Exact internal controllability for a hyperbolic problem in a domain with highly oscillating boundary

In this paper, by using the Hilbert Uniqueness Method (HUM), we study the exact controllability problem described by the wave equation in a three-dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities whose size depends on a small parameter epsilon > 0, and with a fixed height. Our aim is to obtain the exact controllability for the homogenized equation. In the process, we study the asymptotic analysis of wave equation in two setups, namely solution by standard weak formulation and solution by transposition method.

Fast Eigen solution for homogeneous quadratic minimization with at most three constraints

We propose an eigenvalue based technique to solve the Homogeneous Quadratic Constrained Quadratic Programming problem (HQCQP) with at most three constraints which arise in many signal processing problems. Semi-Definite Relaxation (SDR) is the only known approach and is computationally intensive. We study the performance of the proposed fast eigen approach through simulations in the context of MIMO relays and show that the solution converges to the solution obtained using the SDR approach with significant reduction in complexity.

The role of tusks, musth and body size in male-male competition among Asian elephants, Elephas maximus

The evolution of sexually dimorphic, elaborate male traits that are seemingly maladaptive may be driven by sexual selection (male-male competition and or female mate choice). Tusk possession in the Asian elephant is sexually dimorphic and exaggerated but its role in male-male competition has not yet been determined. We examined the role of the tusks in establishing dominance along with two other known male-male signals, namely, body size and musth (a temporary physiologically heightened sexual state) in an Asian elephant population in northeastern India with equal proportions of tusked and tuskless males. We observed 116 agonistic interactions with clear dominance outcomes between adult (>15 years) males during 458 field days in the dry season months of 2008-2011. A generalized linear mixed-effects model was used to predict the probability of winning as a function of body size, tusk possession and musth status relative to the opponent. A hierarchy of the three male-male signals emerged from this analysis, with musth overriding body size and body size overriding tusk possession. In this elephant population tusk possession thus plays a relatively minor role in male-male competition. An important implication of musth and body size being stronger determinants of dominance than tusk possession is that it could facilitate rapid evolution of tuskless males in the population under artificial selection against tusked individuals, which are poached for ivory. (C) 2013 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

Three dimensional PN based impact angle control for higher speed nonmaneuvering targets

Terminal impact angle control is crucial for enhancement of warhead effectiveness. In the literature, this problem has been addressed in the context of targets with lower speeds than the interceptor. However, in the current defence scenario, targets of much higher speed than the interceptor is a reality. This paper presents a generic proportional navigation (PN) based guidance law, that uses the standard PN and novel Retro-PN guidance laws based on the initial engagement geometry and terminal engagement requirements, for three dimensional engagement scenario against higher speed nonmaneuvering targets to control terminal impact angle. Results are obtained on the set of achievable impact angles and conditions on the navigation constant to achieve them. Simulation results are given to support the theoretical findings.

STOKES' SYSTEM IN A DOMAIN WITH OSCILLATING BOUNDARY: HOMOGENIZATION AND ERROR ANALYSIS OF AN INTERIOR OPTIMAL CONTROL PROBLEM

Homogenization and error analysis of an optimal interior control problem in the framework of Stokes' system, on a domain with rapidly oscillating boundary, are the subject matters of this article. We consider a three dimensional domain constituted of a parallelepiped with a large number of rectangular cylinders at the top of it. An interior control is applied in a proper subdomain of the parallelepiped, away from the oscillating volume. We consider two types of functionals, namely a functional involving the L-2-norm of the state variable and another one involving its H-1-norm. The asymptotic analysis of optimality systems for both cases, when the cross sectional area of the rectangular cylinders tends to zero, is done here. Our major contribution is to derive error estimates for the state, the co-state and the associated pressures, in appropriate functional spaces.

Optimal trajectory planning for path convergence in three-dimensional space

This article addresses the problem of determining the shortest path that connects a given initial configuration (position, heading angle, and flight path angle) to a given rectilinear or a circular path in three-dimensional space for a constant speed and turn-rate constrained aerial vehicle. The final path is assumed to be located relatively far from the starting point. Due to its simplicity and low computational requirements the algorithm can be implemented on a fixed-wing type unmanned air vehicle in real time in missions where the final path may change dynamically. As wind has a very significant effect on the flight of small aerial vehicles, the method of optimal path planning is extended to meet the same objective in the presence of wind comparable to the speed of the aerial vehicles. But, if the path to be followed is closer to the initial point, an off-line method based on multiple shooting, in combination with a direct transcription technique, is used to obtain the optimal solution. Optimal paths are generated for a variety of cases to show the efficiency of the algorithm. Simulations are presented to demonstrate tracking results using a 6-degrees-of-freedom model of an unmanned air vehicle.

Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics

This paper attempts to unravel any relations that may exist between turbulent shear flows and statistical mechanics through a detailed numerical investigation in the simplest case where both can be well defined. The flow considered for the purpose is the two-dimensional (2D) temporal free shear layer with a velocity difference Delta U across it, statistically homogeneous in the streamwise direction (x) and evolving from a plane vortex sheet in the direction normal to it (y) in a periodic-in-x domain L x +/-infinity. Extensive computer simulations of the flow are carried out through appropriate initial-value problems for a ``vortex gas'' comprising N point vortices of the same strength (gamma = L Delta U/N) and sign. Such a vortex gas is known to provide weak solutions of the Euler equation. More than ten different initial-condition classes are investigated using simulations involving up to 32 000 vortices, with ensemble averages evaluated over up to 10(3) realizations and integration over 10(4)L/Delta U. The temporal evolution of such a system is found to exhibit three distinct regimes. In Regime I the evolution is strongly influenced by the initial condition, sometimes lasting a significant fraction of L/Delta U. Regime III is a long-time domain-dependent evolution towards a statistically stationary state, via ``violent'' and ``slow'' relaxations P.-H. Chavanis, Physica A 391, 3657 (2012)], over flow time scales of order 10(2) and 10(4)L/Delta U, respectively (for N = 400). The final state involves a single structure that stochastically samples the domain, possibly constituting a ``relative equilibrium.'' The vortex distribution within the structure follows a nonisotropic truncated form of the Lundgren-Pointin (L-P) equilibrium distribution (with negatively high temperatures; L-P parameter lambda close to -1). The central finding is that, in the intermediate Regime II, the spreading rate of the layer is universal over the wide range of cases considered here. The value (in terms of momentum thickness) is 0.0166 +/- 0.0002 times Delta U. Regime II, extensively studied in the turbulent shear flow literature as a self-similar ``equilibrium'' state, is, however, a part of the rapid nonequilibrium evolution of the vortex-gas system, which we term ``explosive'' as it lasts less than one L/Delta U. Regime II also exhibits significant values of N-independent two-vortex correlations, indicating that current kinetic theories that neglect correlations or consider them as O(1/N) cannot describe this regime. The evolution of the layer thickness in present simulations in Regimes I and II agree with the experimental observations of spatially evolving (3D Navier-Stokes) shear layers. Further, the vorticity-stream-function relations in Regime III are close to those computed in 2D Navier-Stokes temporal shear layers J. Sommeria, C. Staquet, and R. Robert, J. Fluid Mech. 233, 661 (1991)]. These findings suggest the dominance of what may be called the Kelvin-Biot-Savart mechanism in determining the growth of the free shear layer through large-scale momentum and vorticity dispersal.

A reexamination of some puzzling results in linearized elasticity

In this paper, we analyse three commonly discussed `flaws' of linearized elasticity theory and attempt to resolve them. The first `flaw' concerns cylindrically orthotropic material models. Since the work of Lekhnitskii (1968), there has been a growing body of work that continues to this day, that shows that infinite stresses arise with the use of a cylindrically orthotropic material model even in the case of linearized elasticity. Besides infinite stresses, interpenetration of matter is also shown to occur. These infinite stresses and interpenetration occur when the ratio of the circumferential Young modulus to the radial Young modulus is less than one. If the ratio is greater than one, then the stresses at the center of a spinning disk are found to be zero (recall that for an isotropic material model, the stresses are maximum at the center). Thus, the stresses go abruptly from a maximum value to a value of zero as the ratio is increased to a value even slightly above one! One of the explanations provided for this extremely anomalous behaviour is the failure of linearized elasticity to satisfy material frame-indifference. However, if this is the true cause, then the anomalous behaviour should also occur with the use of an isotropic material model, where, no such anomalies are observed. We show that the real cause of the problem is elsewhere and also show how these anomalies can be resolved. We also discuss how the formulation of linearized elastodynamics in the case of small deformations superposed on a rigid motion can be given in a succinct manner. Finally, we show how the long-standing problem of devising three compatibility relations instead of six can be resolved.

Cubic Sieve Congruence of the Discrete Logarithm Problem, and fractional part sequences

The Cubic Sieve Method for solving the Discrete Logarithm Problem in prime fields requires a nontrivial solution to the Cubic Sieve Congruence (CSC) x(3) equivalent to y(2)z (mod p), where p is a given prime number. A nontrivial solution must also satisfy x(3) not equal y(2)z and 1 <= x, y, z < p(alpha), where alpha is a given real number such that 1/3 < alpha <= 1/2. The CSC problem is to find an efficient algorithm to obtain a nontrivial solution to CSC. CSC can be parametrized as x equivalent to v(2)z (mod p) and y equivalent to v(3)z (mod p). In this paper, we give a deterministic polynomial-time (O(ln(3) p) bit-operations) algorithm to determine, for a given v, a nontrivial solution to CSC, if one exists. Previously it took (O) over tilde (p(alpha)) time in the worst case to determine this. We relate the CSC problem to the gap problem of fractional part sequences, where we need to determine the non-negative integers N satisfying the fractional part inequality {theta N} < phi (theta and phi are given real numbers). The correspondence between the CSC problem and the gap problem is that determining the parameter z in the former problem corresponds to determining N in the latter problem. We also show in the alpha = 1/2 case of CSC that for a certain class of primes the CSC problem can be solved deterministically in <(O)over tilde>(p(1/3)) time compared to the previous best of (O) over tilde (p(1/2)). It is empirically observed that about one out of three primes is covered by the above class. (C) 2013 Elsevier B.V. All rights reserved.

Partial Integrated Guidance and Control of Interceptors for High-Speed Ballistic Targets

A new partial integrated guidance and control design approach is proposed in this paper, which combines the benefits of both integrated guidance and control as well as the conventional guidance and control design philosophies. The proposed technique essentially operates in a two-loop structure. In the outer loop, an optimal guidance problem is formulated considering the nonlinear six degrees-of-freedom equation of motion of the interceptor. From this loop, the required pitch and yaw rates are generated by solving a nonlinear suboptimal guidance formulation in a computationally efficient manner while simultaneously assuring roll stabilization. Next, the inner loop tracks these outer loop body rate commands. This manipulation of the six degrees-of-freedom dynamics in both loops preserves the inherent time scale separation property between the translational and rotational dynamics, while retaining the philosophy of integrated guidance and control design as well. Because of this, the tuning process is quite straightforward and nontedious as well. Extensive six degrees-of-freedom simulations studies have been carried out, considering three-dimensional engagement geometry, to demonstrate the effectiveness of the proposed new design approach engaging high-speed ballistic targets. A variety of comparison studies have also been carried out to demonstrate the effectiveness of the proposed approach.

Accurate prediction of interfacial residues in two-domain proteins using evolutionary information: Implications for three-dimensional modeling

With the preponderance of multidomain proteins in eukaryotic genomes, it is essential to recognize the constituent domains and their functions. Often function involves communications across the domain interfaces, and the knowledge of the interacting sites is essential to our understanding of the structure-function relationship. Using evolutionary information extracted from homologous domains in at least two diverse domain architectures (single and multidomain), we predict the interface residues corresponding to domains from the two-domain proteins. We also use information from the three-dimensional structures of individual domains of two-domain proteins to train naive Bayes classifier model to predict the interfacial residues. Our predictions are highly accurate (approximate to 85%) and specific (approximate to 95%) to the domain-domain interfaces. This method is specific to multidomain proteins which contain domains in at least more than one protein architectural context. Using predicted residues to constrain domain-domain interaction, rigid-body docking was able to provide us with accurate full-length protein structures with correct orientation of domains. We believe that these results can be of considerable interest toward rational protein and interaction design, apart from providing us with valuable information on the nature of interactions. Proteins 2014; 82:1219-1234. (c) 2013 Wiley Periodicals, Inc.

Boundary perturbations and the Helmholtz equation in three dimensions

We propose an analytic perturbative scheme in the spirit of Lord Rayleigh's work for determining the eigenvalues of the Helmholtz equation in three dimensions inside an arbitrary boundary where the eigenfunction satisfies either the Dirichlet boundary condition or the Neumann boundary condition. Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to the best of our knowledge the formulation in three dimensions is proposed for the first time. In this novel prescription, we have expanded the arbitrary boundary in terms of spherical harmonics about an equivalent sphere and obtained perturbative closed-form solutions at each order for the problem in terms of corrections to the equivalent spherical boundary for both the boundary conditions. This formulation is in parallel with the standard time-independent Rayleigh-Schrodinger perturbation theory. The efficacy of the method is tested by comparing the perturbative values against the numerically calculated eigenvalues for spheroidal, superegg and superquadric shaped boundaries. It is shown that this perturbation works quite well even for wide departure from spherical shape and for higher excited states too. We believe this formulation would find applications in the field of quantum dots and acoustical cavities.

Long-Term Sustained Release of Salicylic Acid from Cross-Linked Biodegradable Polyester Induces a Reduced Foreign Body Response in Mice

There has been a continuous surge toward developing new biopolymers that exhibit better in vivo biocompatibility properties in terms of demonstrating a reduced foreign body response (FBR). One approach to mitigate the undesired FBR is to develop an implant capable of releasing anti-inflammatory molecules in a sustained manner over a long time period. Implants causing inflammation are also more susceptible to infection. In this article, the in vivo biocompatibility of a novel, biodegradable salicylic acid releasing polyester (SAP) has been investigated by subcutaneous implantation in a mouse model. The tissue response to SAP was compared with that of a widely used biodegradable polymer, poly(lactic acid-co-glycolic acid) (PLGA), as a control over three time points: 2, 4, and 16 weeks postimplantation. A long-term in vitro study illustrates a continuous, linear (zero order) release of salicylic acid with a cumulative mass percent release rate of 7.34 x 10(-4) h(-1) over similar to 1.5-17 months. On the basis of physicochemical analysis, surface erosion for SAP and bulk erosion for PLGA have been confirmed as their dominant degradation modes in vivo. On the basis of the histomorphometrical analysis of inflammatory cell densities and collagen distribution as well as quantification of proinflammatory cytokine levels (TNF-alpha and IL-1 beta), a reduced foreign body response toward SAP with respect to that generated by PLGA has been unambiguously established. The favorable in vivo tissue response to SAP, as manifest from the uniform and well-vascularized encapsulation around the implant, is consistent with the decrease in inflammatory cell density and increase in angiogenesis with time. The above observations, together with the demonstration of long-term and sustained release of salicylic acid, establish the potential use of SAP for applications in improved matrices for tissue engineering and chronic wound healing.

On the impact of a concave nosed axisymmetric body on a free surface

We report on an experimental study of the vertical impact of a concave nosed axisymmetric body on a free surface. Previous studies have shown that bodies with a convex nose, like a sphere, produce a well defined splash with a relatively large cavity behind the model. In contrast, we find that with a concave nose, there is hardly a splash and the cavity extent is greatly reduced. This may be explained by the fact that in the concave nosed case, the initial impact is between a confined air pocket and the free surface unlike in the convex nosed case. From measurements of the unsteady pressure in the concave nose portion, we show that in this case, the maximum pressures are significantly lower than the classically expected ``water hammer'' pressures and also lower than those generally measured on other geometries. Thus, the presence of an air pocket in the case of a concave nosed body adds an interesting dimension to the classical problem of impact of solid bodies on to a free surface. (C) 2015 AIP Publishing LLC.

Ultra-sensitive pressure dependence of bandgap of rutile-GeO2 revealed by many body perturbation theory

The reported values of bandgap of rutile GeO2 calculated by the standard density functional theory within local-density approximation (LDA)/generalized gradient approximation (GGA) show a wide variation (similar to 2 eV), whose origin remains unresolved. Here, we investigate the reasons for this variation by studying the electronic structure of rutile-GeO2 using many-body perturbation theory within the GW framework. The bandgap as well as valence bandwidth at Gamma-point of rutile phase shows a strong dependence on volume change, which is independent of bandgap underestimation problem of LDA/GGA. This strong dependence originates from a change in hybridization among O-p and Ge-(s and p) orbitals. Furthermore, the parabolic nature of first conduction band along X-Gamma-M direction changes towards a linear dispersion with volume expansion. (C) 2015 AIP Publishing LLC.