Boundary Conditions

The turbulent flow through a plane channel bounded by a single permeable wall is considered; this is a problem of interest since a carefully chosen distribution of grains and voids in the porous medium can result in skin friction reduction for the flow in the channel. In the homogenization approach followed here, the flow is not resolved in the porous layer, but an effective velocity boundary condition is developed (and later enforced) at a virtual interface between the porous bed and the channel flow. The condition is valid up to order two in terms of a small gauge factor, the ratio of microscopic to macroscopic length scales; it contains slip coefficients, plus surface and bulk permeability coefficients, which arise from the solution of microscale problems solved in a representative elementary volume. Using the effective boundary conditions, free of empirical parameters, direct numerical simulations are then performed in the channel, considering a few different porous substrates. The results, examined in terms of mean values and turbulence statistics, demonstrate the drag-reducing effects of porous substrates with streamwise-preferential alignment of the solid grains

Evolution of an elliptical bubble in an accelerating extensional flow

Mathematical models that describe the dynamical behavior of a thin gas bubble embedded in a glass fiber during a fiber drawing process have been discussed and analyzed. The starting point for the mathematical modeling was the equations presented in [1] for a glass fiber with a hole undergoing extensional flow. These equations were reconsidered here with the additional reduction that the hole, i.e. the gas bubble, was thin as compared to the radius of the fiber and of finite extent. The primary model considered was one in which the mass of the gas inside the bubble was fixed. This fixed-mass model involved equations for the axial velocity and fiber radius, and equations for the radius of the bubble and the gas pressure inside the bubble. The model equations assumed that the temperature of the furnace of the drawing tower was known. The governing equations of the bubble are hyperbolic and predict that the bubble cannot extend beyond the limiting characteristics specified by the ends of the initial bubble shape. An analysis of pinch-off was performed, and it was found that pinch-off can occur, depending on the parameters of the model, due to surface tension when the bubble radius is small. In order to determine the evolution of a bubble, a numerical method of solution was presented. The method was used to study the evolution of two different initial bubble shapes, one convex and the other non-convex. Both initial bubble shapes had fore-aft symmetry, and it was found that the bubbles stretched and elongated severely during the drawing process. For the convex shape, fore-aft symmetry was lost in the middle of the drawing process, but the symmetry was re-gained by the end of the drawing tower. A small amount of pinch-off was observed at each end for this case, so that the final bubble length was slightly shorter than its theoretical maximum length. For the non-convex initial shape, pinch-off occurred in the middle of the bubble resulting in two bubbles by the end of the fiber draw. The two bubbles had different final pressures and did not have fore-aft symmetry. An extension of the fixed-mass model was considered in which the gas in the bubble was allowed to diffuse into the surrounding glass. The governing equations for this leaky-mass model were developed and manipulated into a form suitable for a numerical treatment

Psychological Security and Its Relationship to Empathy Among a Sample of Early Childhood in Jubail Industrial City

The current research aims at revealing the relationship between psychological security and empathy in the stage of early childhood at the Jubail Industrial City. Its significance can be attributed to the importance of developing empathy among children, enlightening the community and educators about the importance of psychological security and its relationship to empathy among children in the early childhood stage. An analytical descriptive approach was employed as it suits the nature of the current research. A random sample comprising 204 children in the early childhood stage. Having applied the psychological security [1] and empathy scales [2] to the research sample, the following result was reached. There is a statistically significant correlation between psychological security and empathy in a sample of children in the early childhood stage in Jubail Industrial City

MAT-741: IMPACT BEHAVIOUR OF SHAPE MEMORY ALLOY HYBRID FIBRE-REINFORCED ENGINEERED CEMENTITIOUS COMPOSITE

An experimental study was conducted to evaluate the impact behaviour of an innovative hybrid-fibre engineered cementitious composite (ECC) incorporating randomly dispersed short shape memory alloy fibres (SMA). A modified drop weight test was conducted on specimens from various ECC mixtures with and without SMA fibres. The impact behaviour was evaluated and compared based on the ability to dissipate energy and sustain impact load without damage. Results show that the addition of SMA to ECC mixtures significantly enhanced their performance under impact loading. The amount of dissipated energy by ECC increased by about 51% as a result of SMA fibre addition. This highlights the potential benefits of incorporating SMA in composite materials exposed to impact loads, paving the way for a wider implementation in the field of fortified structures

The \tau -> \mu \bar{\nu_i} \nu_i decay in the Randall Sundrum background with localized U(1)_Y gauge boson

We study the effects of localization of the U(1)_Y gauge boson around the visible brane and the contributions of the KK modes of Z bosons on the BR of the LFV \tau -> \mu \bar{\nu_i} \nu_i decay. We observe that the BR is sensitive to the amount of localization of Z boson in the bulk of the Randall Sundrum background.Comment: 13 pages, 4 figures,1 tabl