Conformal mapping of unbounded multiply connected regions onto canonical slit regions

We present a boundary integral equation method for conformal mapping of unbounded multiply connected regions onto five types of canonical slit regions. For each canonical region, three linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unboundedmultiply connected region. The integral equations are uniquely solvable. The kernels involved in these integral equations are the modified Neumann kernels and the adjoint generalized Neumann kernels

Tight lower bound to the geometric measure of quantum discord

Dakic, Vedral and Brukner [Physical Review Letters \tf{105},190502 (2010)] gave a geometric measure of quantum discord in a bipartite quantum state as the distance of the state from the closest classical quantum (or zero discord) state and derived an explicit formula for a two qubit state. Further, S.Luo and S.Fu [Physical Review A \tf{82}, 034302 (2010)] obtained a generic form of this geometric measure for a general bipartite state and established a lower bound. In this brief report we obtain a rigorous lower bound to the geometric measure of quantum discord in a general bipartite state which dominates that obtained by S.Luo and S.Fu.Comment: 10 pages,2 figures. In the previous versions, a constraint was ignored while optimizing the second term in Eq.(5), in which case, only a lower bound on the geometric discord can be obtained. The title is also consequently changed. Accepted in Phys.Rev.

Stability of Triangular Libration Points in the Sun - Jupiter System under Szebehely’s Criterion

In the present study, the classical fourth-order Runge-Kutta method with seventh-order automatic step-size control has been carried out to examine the stability of triangular libration points in the Sun-Jupiter system. The Sun is a highly luminous body and Jupiter is a highly spinning body, so radiation pressure of the Sun and oblateness of the Jupiter cannot be neglected. These factors must have some effects on the motion of the infinitesimal mass (spacecraft) and consequent effects on the stability of the triangular libration points. It is to be noted that in our problem, infinitesimal mass exerts no influence of attraction on the primaries (Sun and Jupiter) but its motion is influenced by the primaries. Therefore, the equations of motion of the infinitesimal mass moving in the gravitational field of the radiating Sun and oblate Jupiter have been established for numerical integration. To check the stability of the libration points, the infinitesimal mass is allowed to librate for trajectory generation in the vicinity of one of the triangular libration points. Using double-precision computation, the Jacobian constant was calculated in order to observe the validity of the trajectory generation throughout the numerical integration. This constant of integration was checked to make sure that it remained constant at least to eight decimal places, so that other data may be accurate. Following all the above computational techniques, the maximum displacement and maximum velocity envelopes were constructed in the light of previous authors. The reason behind the assumption of the maximum displacement and maximum velocity envelopes is that the spacecraft (infinitesimal mass) will librate for a long time within the region of the envelopes without crossing the x-axis. If the area of the envelope is not maximum within the given time limit and the infinitesimal mass crosses the x-axis, then by changing the initial conditions; we attempt to construct the envelopes of maximum area following previous authors. If the area of the envelope is maximum it means spacecraft (infinitesimal mass) will librate in wider area for a long time without crossing the x-axis and longtime libration will give the higher range of stability. From our observation, it is found that due to the oblateness of Jupiter, the range of stability is reduced but photogravitation of the Sun has no significant effect on the triangular libration points

Entanglement Capacity of Nonlocal Hamiltonians : A Geometric Approach

We develop a geometric approach to quantify the capability of creating entanglement for a general physical interaction acting on two qubits. We use the entanglement measure proposed by us for $N$-qubit pure states (PRA \textbf{77}, 062334 (2008)). Our procedure reproduces the earlier results (PRL \textbf{87}, 137901 (2001)). The geometric method has the distinct advantage that it gives an experimental way to monitor the process of optimizing entanglement production.Comment: 8 pages, 1 figure

Purification and biochemical characterization of a Ca2+- independent, thermostable and acidophilic α-amylase from Bacillus sp. RM16

Bacillus sp. RM16 was isolated from a hot spring in Karachi and screened for the production of α- amylase. The enzyme was obtained after 72 h cultivation of strain in Luria broth containing 1% starch (w/v). Enzyme Amy RM16 was purified to electrophoretic homogeneity by a series of sequential steps including precipitation with ammonium sulfate at 70% saturation, Q-Sepharose, Phenyl Sepharose and reversed phase chromatography. The purified enzyme is made up of a single polypeptide chain of 66 kDa as established by a combination of SDS-PAGE and zymographic analysis. In our experimental conditions, a total yield of 1.35% with specific activity of 6380U/mg was obtained providing 17 fold final purification of the enzyme. Biochemical characterization of the Amy RM16 such as optimum temperature and pH, substrate specificity and enzymatic susceptibilities towards different metal ions and inhibitors were also performed. Results of these studies revealed that, the enzyme is active at wide temperature range with optimum activity at 80°C and retained 85% of the activity for 3 h at 50°C and around 50% of remaining activity for 1 h at 80°C. The enzyme showed optimum activity at pH 5.0. On the other hand, Ca+2 and EDTA (1 to 5 mM) did not significantly affect the enzyme activity. The main substrate for the enzyme was found to be starch but it could also hydrolyze raw starch, dextrin, γ-cyclodextrin and pullulan.Key words: Ca2+-independent, Bacillus sp, thermostable α-amylases, low pH profile, enzyme, raw starch digestion, HPLC

A study on the different finite element approaches for laser cutting of aluminum alloy sheet

The effectiveness of finite element simulation techniques for laser cutting of 1.2-mm-thick aluminium sheets has been studied. Lagrangian and Arbitrary Lagrangian-Eulerian techniques were used to model and simulate laser cutting process. The reliability of finite element results were evaluated by general energy balance analysis and experimental results. Temperature and stress distribution along with heat-affected zone were predicted during the laser-induced process in line with experimental conditions under ABAQUS finite element code. Heat transfer analysis relying on thermal loading was employed to reach the best efficiency. By using field-emission scanning electron microscope, morphological, structural, and elemental changes in the cutting sections were analyzed along with the X-ray diffraction technique. Obtained stress and heat-affected zone are highly dependent on the element type as well as numerical method. Both numerical method, ALE and Lagrangian, are compared to each other in terms of power absorption, cut surface morphology, and cutting efficiency. The results show that ALE method is in good agreement with experimental data. A study on the different finite element approaches for laser cutting of aluminum alloy sheet. Available from: https://www.researchgate.net/publication/317579195_A_study_on_the_different_finite_element_approaches_for_laser_cutting_of_aluminum_alloy_sheet [accessed Jul 3, 2017]

Thermal quantum and classical correlations in two qubit XX model in a nonuniform external magnetic field

We investigate how thermal quantum discord (QD) and classical correlations (CC) of a two-qubit one-dimensional XX Heisenberg chain in thermal equilibrium depend on the temperature of the bath as well as on nonuniform external magnetic fields applied to two qubits and varied separately. We show that the behavior of QD differs in many unexpected ways from the thermal entanglement (EOF). For the nonuniform case (B1 = -B2), we find that QD and CC are equal for all values of (B1 = -B2) and for different temperatures. We show that, in this case, the thermal states of the system belong to a class of mixed states and satisfy certain conditions under which QD and CC are equal. The specification of this class and the corresponding conditions are completely general and apply to any quantum system in a state in this class satisfying these conditions. We further find that the relative contributions of QD and CC can be controlled easily by changing the relative magnitudes of B1 and B2. Finally, we connect our results with the monogamy relations between the EOF, CC and the QD of two qubits and the environment.Comment: 8 pages, 13 figures. We connect our results with the monogamy relations between the EOF, CC and the QD of two qubits and the environmen