Scalar transport in diffusion flame wrapped up by an air and fuel side vortex

The present work involves a computational study of soot (chosen as a scalar which is a primary pollutant source) formation and transport in a laminar acetylene diffusion flame perturbed by a convecting line vortex. The topology of soot contours resulting from flame vortex interactions has been investigated. More soot was produced when vortex was introduced from the air side in comparison to the fuel side. Also, the soot topography was spatially more diffuse in the case of air side vortex. The computational model was found to be in good agreement with the experimental work previously reported in the literature. The computational simulation enabled a study of various parameters like temperature, equivalence ratio and temperature gradient affecting the soot production and transport. Temperatures were found to be higher in the case of air side vortex in contrast to the fuel side one. In case of fuel side vortex, abundance of fuel in the vortex core resulted in fuel-rich combustion zone in the core and a more discrete soot topography. Besides, the overall soot production was observed to be low in the fuel side vortex. However, for the air side vortex, air abundance in the core resulted in higher temperatures and greater soot production. Probability density functions (PDFs) have been introduced to investigate the spatiotemporal variation of soot yield and transport and their dependence on temperature and acetylene concentration from statistical view point. In addition, the effect of flame curvature on soot production is also studied. The regions convex to fuel stream side witnessed thicker soot layer. All numerical simulations have been carried out on Fluent 6.3.26. (C) 2013 Elsevier Ltd. All rights reserved.

On the Erdos-Szekeres n-interior-point problem

The n-interior-point variant of the Erdos Szekeres problem is the following: for every n, n >= 1, does there exist a g(n) such that every point set in the plane with at least g(n) interior points has a convex polygon containing exactly n interior points. The existence of g(n) has been proved only for n <= 3. In this paper, we show that for any fixed r >= 2, and for every n >= 5, every point set having sufficiently large number of interior points and at most r convex layers contains a subset with exactly n interior points. We also consider a relaxation of the notion of convex polygons and show that for every n, n >= 1, any point set with at least n interior points has an almost convex polygon (a simple polygon with at most one concave vertex) that contains exactly n interior points. (C) 2013 Elsevier Ltd. All rights reserved.

On piercing (pseudo)lines and boxes

We say a family of geometric objects C has (l;k)-property if every subfamily C0C of cardinality at most lisk- piercable. In this paper we investigate the existence of g(k;d)such that if any family of objects C in Rd has the (g(k;d);k)-property, then C is k-piercable. Danzer and Gr̈ unbaum showed that g(k;d)is infinite for fami-lies of boxes and translates of centrally symmetric convex hexagons. In this paper we show that any family of pseudo-lines(lines) with (k2+k+ 1;k)-property is k-piercable and extend this result to certain families of objects with discrete intersections. This is the first positive result for arbitrary k for a general family of objects. We also pose a relaxed ver-sion of the above question and show that any family of boxes in Rd with (k2d;k)-property is 2dk- piercable.

Classification calibration dimension for general multiclass losses

We study consistency properties of surrogate loss functions for general multiclass classification problems, defined by a general loss matrix. We extend the notion of classification calibration, which has been studied for binary and multiclass 0-1 classification problems (and for certain other specific learning problems), to the general multiclass setting, and derive necessary and sufficient conditions for a surrogate loss to be classification calibrated with respect to a loss matrix in this setting. We then introduce the notion of \emph{classification calibration dimension} of a multiclass loss matrix, which measures the smallest `size' of a prediction space for which it is possible to design a convex surrogate that is classification calibrated with respect to the loss matrix. We derive both upper and lower bounds on this quantity, and use these results to analyze various loss matrices. In particular, as one application, we provide a different route from the recent result of Duchi et al.\ (2010) for analyzing the difficulty of designing `low-dimensional' convex surrogates that are consistent with respect to pairwise subset ranking losses. We anticipate the classification calibration dimension may prove to be a useful tool in the study and design of surrogate losses for general multiclass learning problems.

Curvature based mobility analysis and form closure of smooth planar curves with multiple contacts

This paper presents a simple second-order, curvature based mobility analysis of planar curves in contact. The underlying theory deals with penetration and separation of curves with multiple contacts, based on relative configuration of osculating circles at points of contact for a second-order rotation about each point of the plane. Geometric and analytical treatment of mobility analysis is presented for generic as well as special contact geometries. For objects with a single contact, partitioning of the plane into four types of mobility regions has been shown. Using point based composition operations based on dual-number matrices, analysis has been extended to computationally handle multiple contacts scenario. A novel color coded directed line has been proposed to capture the contact scenario. Multiple contacts mobility is obtained through intersection of the mobility half-spaces. It is derived that mobility region comprises a pair of unbounded or a single bounded convex polygon. The theory has been used for analysis and synthesis of form closure configurations, revolute and prismatic kinematic pairs. (C) 2013 Elsevier Ltd. All rights reserved.

Scalable sequential alternating proximal methods for sparse structural SVMs and CRFs

Structural Support Vector Machines (SSVMs) and Conditional Random Fields (CRFs) are popular discriminative methods used for classifying structured and complex objects like parse trees, image segments and part-of-speech tags. The datasets involved are very large dimensional, and the models designed using typical training algorithms for SSVMs and CRFs are non-sparse. This non-sparse nature of models results in slow inference. Thus, there is a need to devise new algorithms for sparse SSVM and CRF classifier design. Use of elastic net and L1-regularizer has already been explored for solving primal CRF and SSVM problems, respectively, to design sparse classifiers. In this work, we focus on dual elastic net regularized SSVM and CRF. By exploiting the weakly coupled structure of these convex programming problems, we propose a new sequential alternating proximal (SAP) algorithm to solve these dual problems. This algorithm works by sequentially visiting each training set example and solving a simple subproblem restricted to a small subset of variables associated with that example. Numerical experiments on various benchmark sequence labeling datasets demonstrate that the proposed algorithm scales well. Further, the classifiers designed are sparser than those designed by solving the respective primal problems and demonstrate comparable generalization performance. Thus, the proposed SAP algorithm is a useful alternative for sparse SSVM and CRF classifier design.

Sensitivity of Water Dynamics to Biologically Significant Surfaces of Monomeric Insulin: Role of Topology and Electrostatic Interactions

In addition to the biologically active monomer of the protein insulin circulating in human blood, the molecule also exists in dimeric and hexameric forms that are used as storage. The insulin monomer contains two distinct surfaces, namely, the dimer forming surface (DFS) and the hexamer forming surface (HFS), that are specifically designed to facilitate the formation of the dimer and the hexamer, respectively. In order to characterize the structural and dynamical behavior of interfacial water molecules near these two surfaces (DFS and HFS), we performed atomistic molecular dynamics simulations of insulin with explicit water. Dynamical characterization reveals that the structural relaxation of the hydrogen bonds formed between the residues of DFS and the interfacial water molecules is faster than those formed between water and that of the HFS. Furthermore, the residence times of water molecules in the protein hydration layer for both the DFS and HFS are found to be significantly higher than those for some of the other proteins studied so far, such as HP-36 and lysozyme. In particular, we find that more structured water molecules, with higher residence times (similar to 300-500 ps), are present near HFS than those near DFS. A significant slowing down is observed in the decay of associated rotational auto time correlation functions of O-H bond vector of water in the vicinity of HFS. The surface topography and the arrangement of amino acid residues work together to organize the water molecules in the hydration layer in order to provide them with a preferred orientation. HFS having a large polar solvent accessible surface area and a convex extensive nonpolar region, drives the surrounding water molecules to acquire predominantly an outward H-atoms directed, clathrate-like structure. In contrast, near the DFS, the surrounding water molecules acquire an inward H-atoms directed orientation owing to the flat curvature of hydrophobic surface and the interrupted hydrophilic residual alignment. We have followed escape trajectory of several such quasi-bound water molecules from both the surfaces that reveal the significant differences between the two hydration layers.

Static shear strength and fatigue life of refill friction stir spot welded AA 6061-T6 sheets

This study was aimed at evaluating the static shear strength and fatigue properties of the newly developed refilled friction stir spot welded AA 6061-T6 joints. The keyhole, the process disadvantage of conventional friction stir spot welding, was refilled successfully, using an additional filler plate, with specially designed tools. Two different tool profiles, namely, convex and concave, were used for the refilling process. Sound and defect free joints were obtained by the refilling process. Joints refilled with convex tools showed better static shear strength than those with the concave ones. The variation of microhardness in different regions of the weld was analysed. Fatigue tests were conducted on the lap shear specimens at a stress ratio of R=0.1. The optical micrographs of the welds after fatigue failure in both the conventional and refilled processes were examined to study the fatigue crack propagation and failure modes.

Optimal sequential wireless relay placement on a random lattice path

Our work is motivated by impromptu (or ``as-you-go'') deployment of wireless relay nodes along a path, a need that arises in many situations. In this paper, the path is modeled as starting at the origin (where there is the data sink, e.g., the control center), and evolving randomly over a lattice in the positive quadrant. A person walks along the path deploying relay nodes as he goes. At each step, the path can, randomly, either continue in the same direction or take a turn, or come to an end, at which point a data source (e.g., a sensor) has to be placed, that will send packets to the data sink. A decision has to be made at each step whether or not to place a wireless relay node. Assuming that the packet generation rate by the source is very low, and simple link-by-link scheduling, we consider the problem of sequential relay placement so as to minimize the expectation of an end-to-end cost metric (a linear combination of the sum of convex hop costs and the number of relays placed). This impromptu relay placement problem is formulated as a total cost Markov decision process. First, we derive the optimal policy in terms of an optimal placement set and show that this set is characterized by a boundary (with respect to the position of the last placed relay) beyond which it is optimal to place the next relay. Next, based on a simpler one-step-look-ahead characterization of the optimal policy, we propose an algorithm which is proved to converge to the optimal placement set in a finite number of steps and which is faster than value iteration. We show by simulations that the distance threshold based heuristic, usually assumed in the literature, is close to the optimal, provided that the threshold distance is carefully chosen. (C) 2014 Elsevier B.V. All rights reserved.

Small strong epsilon nets

Let P be a set of n points in R-d. A point x is said to be a centerpoint of P if x is contained in every convex object that contains more than dn/d+1 points of P. We call a point x a strong centerpoint for a family of objects C if x is an element of P is contained in every object C is an element of C that contains more than a constant fraction of points of P. A strong centerpoint does not exist even for halfspaces in R-2. We prove that a strong centerpoint exists for axis-parallel boxes in Rd and give exact bounds. We then extend this to small strong epsilon-nets in the plane. Let epsilon(S)(i) represent the smallest real number in 0, 1] such that there exists an epsilon(S)(i)-net of size i with respect to S. We prove upper and lower bounds for epsilon(S)(i) where S is the family of axis-parallel rectangles, halfspaces and disks. (C) 2014 Elsevier B.V. All rights reserved.

Mixed finite elements for electromagnetic analysis

The occurrence of spurious solutions is a well-known limitation of the standard nodal finite element method when applied to electromagnetic problems. The two commonly used remedies that are used to address this problem are (i) The addition of a penalty term with the penalty factor based on the local dielectric constant, and which reduces to a Helmholtz form on homogeneous domains (regularized formulation); (ii) A formulation based on a vector and a scalar potential. Both these strategies have some shortcomings. The penalty method does not completely get rid of the spurious modes, and both methods are incapable of predicting singular eigenvalues in non-convex domains. Some non-zero spurious eigenvalues are also predicted by these methods on non-convex domains. In this work, we develop mixed finite element formulations which predict the eigenfrequencies (including their multiplicities) accurately, even for nonconvex domains. The main feature of the proposed mixed finite element formulation is that no ad-hoc terms are added to the formulation as in the penalty formulation, and the improvement is achieved purely by an appropriate choice of finite element spaces for the different variables. We show that the formulation works even for inhomogeneous domains where `double noding' is used to enforce the appropriate continuity requirements at an interface. For two-dimensional problems, the shape of the domain can be arbitrary, while for the three-dimensional ones, with our current formulation, only regular domains (which can be nonconvex) can be modeled. Since eigenfrequencies are modeled accurately, these elements also yield accurate results for driven problems. (C) 2014 Elsevier Ltd. All rights reserved.

An Eigen Approach to Transmit Beamforming in Wireless Networks With Single Antenna Receivers

In this paper, we propose an eigen framework for transmit beamforming for single-hop and dual-hop network models with single antenna receivers. In cases where number of receivers is not more than three, the proposed Eigen approach is vastly superior in terms of ease of implementation and computational complexity compared with the existing convex-relaxation-based approaches. The essential premise is that the precoding problems can be posed as equivalent optimization problems of searching for an optimal vector in the joint numerical range of Hermitian matrices. We show that the latter problem has two convex approximations: the first one is a semi-definite program that yields a lower bound on the solution, and the second one is a linear matrix inequality that yields an upper bound on the solution. We study the performance of the proposed and existing techniques using numerical simulations.

On strong centerpoints

Let P be a set of n points in R-d and F be a family of geometric objects. We call a point x is an element of P a strong centerpoint of P w.r.t..F if x is contained in all F is an element of F that contains more than cn points of P, where c is a fixed constant. A strong centerpoint does not exist even when F is the family of halfspaces in the plane. We prove the existence of strong centerpoints with exact constants for convex polytopes defined by a fixed set of orientations. We also prove the existence of strong centerpoints for abstract set systems with bounded intersection. (C) 2014 Elsevier B.V. All rights reserved.

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.

GLOBAL REGISTRATION OF MULTIPLE POINT CLOUDS USING SEMIDEFINITE PROGRAMMING

Consider N points in R-d and M local coordinate systems that are related through unknown rigid transforms. For each point, we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the N points (up to a rigid transform) from such measurements comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics. The least-squares formulation of this problem, although nonconvex, has a well-known closed-form solution when M = 2 (based on the singular value decomposition (SVD)). However, no closed-form solution is known for M >= 3. In this paper, we demonstrate how the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP). By setting up connections between the uniqueness of this SDP and results from rigidity theory, we prove conditions for exact and stable recovery for the SDP relaxation. In particular, we prove that the SDP relaxation can guarantee recovery under more adversarial conditions compared to earlier proposed spectral relaxations, and we derive error bounds for the registration error incurred by the SDP relaxation. We also present results of numerical experiments on simulated data to confirm the theoretical findings. We empirically demonstrate that (a) unlike the spectral relaxation, the relaxation gap is mostly zero for the SDP (i.e., we are able to solve the original nonconvex least-squares problem) up to a certain noise threshold, and (b) the SDP performs significantly better than spectral and manifold-optimization methods, particularly at large noise levels.