Unsteady compressible boundary layer flow in the stagnation region of a sphere with a magnetic field

Abstract: An analysis is performed to study the unsteady compressible laminar boundary layer flow in the forward stagnation-point region of a sphere with a magnetic field applied normal, to the surface. We have considered the case where there is an initial steady state that is perturbed by the step change in the total enthalpy at the wall. The nonlinear coupled parabolic partial differential equations governing the flow and heat transfer have been solved numerically using a finite-difference scheme. The numerical results are presented, which show the temporal development of the boundary layer. The magnetic field in the presence of variable electrical conductivity causes an overshoot in the velocity profile. Also, when the total enthalpy at the wall is suddenly increased, there is a change in the direction of transfer of heat in a small interval of time.

Full Sphere Axisymmetric Simulations of the Solar Dynamo

We explore a full sphere (2D axisymmetric) kinematic solar dynamo model based on the Babcock-Leighton idea that the poloidal field is generated in the surface layers from the decay of tilted bipolar solar active regions. This model incorporates the helioseismically deduced solar rotation profile and an algorithm for buoyancy motivated from simulations of flux tube dynamics. A prescribed deep meridional circulation plays an important role in the advection of magnetic flux. We specifically address the parity issue and show that – contrary to some recent claims – the Babcock-Leighton dynamo can reproduce solar-like dipolar parity if certain reasonable conditions are satisfied in the solar interior, the most important requirement being that the poloidal field of the two hemispheres be efficiently coupled across the equator.

Unsteady MUD rotating flow over a rotating sphere near the equator

The unsteady rotating flow of a laminar incompressible viscous electrically conducting fluid over a rotating sphere in the vicinity of the equator has been studied. The fluid and the body rotate either in the same direction or in opposite directions. The effects of surface suction and magnetic field have been included in the analysis. There is an initial steady state that is perturbed by a sudden change in the rotational velocity of the sphere, and this causes unsteadiness in the flow field. The nonlinear coupled parabolic partial differential equations governing the boundary-layer flow have been solved numerically by using an implicit finite-difference scheme. For large suction or magnetic field, analytical solutions have also been obtained. The magnitude of the radial, meridional and rotational velocity components is found to be higher when the fluid and the body rotate in opposite directions than when they rotate in the same direction. The surface shear stresses in the meridional and rotational directions change sign when the ratio of the angular velocities of the sphere and the fluid lambda greater than or equal to lambda(0). The final (new) steady state is reached rather quickly which implies that the spin-up time is small. The magnetic field and surface suction reduce the meridional shear stress, but increase the surface shear stress in the rotational direction.

Effective thermal conductivity of a heat generating rod bundle dissipating heat by natural convection and radiation

A numerical study of conjugate natural convection and surface radiation in a horizontal hexagonal sheath housing 19 solid heat generating rods with cladding and argon as the fill gas, is performed. The natural convection in the sheath is driven by the volumetric heat generation in the solid rods. The problem is solved using the FLUENT CFD code. A correlation is obtained to predict the maximum temperature in the rod bundle for different pitch-to-diameter ratios and heat generating rates. The effective thermal conductivity is related to the heat generation rate, maximum temperature and the sheath temperature. Results are presented for the dimensionless maximum temperature, Rayleigh number and the contribution of radiation with changing emissivity, total wattage and the pitch-to-diameter ratio. In the simulation of a larger system that contains a rod bundle, the effective thermal conductivity facilitates simplified modelling of the rod bundle by treating it as a solid of effective thermal conductivity. The parametric studies revealed that the contribution of radiation can be 38-65% of the total heat generation, for the parameter ranges chosen. Data for critical Rayleigh number above which natural convection comes into effect is also presented. (C) 2011 Elsevier B.V. All rights reserved.

Exciting forces due to interaction of water waves with a submerged sphere in an ice-covered two-layer fluid of finite depth

Scattering of water waves by a sphere in a two-layer fluid, where the upper layer has an ice-cover modelled as an elastic plate of very small thickness, while the lower one has a rigid horizontal bottom surface, is investigated within the framework of linearized water wave theory. The effects of surface tension at the surface of separation is neglected. There exist two modes of time-harmonic waves - the one with lower wave number propagating along the ice-cover and the one with higher wave number along the interface. Method of multipole expansions is used to find the particular solution for the problem of wave scattering by a submerged sphere placed in either of the layers. The exciting forces for vertical and horizontal directions are derived and plotted against different values of the wave number for different submersion depths of the sphere and flexural rigidity of the ice-cover. When the flexural rigidity and the density of the ice-cover are taken to be zero, the numerical results for the exciting forces for the problem with free surface are recovered as particular cases. (C) 2011 Elsevier Ltd. All rights reserved.

A novel variable resolution global spectral method on the sphere

A variable resolution global spectral method is created on the sphere using High resolution Tropical Belt Transformation (HTBT). HTBT belongs to a class of map called reparametrisation maps. HTBT parametrisation of the sphere generates a clustering of points in the entire tropical belt; the density of the grid point distribution decreases smoothly in the domain outside the tropics. This variable resolution method creates finer resolution in the tropics and coarser resolution at the poles. The use of FFT procedure and Gaussian quadrature for the spectral computations retains the numerical efficiency available with the standard global spectral method. Accuracy of the method for meteorological computations are demonstrated by solving Helmholtz equation and non-divergent barotropic vorticity equation on the sphere. (C) 2011 Elsevier Inc. All rights reserved.

Subdiffusion in hair bundle dynamics: The role of protein conformational fluctuations

The detection of sound signals in vertebrates involves a complex network of different mechano-sensory elements in the inner ear. An especially important element in this network is the hair bundle, an antenna-like array of stereocilia containing gated ion channels that operate under the control of one or more adaptation motors. Deflections of the hair bundle by sound vibrations or thermal fluctuations transiently open the ion channels, allowing the flow of ions through them, and producing an electrical signal in the process, eventually causing the sensation of hearing. Recent high frequency (0.1-10 kHz) measurements by Kozlov et al. Proc. Natl. Acad. Sci. U. S. A. 109, 2896 (2012)] of the power spectrum and the mean square displacement of the thermal fluctuations of the hair bundle suggest that in this regime the dynamics of the hair bundle are subdiffusive. This finding has been explained in terms of the simple Brownian motion of a filament connecting neighboring stereocilia (the tip link), which is modeled as a viscoelastic spring. In the present paper, the diffusive anomalies of the hair bundle are ascribed to tip link fluctuations that evolve by fractional Brownian motion, which originates in fractional Gaussian noise and is characterized by a power law memory. The predictions of this model for the power spectrum of the hair bundle and its mean square displacement are consistent with the experimental data and the known properties of the tip link. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4768902]

Minimizing the complexity of fast sphere decoding of STBCs

Decoding of linear space-time block codes (STBCs) with sphere-decoding (SD) is well known. A fast-version of the SD known as fast sphere decoding (FSD) has been recently studied by Biglieri, Hong and Viterbo. Viewing a linear STBC as a vector space spanned by its defining weight matrices over the real number field, we define a quadratic form (QF), called the Hurwitz-Radon QF (HRQF), on this vector space and give a QF interpretation of the FSD complexity of a linear STBC. It is shown that the FSD complexity is only a function of the weight matrices defining the code and their ordering, and not of the channel realization (even though the equivalent channel when SD is used depends on the channel realization) or the number of receive antennas. It is also shown that the FSD complexity is completely captured into a single matrix obtained from the HRQF. Moreover, for a given set of weight matrices, an algorithm to obtain a best ordering of them leading to the least FSD complexity is presented. The well known classes of low FSD complexity codes (multi-group decodable codes, fast decodable codes and fast group decodable codes) are presented in the framework of HRQF.

Black hole formation in fuzzy sphere collapse

We study the collapse of a fuzzy sphere, that is a spherical membrane built out of D0-branes, in the Banks-Fischler-Shenker-Susskind model. At weak coupling, as the sphere shrinks, open strings are produced. If the initial radius is large then open string production is not important and the sphere behaves classically. At intermediate initial radius the backreaction from open string production is important but the fuzzy sphere retains its identity. At small initial radius the sphere collapses to form a black hole. The crossover between the later two regimes is smooth and occurs at the correspondence point of Horowitz and Polchinski.

Monopoles on S-F(2) from the fuzzy conifold

The intersection of the conifold z(1)(2) + z(2)(2) + z(3)(2) = 0 and S-5 is a compact 3-dimensional manifold X-3. We review the description of X-3 as a principal U(1) bundle over S-2 and construct the associated monopole line bundles. These monopoles can have only even integers as their charge. We also show the Kaluza-Klein reduction of X-3 to S-2 provides an easy construction of these monopoles. Using the analogue of the Jordan-Schwinger map, our techniques are readily adapted to give the fuzzy version of the fibration X-3 -> S-2 and the associated line bundles. This is an alternative new realization of the fuzzy sphere S-F(2) and monopoles OH it.

On the sphere decoding complexity of high-rate multigroup decodable STBCs in asymmetric MIMO systems

A space-time block code (STBC) is said to be multigroup decodable if the information symbols encoded by it can be partitioned into two or more groups such that each group of symbols can be maximum-likelihood (ML) decoded independently of the other symbol groups. In this paper, we show that the upper triangular matrix encountered during the sphere decoding of a linear dispersion STBC can be rank-deficient even when the rate of the code is less than the minimum of the number of transmit and receive antennas. We then show that all known families of high-rate (rate greater than 1) multigroup decodable codes have rank-deficient matrix even when the rate is less than the number of transmit and receive antennas, and this rank-deficiency problem arises only in asymmetric MIMO systems when the number of receive antennas is strictly less than the number of transmit antennas. Unlike the codes with full-rank matrix, the complexity of the sphere decoding-based ML decoder for STBCs with rank-deficient matrix is polynomial in the constellation size, and hence is high. We derive the ML sphere decoding complexity of most of the known high-rate multigroup decodable codes, and show that for each code, the complexity is a decreasing function of the number of receive antennas.

Construction of Block Orthogonal STBCs and Reducing Their Sphere Decoding Complexity

Construction of high rate Space Time Block Codes (STBCs) with low decoding complexity has been studied widely using techniques such as sphere decoding and non Maximum-Likelihood (ML) decoders such as the QR decomposition decoder with M paths (QRDM decoder). Recently Ren et al., presented a new class of STBCs known as the block orthogonal STBCs (BOSTBCs), which could be exploited by the QRDM decoders to achieve significant decoding complexity reduction without performance loss. The block orthogonal property of the codes constructed was however only shown via simulations. In this paper, we give analytical proofs for the block orthogonal structure of various existing codes in literature including the codes constructed in the paper by Ren et al. We show that codes formed as the sum of Clifford Unitary Weight Designs (CUWDs) or Coordinate Interleaved Orthogonal Designs (CIODs) exhibit block orthogonal structure. We also provide new construction of block orthogonal codes from Cyclic Division Algebras (CDAs) and Crossed-Product Algebras (CPAs). In addition, we show how the block orthogonal property of the STBCs can be exploited to reduce the decoding complexity of a sphere decoder using a depth first search approach. Simulation results of the decoding complexity show a 30% reduction in the number of floating point operations (FLOPS) of BOSTBCs as compared to STBCs without the block orthogonal structure.