An Online Actor-Critic Algorithm with Function Approximation for Constrained Markov Decision Processes

We develop an online actor-critic reinforcement learning algorithm with function approximation for a problem of control under inequality constraints. We consider the long-run average cost Markov decision process (MDP) framework in which both the objective and the constraint functions are suitable policy-dependent long-run averages of certain sample path functions. The Lagrange multiplier method is used to handle the inequality constraints. We prove the asymptotic almost sure convergence of our algorithm to a locally optimal solution. We also provide the results of numerical experiments on a problem of routing in a multi-stage queueing network with constraints on long-run average queue lengths. We observe that our algorithm exhibits good performance on this setting and converges to a feasible point.

Numerical Investigation of Heat Transfer from a Two-Dimensional Sudden Expansion Flow Using Nanofluids

Laminar forced convection heat transfer from two-dimensional sudden expansion flow of different nanofluids is studied numerically. The governing equations are solved using the unsteady stream function-vorticity method. The effect of volume fraction of the nanoparticles and type of nanoparticles on heat transfer is examined and found to have a significant impact. Local and average Nusselt numbers are reported in connection with various nanoparticle, volume fraction, and Reynolds number for expansion ratio 2. The Nusselt number reaches peak values near the reattachment point and reaches asymptotic value in the downstream. Bottom wall eddy and volume fraction shows a significant impact on the average Nusselt number.

Spacelike pion form factor from analytic continuation and the onset of perturbative QCD

The factorization theorem for exclusive processes in perturbative QCD predicts the behavior of the pion electromagnetic form factor F(t) at asymptotic spacelike momenta t(= -Q(2)) < 0. We address the question of the onset energy using a suitable mathematical framework of analytic continuation, which uses as input the phase of the form factor below the first inelastic threshold, known with great precision through the Fermi-Watson theorem from pi pi elastic scattering, and the modulus measured from threshold up to 3 GeV by the BABAR Collaboration. The method leads to almost model-independent upper and lower bounds on the spacelike form factor. Further inclusion of the value of the charge radius and the experimental value at -2.45 GeV2 measured at JLab considerably increases the strength of the bounds in the region Q(2) less than or similar to 10 GeV2, excluding the onset of the asymptotic perturbative QCD regime for Q(2) < 7 GeV2. We also compare the bounds with available experimental data and with several theoretical models proposed for the low and intermediate spacelike region.

Radial infall of two compact objects: 2.5-post-Newtonian linear momentum flux and associated recoil

The loss rate of linear momentum from a binary system composed of compact objects (radially falling towards each other under mutual gravitational influence) has been investigated using the multipolar post-Minkowskian approach. The 2.5PN accurate analytical formula for the linear momentum flux is provided, in terms of the separation of the two objects, in harmonic coordinates, both for a finite and an infinite initial separation. The 2.5PN formulas for the linear momentum flux are finally used to estimate the recoil velocity accumulated during a premerger phase of the binary evolution.

Geometrically non-linear dynamics of composite four-bar mechanisms

This work intends to demonstrate the importance of a geometrically nonlinear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional non-linearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the non-linear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the non-linear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the non-linear, flexible four-bar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we identify and investigate a few four-bar mechanism problems where the cross-sectional non-linearities are significant in predicting better and critical system dynamic characteristics. This is carried out by varying stacking sequences (i.e. the arrangement of ply orientations within a laminate) and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form non-linear beam stiffness matrix. A numerical example is presented which illustrates the importance of 2-D cross-sectional non-linearities and the behavior of the system is also observed by using commercial software (I-DEAS + NASTRAN + ADAMS). (C) 2012 Elsevier Ltd. All rights reserved.

A Rare Phenoxido/Acetato/Azido Bridged Trinuclear and an Unprecedented Phenoxido/Azido Bridged One-Dimensional Polynuclear Nickel(II) Complexes: Synthesis, Crystal Structure, and Magnetic Properties with Theoretical Investigations on the Exchange Mechanism

The reaction of a tridentate Schiff base ligand HL (2-(3-dimethylaminopropylimino)-methyl]-phenol) with Ni(II) acetate or perchlorate salts in the presence of azide as coligand has led to two new Ni(II) complexes of formulas Ni3L2(OAc)(2)(mu(1,1)-N-3)(2)(H2O)(2)]center dot 2H(2)O (1) and Ni2L2(mu(1,1)-N-3) (mu(1,3)-N-3)](n)(2). Single crystal X-ray structures show that complex 1 is a linear trinuclear Ni(II) compound containing a mu(2)-phenwddo, an end-on (EO) azido and a syn-syn acetato bridge between the terminal and the central Ni(II) ions. Complex 2 can be viewed as a one-dimensional (1D) chain in which the triply bridged (di-mu(2)-phenoxido and EO azido) dimeric Ni-2 units are linked to each other in a zigzag pattern by a single end-to-end (EE) azido bridge. Variable-temperature magnetic susceptibility studies indicate the presence of moderate ferromagnetic exchange coupling in complex 1 with J value of 16.51(6) cm(-1). The magnetic behavior of 2 can be fitted in an alternating ferro- and antiferromagnetic model J(FM) = +34.2(2.8) cm(-1) and J(AF) = -21.6(1.1) cm(-1)] corresponding to the triple bridged dinuclear core and EE azido bridge respectively. Density functional theory (DFT) calculations were performed to corroborate the magnetic results of 1 and 2. The contributions of the different bridges toward magnetic interactions in both compounds have also been calculated.

VAM applied to dimensional reduction of non-linear hyperelastic plates

This work aims at dimensional reduction of non-linear isotropic hyperelastic plates in an asymptotically accurate manner. The problem is both geometrically and materially non-linear. The geometric non-linearity is handled by allowing for finite deformations and generalized warping while the material non-linearity is incorporated through hyperelastic material model. The development, based on the Variational Asymptotic Method (VAM) with moderate strains and very small thickness to shortest wavelength of the deformation along the plate reference surface as small parameters, begins with three-dimensional (3-D) non-linear elasticity and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a two-dimensional (2-D) plate analysis. Major contributions of this paper are derivation of closed-form analytical expressions for warping functions and stiffness coefficients and a set of recovery relations to express approximately the 3-D displacement, strain and stress fields. Consistent with the 2-D non-linear constitutive laws, 2-D plate theory and corresponding finite element program have been developed. Validation of present theory is carried out with a standard test case and the results match well. Distributions of 3-D results are provided for another test case. (c) 2012 Elsevier Ltd. All rights reserved.

3-MANIFOLD GROUPS, KÄHLER GROUPS AND COMPLEX SURFACES

Let G be a Kahler group admitting a short exact sequence 1 -> N -> G -> Q -> 1 where N is finitely generated. (i) Then Q cannot be non-nilpotent solvable. (ii) Suppose in addition that Q satisfies one of the following: (a) Q admits a discrete faithful non-elementary action on H-n for some n >= 2. (b) Q admits a discrete faithful non-elementary minimal action on a simplicial tree with more than two ends. (c) Q admits a (strong-stable) cut R such that the intersection of all conjugates of R is trivial. Then G is virtually a surface group. It follows that if Q is infinite, not virtually cyclic, and is the fundamental group of some closed 3-manifold, then Q contains as a finite index subgroup either a finite index subgroup of the three-dimensional Heisenberg group or the fundamental group of the Cartesian product of a closed oriented surface of positive genus and the circle. As a corollary, we obtain a new proof of a theorem of Dimca and Suciu in Which 3-manifold groups are Kahler groups? J. Eur. Math. Soc. 11 (2009) 521-528] by taking N to be the trivial group. If instead, G is the fundamental group of a compact complex surface, and N is finitely presented, then we show that Q must contain the fundamental group of a Seifert-fibered 3-manifold as a finite index subgroup, and G contains as a finite index subgroup the fundamental group of an elliptic fibration. We also give an example showing that the relation of quasi-isometry does not preserve Kahler groups. This gives a negative answer to a question of Gromov which asks whether Kahler groups can be characterized by their asymptotic geometry.

Highly luminescent and thermally stable lanthanide coordination polymers designed from 4-(dipyridin-2-yl)aminobenzoate: efficient energy transfer from Tb3+ to Eu3+ in a mixed lanthanide coordination compound

Herein, a new aromatic carboxylate ligand, namely, 4-(dipyridin-2-yl)aminobenzoic acid (HL), has been designed and employed for the construction of a series of lanthanide complexes (Eu3+ = 1, Tb3+ = 2, and Gd3+ = 3). Complexes of 1 and 2 were structurally authenticated by single-crystal X-ray diffraction and were found to exist as infinite 1D coordination polymers with the general formulas {Eu(L)(3)(H2O)(2)]}(n) (1) and {Tb(L)(3)(H2O)]center dot(H2O)}(n) (2). Both compounds crystallize in monoclinic space group C2/c. The photophysical properties demonstrated that the developed 4-(dipyridin-2-yl)aminobenzoate ligand is well suited for the sensitization of Tb3+ emission (Phi(overall) = 64%) thanks to the favorable position of the triplet state ((3)pi pi*) of the ligand the energy difference between the triplet state of the ligand and the excited state of Tb3+ (Delta E) = (3)pi pi* - D-5(4) = 3197 cm(-1)], as investigated in the Gd3+ complex. On the other hand, the corresponding Eu3+ complex shows weak luminescence efficiency (Phi(overall) = 7%) due to poor matching of the triplet state of the ligand with that of the emissive excited states of the metal ion (Delta E = (3)pi pi* - D-5(0) = 6447 cm(-1)). Furthermore, in the present work, a mixed lanthanide system featuring Eu3+ and Tb3+ ions with the general formula {Eu0.5Tb0.5(L)(3)(H2O)(2)]}(n) (4) was also synthesized, and the luminescent properties were evaluated and compared with those of the analogous single-lanthanide-ion systems (1 and 2). The lifetime measurements for 4 strongly support the premise that efficient energy transfer occurs between Tb3+ and Eu3+ in a mixed lanthanide system (eta = 86%).

Mechanistic Aspects for the Formation of Copper Dimer Bridged by Phosphonic Acid and Extending Its Dimensionality by Organic and Inorganic Linkers: Synthesis, Structural Characterization, Magnetic Properties, and Theoretical Studies

Six new copper metal complexes with formulas Cu(H2O)(2,2'-bpy) (H2L)](2) center dot H4L center dot 4 H2O (1), {Cu(H2O)(2,2'-bpy)-(H3L)}(2)(H2L)]center dot 2H(2)O (2), Cu(H2O)(1,10-phen)(H2L)](2)center dot 6H(2)O (3), Cu(2,2'-bpy)(H2L)](n)center dot nH(2)O (4), Cu(1,10-phen)(H2L)](n)center dot 3nH(2)O (5), and {Cu(2,2'-bpy)(MoO3)}(2)(L)](n)center dot 2nH(2)O (6) have been synthesized starting from p-xylylenediphosphonic acid (H4L) and 2,2'-bipyridine (2,2'-bpy) or 1,10-phenanthroline (1,10-phen) as secondary linkers and characterized by single crystal X-ray diffraction analysis, IR spectroscopy, and thermogravimetric (TG) analysis. All the complexes were synthesized by hydrothermal methods. A dinuclear motif (Cu-dimer) bridged by phosphonic acid represents a new class of simple building unit (SBU) in the construction of coordination architectures in metal phosphonate chemistry. The initial pH of the reaction mixture induced by the secondary linker plays an important role in the formation of the molecular phosphonates 1, 2, and 3. Temperature dependent hydrothermal synthesis of the compounds 1, 2, and 3 reveals the mechanism of the self assembly of the compounds based on the solubility of the phosphonic acid H4L. Two-dimensional coordination polymers 4, 5, and 6, which are formed by increasing the pH of the reaction mixture, comprise Cu-dimers as nodes, organic (H2L) and inorganic (Mo4O12) ligands as linkers. The void space-areas, created by the (4,4) connected nets in compounds 4 and 5, are occupied by lattice water molecules. Thus compounds 4 and 5 have the potential to accommodate guest species/molecules. Variable temperature magnetic studies of the compounds 3, 4, 5, and 6 reveal the antiferromagnetic interactions between the two Cu(II) ions in the eight membered ring, observed in their crystal structures. A density functional theory (DFT) calculation correlates the conformation of the Cu-dimer ring with the magnitude of the exchange parameter based on the torsion angle of the conformation.

Radial Deformation of Cylinders Due to Torsion

Classical literature on solid mechanics claims existence of radial deformation due to torsion but there is hardly any literature on analytic solutions capturing this phenomenon. This paper tries to solve this problem in an asymptotic sense using the variational asymptotic method (VAM). The method makes no ad hoc assumptions and hence asymptotic correctness is assured. The VAM splits the 3D elasticity problem into two parts: A 1D problem along the length of the cylinder which gives the twist and a 2D cross-sectional problem which gives the radial deformation. This enables closed form solutions, even for some complex problems. Starting with a hollow cylinder, made up of orthotropic but transversely isotropic material, the 3D problem has been formulated and solved analytically despite the presence of geometric nonlinearity. The general results have been specialized for particularly useful cases, such as solid cylinders and/or cylinders with isotropic material. DOI: 10.1115/1.4006803]

Optimal control problem for the time-dependent Kirchhoff-Love plate in a domain with rough boundary

In this paper, we study the asymptotic behavior of an optimal control problem for the time-dependent Kirchhoff-Love plate whose middle surface has a very rough boundary. We identify the limit problem which is an optimal control problem for the limit equation with a different cost functional.

A channel-aware, fast sub-channel to user assignment algorithm in OFDMA systems

Channel-aware assignment of sub-channels to users in the downlink of an OFDMA system demands extensive feedback of channel state information (CSI) to the base station. Since the feedback bandwidth is often very scarce, schemes that limit feedback are necessary. We develop a novel, low feedback splitting-based algorithm for assigning each sub-channel to its best user, i.e., the user with the highest gain for that sub-channel among all users. The key idea behind the algorithm is that, at any time, each user contends for the sub-channel on which it has the largest channel gain among the unallocated sub-channels. Unlike other existing schemes, the algorithm explicitly handles multiple access control aspects associated with the feedback of CSI. A tractable asymptotic analysis of a system with a large number of users helps design the algorithm. It yields 50% to 65% throughput gains compared to an asymptotically optimal one-bit feedback scheme, when the number of users is as small as 10 or as large as 1000. The algorithm is fast and distributed, and scales with the number of users.

Quadrature approximation properties of the spiral-phase quadrature transform

The notion of the 1-D analytic signal is well understood and has found many applications. At the heart of the analytic signal concept is the Hilbert transform. The problem in extending the concept of analytic signal to higher dimensions is that there is no unique multidimensional definition of the Hilbert transform. Also, the notion of analyticity is not so well under stood in higher dimensions. Of the several 2-D extensions of the Hilbert transform, the spiral-phase quadrature transform or the Riesz transform seems to be the natural extension and has attracted a lot of attention mainly due to its isotropic properties. From the Riesz transform, Larkin et al. constructed a vortex operator, which approximates the quadratures based on asymptotic stationary-phase analysis. In this paper, we show an alternative proof for the quadrature approximation property by invoking the quasi-eigenfunction property of linear, shift-invariant systems. We show that the vortex operator comes up as a natural consequence of applying this property. We also characterize the quadrature approximation error in terms of its energy as well as the peak spatial-domain error. Such results are available for 1-D signals, but their counter part for 2-D signals have not been provided. We also provide simulation results to supplement the analytical calculations.

Evaluation of strength of component-laminates in strip-based mechanisms

This paper deals with the evaluation of the component-laminate load-carrying capacity, i.e., to calculate the loads that cause the failure of the individual layers and the component-laminate as a whole in four-bar mechanism. The component-laminate load-carrying capacity is evaluated using the Tsai-Wu-Hahn failure criterion for various lay-ups. The reserve factor of each ply in the component-laminate is calculated by using the maximum resultant force and the maximum resultant moment occurring at different time steps at the joints of the mechanism. Here, all component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (strip-like beam). Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the non-linear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the non-linear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict more quickly and accurately than would otherwise be possible. Local 3-D stress, strain and displacement fields for representative sections in the component-bars are recovered, based on the stress resultants from the 1-D global beam analysis. A numerical example is presented which illustrates the failure of each component-laminate and the mechanism as a whole.