Hanle-Zeeman redistribution matrix. I. Classical theory expressions in the laboratory frame

Polarized scattering in spectral lines is governed by a 4; 4 matrix that describes how the Stokes vector is scattered and redistributed in frequency and direction. Here we develop the theory for this redistribution matrix in the presence of magnetic fields of arbitrary strength and direction. This general magnetic field case is called the Hanle- Zeeman regime, since it covers both of the partially overlapping weak- and strong- field regimes in which the Hanle and Zeeman effects dominate the scattering polarization. In this general regime, the angle-frequency correlations that describe the so-called partial frequency redistribution (PRD) are intimately coupled to the polarization properties. We develop the theory for the PRD redistribution matrix in this general case and explore its detailed mathematical properties and symmetries for the case of a J = 0 -> 1 -> 0 scattering transition, which can be treated in terms of time-dependent classical oscillator theory. It is shown how the redistribution matrix can be expressed as a linear superposition of coherent and noncoherent parts, each of which contain the magnetic redistribution functions that resemble the well- known Hummer- type functions. We also show how the classical theory can be extended to treat atomic and molecular scattering transitions for any combinations of quantum numbers.

Field Flow Sensitive Pointer and Escape Analysis for Java Using Heap Array SSA

Context sensitive pointer analyses based on Whaley and Lam’s bddbddb system have been shown to scale to large Java programs. We provide a technique to incorporate flow sensitivity for Java fields into one such analysis and obtain an escape analysis based on it. First, we express an intraprocedural field flow sensitive analysis, using Fink et al.’s Heap Array SSA form in Datalog. We then extend this analysis interprocedurally by introducing two new φ functions for Heap Array SSA Form and adding deduction rules corresponding to them. Adding a few more rules gives us an escape analysis. We describe two types of field flow sensitivity: partial (PFFS) and full (FFFS), the former without strong updates to fields and the latter with strong updates. We compare these analyses with two different (field flow insensitive) versions of Whaley-Lam analysis: one of which is flow sensitive for locals (FS) and the other, flow insensitive for locals (FIS). We have implemented this analysis on the bddbddb system while using the SOOT open source framework as a front end. We have run our analysis on a set of 15 Java programs. Our experimental results show that the time taken by our field flow sensitive analyses is comparable to that of the field flow insensitive versions while doing much better in some cases. Our PFFS analysis achieves average reductions of about 23% and 30% in the size of the points-to sets at load and store statements respectively and discovers 71% more “caller-captured” objects than FIS.

Influence of quantum confinement on the photoemission from superlattices of optoelectronic materials

We study the photoemission from quantum wire and quantum dot superlattices with graded interfaces of optoelectronic materials on the basis of newly formulated electron dispersion relations in the presence of external photo-excitation. Besides, the influence of a magnetic field on the photoemission from the aforementioned superlattices together with quantum well superlattices in the presence of a quantizing magnetic field has also been studied in this context. It has been observed taking into account HgTe/Hg1-xCdxTe and InxGa1-xAs/InP that the photoemission from these nanostructures increases with increasing photon energy in quantized steps and exhibits oscillatory dependences with the increase in carrier concentration. Besides, the photoemission decreases with increasing light intensity and wavelength, together with the fact that said emission decreases with increasing thickness exhibiting oscillatory spikes. The strong dependences of the photoemission on the light intensity reflects the direct signature of light waves on the carrier energy spectra. The content of this paper finds six applications in the fields of low dimensional systems in general. (C) 2010 Elsevier Ltd. All rights reserved.

Strong motion compatible source geometry

Strong motion array records are analyzed in this paper to identify and map the source zone of four past earthquakes. The source is represented as a sequence of double couples evolving as ramp functions, triggering at different instants, distributed in a region yet to be mapped. The known surface level ground motion time histories are treated as responses to the unknown double couples on the fault surface. The location, orientation, magnitude, and risetime of the double couples are found by minimizing the mean square error between analytical solution and instrumental data. Numerical results are presented for Chi-Chi, Imperial Valley, San Fernando, and Uttarakashi earthquakes. Results obtained are in good agreement with field investigations and those obtained from conventional finite fault source inversions.

Scattering polarization in the presence of magnetic and electric fields

The polarization of radiation by scattering on an atom embedded in combined external quadrupole electric and uniform magnetic fields is studied theoretically. Limiting cases of scattering under Zeeman effect, and Hanle effect in weak magnetic fields are discussed. The theory is general enough to handle scattering in intermediate magnetic fields (Hanle-Zeeman effect) and for arbitrary orientation of magnetic field. The quadrupolar electric field produces asymmetric line shifts, and causes interesting level-crossing phenomena either in the absence of an ambient magnetic field, or in its presence. It is shown that the quadrupolar electric field produces an additional depolarization in the Q/I profiles and rotation of the plane of polarization in the U/I profile over and above that arising from magnetic field itself. This characteristic may have a diagnostic potential to detect steady-state and time-varying electric fields that surround radiating atoms in solar atmospheric layers. (c) 2007 Elsevier Ltd. All rights reserved.

Influence of External Light Waves on the Thermoelectric Power Under Strong Magnetic Field in Ultrathin Films, Quantum Wires and Quantum Dots of Optoelectronic Materials

In this paper, an attempt is made to study the influence of external light waves on the thermoelectric power under strong magnetic field (TPSM) in ultrathin films (UFs), quantum wires (QWs) and quantum dots (QDs) of optoelectronic materials whose unperturbed dispersion relation of the conduction electrons are defined by three and two band models of Kane together with parabolic energy bands on the basis of newly formulated electron dispersion laws in each case. We have plotted the TPSM as functions of film thickness, electron concentration, light intensity and wavelength for UFs, QWs and ODs of InSb, GaAs, Hg1-xCdxTe and In1-xGaxAsyP1-y respectively. It appears from the figures that for UFs, the TPSM increases with increasing thickness in quantum steps, decreases with increasing electron degeneracy exhibiting entirely different types of oscillations and changes with both light intensity and wavelength and these two latter types of plots are the direct signature of light waves on opto-TPSM. For QWs, the opto-TPSM exhibits rectangular oscillations with increasing thickness and shows enhanced spiky oscillations with electron concentration per unit length. For QDs, the opto-TPSM increases with increasing film thickness exhibiting trapezoidal variations which occurs during quantum jumps and the length and breadth of the trapezoids are totally dependent on energy band constants. Under the condition of non-degeneracy, the results of opto-TPSM gets simplified into the well-known form of classical TPSM equation which the function of three constants only and being invariant of the signature of band structure.

Strong shock with radiation near the surface of a star

The propagation of a shock wave, originating in a stellar interior, is considered when it approaches the surface of the star and assumes a self-similar character, "forgetting" its initial conditions. The flow behind the shock is assumed to be spatially isothermal rather than adiabatic to simulate the conditions of large radiative transfer near the stellar surface. The adiabatic and isothermal flows behind such a shock are compared. The exact shock-propagation laws, obtained by solving the equations in similarity variables, for different values of the parameter δ in the undisturbed density law, ρ0 ∝ xδ, and γ, the ratio of specific heats, are compared with the approximate values calculated by Whitham's characteristic rule and the two show a generally good agreement.

Three-Dimensional simulation of deformation fields underneath vickers indenter:Effects of power-law Plasticity

The effects of power-law plasticity (yield strength and strain hardening exponent) on the plastic strain distribution underneath a Vickers indenter was systematically investigated by recourse to three-dimensional finite element analysis, motivated by the experimental macro-and micro-indentation on heat-treated Al-Zn-Mg alloy. For meaningful comparison between simulated and experimental results, the experimental heat treatment was carefully designed such that Al alloy achieve similar yield strength with different strain hardening exponent, and vice versa. On the other hand, full 3D simulation of Vickers indentation was conducted to capture subsurface strain distribution. Subtle differences and similarities were discussed based on the strain field shape, size and magnitude for the isolated effect of yield strength and strain hardening exponent.

Numerical simulations of crack tip fields in polycrystalline plastic solids

In this paper, modes I and II crack tip fields in polycrystalline plastic solids are studied under plane strain, small scale yielding conditions. Two different initial textures of an Al–Mg alloy, viz., continuous cast AA5754 sheets in the recrystallized and cold rolled conditions, are considered. The former is nearly-isotropic, while the latter displays distinct anisotropy. Finite element simulations are performed by employing crystal plasticity constitutive equations along with a Taylor-type homogenization as well as by using the Hill quadratic yield theory. It is found that significant texture evolution occurs close to the notch tip which profoundly influences the stress and plastic strain distributions. Also, the cold rolling texture gives rise to higher magnitude of plastic strain near the tip.

Numerical simulations of crack tip fields in polycrystalline plastic solids

In this paper, modes I and II crack tip fields in polycrystalline plastic solids are studied under plane strain, small scale yielding conditions. Two different initial textures of an Al-Mg alloy, viz.,continuous cast AA5754 sheets in the recrystallized and cold rolled conditions, are considered. The former is nearly-isotropic, while the latter displays distinct anisotropy. Finite element simulations are performed by employing crystal plasticity constitutive equations along with a Taylor-type homogenization as well as by using the Hill quadratic yield theory. It is found that significant texture evolution occurs close to the notch tip which profoundly influences the stress and plastic strain distributions. Also, the cold rolling texture gives rise to higher magnitude of plastic strain near the tip. (C) 2010 Elsevier Ltd. All rights reserved.

Prospects for wind energy utilisation in Karnataka State

An examination of the data available at 22 meteorological stations in Karnataka State shows that wind velocities in the State as a whole are neither spectacularly high nor negligibly low. The highest winds (annual mean of around 13 km/hr) are experienced in parts of the northern maidan region of the State (Gulbarga, Raichur and Bidar districts) and in Bangalore. The winds are strongly seasonal: typically, the five monsoon months May-September account for about 80% of the annual wind energy flux. Although the data available are inadequate to make precise estimates, they indicate that the total wind energy potential of the State is about an order of magnitude higher than the current electrical energy consumption. The possible exploitation of wind energy for applications in rural areas therefore requires serious consideration, but it is argued that to be successful it is essential to formulate an integrated and carefully planned programme. The output of current windpumps needs to be increased; a doubling should be feasible by the design of suitable load-matching devices. The first cost has to be reduced by careful design, by the use of local materials and skills and by employing a labour-intensive technology. A consideration of the agricultural factors in the northern maidan region of the State shows that there is likely to be a strong need for mechanical assistance in supplemental and life-saving irrigation for the dry crops characteristic of the area. A technological target for a windmill that could find applications in this area would be one with a rotor diameter of about 10 m that can lift about 10,000 litres of water per hour in winds of 10 km/hr (2.8 m/s) hourly average speed and costs less than about Rs 10,000. Although no such windmills exist as of today, the authors believe that achievement of this target is feasible. An examination of various possible scenarios for the use of windmills in this area suggests that with a windpump costing about Rs 12,000, a three hectare farm growing two dry crops a year can expect an annual return of about 150% from an initial investment of about Rs 15,000. It is concluded that it should be highly worthwhile to undertake a coordinated programme for wind energy development that will include more detailed wind surveys in the northern maidan area (as well as some others, such as the Western Ghats), the development of suitable windmill designs and a study of their applications to agriculture as well as to other fields.

Thermal correlation functions of twisted quantum fields

We derive the thermal correlators for twisted quantum fields on noncommutative spacetime. We show that the thermal expectation value of the number operator is same as in commutative spacetime, but that higher correlators are sensitive to the noncommutativity parameters phi(mu nu).

New type of high field electrooptic response in nematics

We have made concurrent measurements of ionic current and optical transmission between crossed polarisers on several nematics with positive dielectric anisotropy under the action of applied low frequency (< 1KHz) square wave voltages. When the field E is low, the measured current is linear in E and there is no electrooptic response. Beyond some value of the field (E(0)similar to 100 esu), the current becomes independent of the field (phenomenon of limiting current). Further an electrooptic signal is measured at twice the frequency of the applied voltage, which exhibits a peak as a function of the field. The width of the peak is 3 to 4 times the value of E-0, and the signal level at the peak decreases as the frequency is increased. These measurements have been made on three highly polar compounds with cyano end groups. Careful observations do not show any evidence of electrohydrodynamic instabilities in the sample. It is argued that the observations can be understood if at the onset of the phenomenon of the limiting current, a strong electric field gradient is established near one of the electrodes due to the sweeping of an ionic species with high mobility. The field gradient produces a flexoelectric deformation of the director field, which in turn gives rise to the electrooptic effect. At higher fields, the stabilising dielectric torque takes over to suppress this instability.

Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework

Partition of unity methods, such as the extended finite element method, allows discontinuities to be simulated independently of the mesh (Int. J. Numer. Meth. Engng. 1999; 45:601-620). This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome re-meshing, as the discontinuity evolves. However, to compute the stiffness matrix of the elements intersected by the discontinuity, a subdivision of the elements into quadrature subcells aligned with the discontinuity is commonly adopted. In this paper, we use a simple integration technique, proposed for polygonal domains (Int. J. Nuttier Meth. Engng 2009; 80(1):103-134. DOI: 10.1002/nme.2589) to suppress the need for element subdivision. Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics and a multi-material problem show that the proposed method yields accurate results. Owing to its simplicity, the proposed integration technique can be easily integrated in any existing code. Copyright (C) 2010 John Wiley & Sons, Ltd.