Generalized Model Predictive Static Programming and Angle-Constrained Guidance of Air-to-Ground Missiles

A new generalized model predictive static programming technique is presented for rapidly solving a class of finite-horizon nonlinear optimal control problems with hard terminal constraints. Two key features for its high computational efficiency include one-time backward integration of a small-dimensional weighting matrix dynamics, followed bya static optimization formulation that requires only a static Lagrange multiplier to update the control history. It turns out that under Euler integration and rectangular approximation of finite integrals it is equivalent to the existing model predictive static programming technique. In addition to the benchmark double integrator problem, usefulness of the proposed technique is demonstrated by solving a three-dimensional angle-constrained guidance problem for an air-to-ground missile, which demands that the missile must meet constraints on both azimuth and elevation angles at the impact point in addition to achieving near-zero miss distance, while minimizing the lateral acceleration demand throughout its flight path. Simulation studies include maneuvering ground targets along with a first-order autopilot lag. Comparison studies with classical augmented proportional navigation guidance and modern general explicit guidance lead to the conclusion that the proposed guidance is superior to both and has a larger capture region as well.

Logarithmic corrections to extremal black hole entropy in N=2, 4 and 8 supergravity

We compute the logarithmic correction to black hole entropy about exponentially suppressed saddle points of the Quantum Entropy Function corresponding to Z(N) orbifolds of the near horizon geometry of the extremal black hole under study. By carefully accounting for zero mode contributions we show that the logarithmic contributions for quarter-BPS black holes in N = 4 supergravity and one-eighth BPS black holes in N = 8 supergravity perfectly match with the prediction from the microstate counting. We also find that the logarithmic contribution for half-BPS black holes in N = 2 supergravity depends non-trivially on the Z(N) orbifold. Our analysis draws heavily on the results we had previously obtained for heat kernel coefficients on Z(N) orbifolds of spheres and hyperboloids in arXiv:1311.6286 and we also propose a generalization of the Plancherel formula to Z(N) orbifolds of hyperboloids to an expression involving the Harish-Chandra character of sl (2, R), a result which is of possible mathematical interest.

A meshless adaptive multiscale method for fracture

The paper presents a multiscale method for crack propagation. The coarse region is modelled by the differential reproducing kernel particle method. Fracture in the coarse scale region is modelled with the Phantom node method. A molecular statics approach is employed in the fine scale where crack propagation is modelled naturally by breaking of bonds. The triangular lattice corresponds to the lattice structure of the (111) plane of an FCC crystal in the fine scale region. The Lennard-Jones potential is used to model the atom-atom interactions. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively refined and coarsened as the crack propagates. The centro symmetry parameter is used to detect the crack tip location. The method is implemented in two dimensions. The results are compared to pure atomistic simulations and show excellent agreement. (C) 2014 Elsevier B. V. All rights reserved.

Multiscale Symmetry Detection in Scalar Fields by Clustering Contours

The complexity in visualizing volumetric data often limits the scope of direct exploration of scalar fields. Isocontour extraction is a popular method for exploring scalar fields because of its simplicity in presenting features in the data. In this paper, we present a novel representation of contours with the aim of studying the similarity relationship between the contours. The representation maps contours to points in a high-dimensional transformation-invariant descriptor space. We leverage the power of this representation to design a clustering based algorithm for detecting symmetric regions in a scalar field. Symmetry detection is a challenging problem because it demands both segmentation of the data and identification of transformation invariant segments. While the former task can be addressed using topological analysis of scalar fields, the latter requires geometry based solutions. Our approach combines the two by utilizing the contour tree for segmenting the data and the descriptor space for determining transformation invariance. We discuss two applications, query driven exploration and asymmetry visualization, that demonstrate the effectiveness of the approach.

Universal correction to higher spin entanglement entropy

We consider conformal field theories in 1 + 1 dimensions with W-algebra symmetries, deformed by a chemical potential mu for the spin-three current. We show that the order mu(2) correction to the Renyi and entanglement entropies of a single interval in the deformed theory, on the infinite spatial line and at finite temperature, is universal. The correction is completely determined by the operator product expansion of two spin-three currents, and by the expectation values of the stress tensor, its descendants and its composites, evaluated on the n-sheeted Riemann surface branched along the interval. This explains the recently found agreement of the order mu(2) correction across distinct free field CFTs and higher spin black hole solutions holographically dual to CFTs with W symmetry.

Logarithmic corrections to twisted indices from the quantum entropy function

We compute logarithmic corrections to the twisted index B-6(g) in four-dimensional N = 4 and N = 8 string theories using the framework of the Quantum Entropy Function. We find that these vanish, matching perfectly with the large-charge expansion of the corresponding microscopic expressions.

Heat kernels on the AdS(2) cone and logarithmic corrections to extremal black hole entropy

We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N = 4 vector multiplet about a Z(N) orbifold of the near-horizon geometry of quarter-BPS black holes in N = 4 supergravity. We find that this vanishes, matching perfectly with the prediction from the microstate counting. We also discuss possible generalisations of our heat kernel results to higher-spin fields over ZN orbifolds of higher-dimensional spheres and hyperboloids.

Relative entropy in higher spin holography

We examine relative entropy in the context of the higher spin/CFT duality. We consider 3D bulk configurations in higher spin gravity which are dual to the vacuum and a high temperature state of a CFT with W-algebra symmetries in the presence of a chemical potential for a higher spin current. The relative entropy between these states is then evaluated using the Wilson line functional for holographic entanglement entropy. In the limit of small entangling intervals, the relative entropy should vanish for a generic quantum system. We confirm this behavior by showing that the difference in the expectation values of the modular Hamiltonian between the states matches with the difference in the entanglement entropy in the short-distance regime. Additionally, we compute the relative entropy of states corresponding to smooth solutions in the SL(2, Z) family with respect to the vacuum.

Driving force of water entry into hydrophobic channels of carbon nanotubes: entropy or energy?

Spontaneous entry of water molecules inside single-wall carbon nanotubes (SWCNTs) has been confirmed by both simulations and experiments. Using molecular dynamics simulations, we have studied the thermodynamics of filling of a (6,6) carbon nanotube in a temperature range from 273 to 353K and with different strengths of the nanotube-water interaction. From explicit energy and entropy calculations using the two-phase thermodynamics method, we have presented a thermodynamic understanding of the filling behaviour of a nanotube. We show that both the energy and the entropy of transfer decrease with increasing temperature. On the other hand, scaling down the attractive part of the carbon-oxygen interaction results in increased energy of transfer while the entropy of transfer increases slowly with decreasing the interaction strength. Our results indicate that both energy and entropy favour water entry into (6,6) SWCNTs. Our results are compared with those of several recent studies of water entry into carbon nanotubes.

Analysis of Entropy Generation During Mixed Convective Heat Transfer of Nanofluids Past a Rotating Circular Cylinder

The entropy generation due to mixed convective heat transfer of nanofluids past a rotating circular cylinder placed in a uniform cross stream is investigated via streamline upwind Petrov-Galerkin based finite element method. Nanosized copper (Cu) particles suspended in water are used with Prandtl number (Pr)=6.9. The computations are carried out at a representative Reynolds number (Re) of 100. The dimensionless cylinder rotation rate, a, is varied between 0 and 2. The range of nanoparticle volume fractions (phi) considered is 0 <= phi <= 5%. Effect of aiding buoyancy is brought about by considering two fixed values of the Richardson number (Ri) as 0.5 and 1.0. A new model for predicting the effective viscosity and thermal conductivity of dilute suspensions of nanoscale colloidal particles is presented. The model addresses the details of the agglomeration-deagglomeration in tune with the pertinent variations in the effective particulate dimensions, volume fractions, as well as the aggregate structure of the particulate system. The total entropy generation is found to decrease sharply with cylinder rotation rates and nanoparticle volume fractions. Increase in nanoparticle agglomeration shows decrease in heat transfer irreversibility. The Bejan number falls sharply with increase in alpha and phi.

Renormalized entanglement entropy for BPS black branes

We compute the renormalized entanglement entropy (REE) for BPS black solutions in N = 2, four-dimensional gauged supergravity. We find that this quantity decreases monotonically with the size of the entangling region until it reaches a critical point, then increases and approaches the entropy density of the brane. This behavior can be understood as a consequence of the renormalized entanglement entropy being driven by two competing factors, namely, entanglement and the mixedness of the black brane. In the UV, entanglement dominates, whereas in the IR, the mixedness takes over.

A note on D1-D5 entropy and geometric quantization

We quantize the space of 2-charge fuzzballs in IIB supergravity on K3. The resulting entropy precisely matches the D1-D5 black hole entropy, including a specific numerical coefficient. A partial match (ie., a smaller coefficient) was found by Rychkov a decade ago using the Lunin-Mathur subclass of solutions - we use a simple observation to generalize his approach to the full moduli space of K3 fuzzballs, filling a small gap in the literature.

Effect of processing route on phase stability in equiatomic multicomponent Ti20Fe20Ni20Co20Cu20 high entropy alloy

The evolution of microstructure and phase formation in equiatomic Ti20Fe20Ni20Co20Cu20 high entropy alloy synthesised by conventional arc melting followed with suction casting and ball milling with spark plasma sintering route is distinctly different. The cast microstructure exhibits one body centre cubic and two face centre cubic high entropy phases based on titanium, cobalt and copper respectively along with a eutectic containing Ti2Ni type Laves phase. On the contrary, spinodal decomposed microstructure consisting of cobalt and copper solid solution is obtained in the sintered sample. However, long term annealing of cast sample at 950 degrees C reveals a eutectoid transformation with different phases than the cast sample. The aforementioned observations are discussed using CALPHAD thermodynamical approach and available literature.

Conformal perturbation theory and higher spin entanglement entropy on the torus

We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential mu, the deformation is related at high temperatures to a higher spin black hole in hs0] theory on AdS(3) spacetime. We calculate the order mu(2) corrections to the single interval Renyi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order mu(2) corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Renyi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Renyi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large-N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems.

Generalized Spatial Modulation in Large-Scale Multiuser MIMO Systems

Generalized spatial modulation (GSM) uses n(t) transmit antenna elements but fewer transmit radio frequency (RF) chains, n(rf). Spatial modulation (SM) and spatial multiplexing are special cases of GSM with n(rf) = 1 and n(rf) = n(t), respectively. In GSM, in addition to conveying information bits through n(rf) conventional modulation symbols (for example, QAM), the indices of the n(rf) active transmit antennas also convey information bits. In this paper, we investigate GSM for large-scale multiuser MIMO communications on the uplink. Our contributions in this paper include: 1) an average bit error probability (ABEP) analysis for maximum-likelihood detection in multiuser GSM-MIMO on the uplink, where we derive an upper bound on the ABEP, and 2) low-complexity algorithms for GSM-MIMO signal detection and channel estimation at the base station receiver based on message passing. The analytical upper bounds on the ABEP are found to be tight at moderate to high signal-to-noise ratios (SNR). The proposed receiver algorithms are found to scale very well in complexity while achieving near-optimal performance in large dimensions. Simulation results show that, for the same spectral efficiency, multiuser GSM-MIMO can outperform multiuser SM-MIMO as well as conventional multiuser MIMO, by about 2 to 9 dB at a bit error rate of 10(-3). Such SNR gains in GSM-MIMO compared to SM-MIMO and conventional MIMO can be attributed to the fact that, because of a larger number of spatial index bits, GSM-MIMO can use a lower-order QAM alphabet which is more power efficient.