Finite element simulation of BAW propagation in inhomogeneous plate due to piezoelectric actuation

A set of finite elements (FEs) is formulated to analyze wave propagation through inhomogeneous material when subjected to mechanical, thermal loading or piezo-electric actuation. Elastic, thermal and electrical properties of the materials axe allowed to vary in length and thickness direction. The elements can act both as sensors and actuators. These elements are used to model wave propagation in functionally graded materials (FGM) and the effect of inhomogeneity in the wave is demonstrated. Further, a surface acoustic wave (SAW) device is modeled and wave propagation due to piezo-electric actuation from interdigital transducers (IDTs) is studied.

On the Compressibility of non-Abelian-Group Sources in a Distributed Source Coding Setting

We consider the problem of compression of a non-Abelian source.This is motivated by the problem of distributed function computation,where it is known that if one is only interested in computing a function of several sources, then one can often improve upon the compression rate required by the Slepian-Wolf bound. Let G be a non-Abelian group having center Z(G). We show here that it is impossible to compress a source with symbols drawn from G when Z(G) is trivial if one employs a homomorphic encoder and a typical-set decoder.We provide achievable upper bounds on the minimum rate required to compress a non-Abelian group with non-trivial center. Also, in a two source setting, we provide achievable upper bounds for compression of any non-Abelian group, using a non-homomorphic encoder.

Structure and Bonding in Stannadiphospholes and their Dianions SnC(2)P(2)R(2)(m) (R=H, tBu m=0,-2): A Comparative Study with C(5)H(5)(+) and C(5)H(5)(-) Analogues

The potential energy surfaces of both neutral and dianionic SnC(2)P(2)R(2) (R=H, tBu) ring systems have been explored at the B3PW91/LANL2DZ (Sn) and 6-311 + G* (other atoms) level. In the neutral isomers the global minimum is a nido structure in which a 1,2-diphosphocyclobutadiene ring (1,2-DPCB) is capped by the Sn. Interestingly, the structure established by Xray diffraction analysis, for R=tBu, is a 1,3-DPCB ring capped by Sn and it is 2.4 kcal mol(-1) higher in energy than the 1,2-DPCB ring isomer. This is possibly related to the kinetic stability of the 1,3-DPCB ring, which might originate from the synthetic precursor ZrCp(2)tBu(2)C(2)P(2). In the case of the dianionic isomers we observe only a 6 pi-electron aromatic structure as the global minimum, similarly to the cases of our previously reported results with other types of heterodiphospholes.([1,4,19]) The existence of large numbers of cluster-type isomers in neutral and 6 pi-planar structures in the dianions SnC(2)P(2)R(2)(2-) (R=H, tBu) is due to 3D aromaticity in neutral clusters and to 2D pi aromaticity of the dianionic rings. Relative energies of positional isomers mainly depend on: 1) the valency and coordination number of the Sn centre, 2) individual bond strengths, and 3) the steric effect of tBu groups. A comparison of neutral stannadiphospholes with other structurally related C(5)H(5)(+) analogues indicates that Sn might be a better isolobal analogue to P(+) than to BH or CH(+). The variation in global minima in these C(5)H(5)(+) analogues is due to characteristic features such as 1) the different valencies of C, B, P and Sn, 2) the electron deficiency of B, 3) weaker p pi-p pi bonding by P and Sn atoms, and 4) the tendency of electropositive elements to donate electrons to nido clusters. Unlike the C5H5+ systems, all C(5)H(5)(-) analogues have 6 pi-planar aromatic structures as global minima. The differences in the relative ordering of the positional isomers and ligating properties are significant and depend on 1) the nature of the pi orbitals involved, and 2) effective overlap of orbitals.

Real-time Computer Simulation of Three Dimensional Elastostatics using the Finite Point Method

Real-time simulation of deformable solids is essential for some applications such as biological organ simulations for surgical simulators. In this work, deformable solids are approximated to be linear elastic, and an easy and straight forward numerical technique, the Finite Point Method (FPM), is used to model three dimensional linear elastostatics. Graphics Processing Unit (GPU) is used to accelerate computations. Results show that the Finite Point Method, together with GPU, can compute three dimensional linear elastostatic responses of solids at rates suitable for real-time graphics, for solids represented by reasonable number of points.

Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength (lambda) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density rho similar to k(F)(3) undergoes a change at a critical value, lambda(T) approximate to k(F) [Phys. Rev. B 84, 014512 ( 2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-1/2 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing.. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling lambda. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

An embedded grid adaptation strategy for unstructured data based finite volume computations

A grid adaptation strategy for unstructured data based codes, employing a combination of hexahedral and prismatic elements, generalizable to tetrahedral and pyramidal elements has been developed.

Interacting fermions in synthetic non-Abelian gauge fields

Generation and study of synthetic gauge fields has enhanced the possibility of using cold atom systems as quantum emulators of condensed matter Hamiltonians. In this article we describe the physics of interacting spin -1/2 fermions in synthetic non-Abelian gauge fields which induce a Rashba spin-orbit interaction on the motion of the fermions. We show that the fermion system can evolve to a Bose-Einstein condensate of a novel boson which we call rashbon. The rashbon-rashbon interaction is shown to be independent of the interaction between the constituent fermions. We also show that spin-orbit coupling can help enhancing superfluid transition temperature of weak superfluids to the order of Fermi temperature. A non-Abelian gauge field, when used in conjunction with another potential, can generate interesting Hamiltonians such as that of a magnetic monopole.

The X-C center dot center dot center dot Y (X = O/F, Y = O/S/F/Cl/Br/N/P) `carbon bond' and hydrophobic interactions

While the tetrahedral face of methane has an electron rich centre and can act as a hydrogen bond acceptor, substitution of one of its hydrogens with some electron withdrawing group (such as -F/OH) can make the opposite face electron deficient. Electrostatic potential calculations confirm this and high level quantum calculations show interactions between the positive face of methanol/methyl fluoride and electron rich centers of other molecules such as H2O. Analysis of the wave functions of atoms in molecules shows the presence of an unusual C center dot center dot center dot Y interaction, which could be called `carbon bonding'. NBO analysis and vibrational frequency shifts confirm the presence of this interaction. Given the properties of alkyl groups bonded to electronegative elements in biological molecules, such interactions could play a significant role, which is yet to be recognized. This and similar interactions could give an enthalpic contribution to what is called the `hydrophobic interactions'.

On interference alignment for symmetrically connected interference networks with line of sight channels at finite powers

In this work, interference alignment for a class of Gaussian interference networks with general message demands, having line of sight (LOS) channels, at finite powers is considered. We assume that each transmitter has one independent message to be transmitted and the propagation delays are uniformly distributed between 0 and (L - 1) (L >; 0). If receiver-j, j ∈{1,2,..., J}, requires the message of transmitter-i, i ∈ {1, 2, ..., K}, we say (i, j) belongs to a connection. A class of interference networks called the symmetrically connected interference network is defined as a network where, the number of connections required at each transmitter-i is equal to ct for all i and the number of connections required at each receiver-j is equal to cr for all j, for some fixed positive integers ct and cr. For such networks with a LOS channel between every transmitter and every receiver, we show that an expected sum-spectral efficiency (in bits/sec/Hz) of at least K/(e+c1-1)(ct+1) (ct/ct+1)ct log2 (1+min(i, j)∈c|hi, j|2 P/WN0) can be achieved as the number of transmitters and receivers tend to infinity, i.e., K, J →∞ where, C denotes the set of all connections, hij is the channel gain between transmitter-i and receiver-j, P is the average power constraint at each transmitter, W is the bandwidth and N0 W is the variance of Gaussian noise at each receiver. This means that, for an LOS symmetrically connected interference network, at any finite power, the total spectral efficiency can grow linearly with K as K, J →∞. This is achieved by extending the time domain interference alignment scheme proposed by Grokop et al. for the k-user Gaussian interference channel to interference networks.

Remarkable Regioisomer Control in the Hydrogel Formation from a Two-Component Mixture of Pyridine-End Oligo(p-phenylenevinylene)s and N-Decanoyl-L-alanine

N-Decanoyl-L-alanine (DA) was mixed with either colorless 4,4-bipyridine (BP) or various derivatives such as chromogenic oligo(p-phenylenevinylene) (OPV) functionalized with isomeric pyridine termini in specific molar ratios. This mixtures form salt-type gels in a water/ethanol (2:1, v/v) mixture. The gelation properties of these two-component mixtures could be modulated by variation of the position of the N atom of the end pyridyl groups in OPVs. The presence of acid-base interactions in the self-assembly of these two-component systems leading to gelation was probed in detail by using stoichiometry-dependent UV/Vis and FTIR spectroscopy. Furthermore, temperature-dependent UV/Vis and fluorescence spectroscopy clearly demonstrated a J-type aggregation mode of these gelator molecules during the sol-to-gel transition process. Morphological features and the arrangement of the molecules in the gels were examined by using scanning electron microscopy (SEM), atomic force microscopy (AFM), and X-ray diffraction (XRD) techniques. Calculation of the length of each molecular system by energy minimization in its extended conformation and comparison with the XRD patterns revealed that this class of gelator molecules adopts lamellar organizations. Rheological properties of these two-component systems provided clear evidence that the flow behavior could be modulated by varying the acid/amine ratio. Polarized optical microscopy (POM), differential scanning calorimetry (DSC), and XRD results revealed that the solid-phase behavior of such two-component mixtures (acid/base=2:1) varied significantly upon changing the proton-acceptor part from BP to OPV. Interestingly, the XRD pattern of these acid/base mixtures after annealing at their associated isotropic temperature was significantly different from that of their xerogels.

Prediction of the stiffness of nanoclay-polypropylene composites using a monte carlo finite element analysis approach

The present work deals with the prediction of stiffness of an Indian nanoclay-reinforced polypropylene composite (that can be termed as a nanocomposite) using a Monte Carlo finite element analysis (FEA) technique. Nanocomposite samples are at first prepared in the laboratory using a torque rheometer for achieving desirable dispersion of nanoclay during master batch preparation followed up with extrusion for the fabrication of tensile test dog-bone specimens. It has been observed through SEM (scanning electron microscopy) images of the prepared nanocomposite containing a given percentage (3–9% by weight) of the considered nanoclay that nanoclay platelets tend to remain in clusters. By ascertaining the average size of these nanoclay clusters from the images mentioned, a planar finite element model is created in which nanoclay groups and polymer matrix are modeled as separate entities assuming a given homogeneous distribution of the nanoclay clusters. Using a Monte Carlo simulation procedure, the distribution of nanoclay is varied randomly in an automated manner in a commercial FEA code, and virtual tensile tests are performed for computing the linear stiffness for each case. Values of computed stiffness modulus of highest frequency for nanocomposites with different nanoclay contents correspond well with the experimentally obtained measures of stiffness establishing the effectiveness of the present approach for further applications.