Cavitation in brittle metallic glasses - Effects of stress state and distributed weak zones

Experimental studies and atomistic simulations have shown that brittle metallic glasses fail by a cavitation mechanism whose origin has been traced to the presence of intrinsic atomic density fluctuations which give rise to weak zones with reduced yield strength. It has been shown recently through continuum analysis that the presence of these zones can lower the cavitation stress considerably under equibiaxial loading. The objective of the present work is to study the effect of the applied stress state on the cavitation behavior of such a heterogeneous plastic solid with distributed weak zones. To this end, 2D plane strain finite element simulations are performed by subjecting a unit cell containing a weak zone to different (biaxiality) stress ratios. The volume fraction and yield strength of the weak zone are varied over a wide range. The results show that unlike in a homogeneous plastic solid, the cavitation stress of the heterogeneous aggregate does not reduce appreciably as the stress ratio decreases from unity when the yield strength of the weak zone is low. It is found that a non-dimensional parameter characterizing the stress state prevailing in the weak zone and its yield properties uniquely control the cavitation stress. The nature of cavitation bifurcation may change from unstable bifurcation to the left at sufficiently low stress ratio to one involving snap cavitation at high stress ratio. (C) 2014 Elsevier Ltd. All rights reserved.

Monopoles, Dirac operator, and index theory for fuzzy SU(3) / (U(1) x U(1))

The intersection of the ten-dimensional fuzzy conifold Y-F(10) with S-F(5) x S-F(5) is the compact eight-dimensional fuzzy space X-F(8). We show that X-F(8) is (the analogue of) a principal U(1) x U(1) bundle over fuzzy SU(3) / U(1) x U(1)) ( M-F(6)). We construct M-F(6) using the Gell-Mann matrices by adapting Schwinger's construction. The space M-F(6) is of relevance in higher dimensional quantum Hall effect and matrix models of D-branes. Further we show that the sections of the monopole bundle can be expressed in the basis of SU(3) eigenvectors. We construct the Dirac operator on M-F(6) from the Ginsparg-Wilson algebra on this space. Finally, we show that the index of the Dirac operator correctly reproduces the known results in the continuum.

Formation of Prestellar Cores via Non-Isothermal Gas Fragmentation

Sheet-like clouds are common in turbulent gas and perhaps form via collisions between turbulent gas flows. Having examined the evolution of an isothermal shocked slab in an earlier contribution, in this work we follow the evolution of a sheet-like cloud confined by (thermal) pressure and gas in it is allowed to cool. The extant purpose of this endeavour is to study the early phases of core-formation. The observed evolution of this cloud supports the conjecture that molecular clouds themselves are three-phase media (comprising viz. a stable cold and warm medium, and a third thermally unstable medium), though it appears, clouds may evolve in this manner irrespective of whether they are gravitationally bound. We report, this sheet fragments initially due to the growth of the thermal instability (TI) and some fragments are elongated, filament-like. Subsequently, relatively large fragments become gravitationally unstable and sub-fragment into smaller cores. The formation of cores appears to be a three stage process: first, growth of the TI leads to rapid fragmentation of the slab; second, relatively small fragments acquire mass via gas-accretion and/or merger and third, sufficiently massive fragments become susceptible to the gravitational instability and sub-fragment to form smaller cores. We investigate typical properties of clumps (and smaller cores) resulting from this fragmentation process. Findings of this work support the suggestion that the weak velocity field usually observed in dense clumps and smaller cores is likely seeded by the growth of dynamic instabilities. Simulations were performed using the smooth particle hydrodynamics algorithm.

Optimal Linear Glauber Model

Contrary to the actual nonlinear Glauber model, the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate () in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

Soft-spring wall based non-periodic boundary conditions for non-equilibrium molecular dynamics of dense fluids

Non-equilibrium molecular dynamics (MD) simulations require imposition of non-periodic boundary conditions (NPBCs) that seamlessly account for the effect of the truncated bulk region on the simulated MD region. Standard implementation of specular boundary conditions in such simulations results in spurious density and force fluctuations near the domain boundary and is therefore inappropriate for coupled atomistic-continuum calculations. In this work, we present a novel NPBC model that relies on boundary atoms attached to a simple cubic lattice with soft springs to account for interactions from particles which would have been present in an untruncated full domain treatment. We show that the proposed model suppresses the unphysical fluctuations in the density to less than 1% of the mean while simultaneously eliminating spurious oscillations in both mean and boundary forces. The model allows for an effective coupling of atomistic and continuum solvers as demonstrated through multiscale simulation of boundary driven singular flow in a cavity. The geometric flexibility of the model enables straightforward extension to nonplanar complex domains without any adverse effects on dynamic properties such as the diffusion coefficient. (c) 2015 AIP Publishing LLC.

Negative hyperconjugation and red-, blue- or zero-shift in X-Z center dot center dot center dot Y complexes

A generalized explanation is provided for the existence of the red-and blue-shifting nature of X-Z bonds (Z = H, halogens, chalcogens, pnicogens, etc.) in X-Z center dot center dot center dot Y complexes based on computational studies on a selected set of weakly bonded complexes and analysis of existing literature data. The additional electrons and orbitals available on Z in comparison to H make for dramatic differences between the H-bond and the rest of the Z-bonds. The nature of the X-group and its influence on the X-Z bond length in the parent X-Z molecule largely controls the change in the X-Z bond length on X-Z center dot center dot center dot Y bond formation; the Y-group usually influences only the magnitude of the effects controlled by X. The major factors which control the X-Z bond length change are: (a) negative hyperconjugative donation of electron density from X-group to X-Z sigma* antibonding molecular orbital (ABMO) in the parent X-Z, (b) induced negative hyperconjugation from the lone pair of electrons on Z to the antibonding orbitals of the X-group, and (c) charge transfer (CT) from the Y-group to the X-Z sigma* orbital. The exchange repulsion from the Y-group that shifts partial electron density at the X-Z sigma* ABMO back to X leads to blue-shifting and the CT from the Y-group to the sigma* ABMO of X-Z leads to red-shifting. The balance between these two opposing forces decides red-, zero- or blue-shifting. A continuum of behaviour of X-Z bond length variation is inevitable in X-Z center dot center dot center dot Y complexes.

Simulations using meshfree methods

In this paper, attempt is made to solve a few problems using the Polynomial Point Collocation Method (PPCM), the Radial Point Collocation Method (RPCM), Smoothed Particle Hydrodynamics (SPH), and the Finite Point Method (FPM). A few observations on the accuracy of these methods are recorded. All the simulations in this paper are three dimensional linear elastostatic simulations, without accounting for body forces.

PERCOLATION ON THE INFORMATION-THEORETICALLY SECURE SIGNAL TO INTERFERENCE RATIO GRAPH

We consider a continuum percolation model consisting of two types of nodes, namely legitimate and eavesdropper nodes, distributed according to independent Poisson point processes in R-2 of intensities lambda and lambda(E), respectively. A directed edge from one legitimate node A to another legitimate node B exists provided that the strength of the signal transmitted from node A that is received at node B is higher than that received at any eavesdropper node. The strength of the signal received at a node from a legitimate node depends not only on the distance between these nodes, but also on the location of the other legitimate nodes and an interference suppression parameter gamma. The graph is said to percolate when there exists an infinitely connected component. We show that for any finite intensity lambda(E) of eavesdropper nodes, there exists a critical intensity lambda(c) < infinity such that for all lambda > lambda(c) the graph percolates for sufficiently small values of the interference parameter. Furthermore, for the subcritical regime, we show that there exists a lambda(0) such that for all lambda < lambda(0) <= lambda(c) a suitable graph defined over eavesdropper node connections percolates that precludes percolation in the graphs formed by the legitimate nodes.

Holographic charge transport in non commutative gauge theories

In this paper, based on the holographic techniques, we explore the hydrodynamics of charge diffusion phenomena in non commutative N = 4 SYM plasma at strong coupling. In our analysis, we compute the R charge diffusion rates both along commutative as well as the non commutative coordinates of the brane. It turns out that unlike the case for the shear viscosity, the DC conductivity along the non commutative direction of the brane differs significantly from that of its cousin corresponding to the commutative direction of the brane. Such a discrepancy however smoothly goes away in the limit of the vanishing non commutativity.

A micropolar cohesive damage model for delamination of composites

A micropolar cohesive damage model for delamination of composites is proposed. The main idea is to embed micropolarity, which brings an additional layer of kinematics through the micro-rotation degrees of freedom within a continuum model to account for the micro-structural effects during delamination. The resulting cohesive model, describing the modified traction separation law, includes micro-rotational jumps in addition to displacement jumps across the interface. The incorporation of micro-rotation requires the model to be supplemented with physically relevant material length scale parameters, whose effects during delamination of modes I and II are brought forth using numerical simulations appropriately supported by experimental evidences. (C) 2015 Elsevier Ltd. All rights reserved.

Anomalous Viscosity Reduction and Hydrodynamic Interactions of Polymeric Nanocolloids in Polymers

One of the central dogmas of fluid physics is the no-slip boundary condition, whose validity has come under scrutiny, especially in the fields of micro and nanofluidics. Although various studies show the violation of the no-slip condition its effect on flow of colloidal particles in viscous media has been rarely explored. Here we report unusually large reduction of effective viscosity experienced by polymeric nano colloids moving through a highly viscous and confined polymer, well above its glass transition temperature. The extent of reduction in effective interface viscosity increases with decreasing temperature and polymer film thickness. Concomitant with the reduction in effective viscosity we also observe apparent divergence of the wave vector dependent hydrodynamic interaction function of these colloids with an anomalous power law exponent of similar to 2 at the lowest temperatures and film thickness studied. Such strong hydrodynamic interactions are not expected for polymeric colloidal motion in polymer melts. We suggest hydrodynamics, especially slip present at the colloid-polymer interface which determines the observed reduction in interface viscosity and presence of strong hydrodynamic interactions.

COMPOSITE AND MULTI-SCALE COMPLIANT MECHANISMS FOR MANIPULATION AND MECHANICAL CHARACTERIZATION

In this paper, we integrate two or more compliant mechanisms to get enhanced functionality for manipulating and mechanically characterizing the grasped objects of varied size (cm to sub-mm), stiffness (1e5 to 10 N/m), and materials (cement to biological cells). The concepts of spring-lever (SL) model, stiffness maps, and non-dimensional kinetoelastostatic maps are used to design composite and multi-scale compliant mechanisms. Composite compliant mechanisms comprise two or more different mechanisms within a single elastic continuum while multi-scale ones possess the additional feature of substantial difference in the sizes of the mechanisms that are combined into one. We present three applications: (i) a composite compliant device to measure the failure load of the cement samples; (ii) a composite multi-scale compliant gripper to measure the bulk stiffness of zebrafish embryos; and (iii) a compliant gripper combined with a negative-stiffness element to reduce the overall stiffness. The prototypes of all three devices are made and tested. The cement sample needed a breaking force of 22.5 N; the zebrafish embryo is found to have bulk stiffness of about 10 N/m; and the stiffness of a compliant gripper was reduced by 99.8 % to 0.2 N/m.

Variations in the cyclotron resonant scattering features during 2011 outburst of 4U 0115+63

We study the variations in the Cyclotron Resonant Scattering Feature (CRSF) during 2011 outburst of the high mass X-ray binary 4U 0115+63 using observations performed with Suzaku, RXTE, Swift and INTEGRAL satellites. The wide-band spectral data with low-energy coverage allowed us to characterize the broad-band continuum and detect the CRSFs. We find that the broad-band continuum is adequately described by a combination of a low temperature (kT similar to 0.8 keV) blackbody and a power law with high energy cutoff (E-cut similar to 5.4 keV) without the need for a broad Gaussian at similar to 10 keV as used in some earlier studies. Though winds from the companion can affect the emission from the neutron star at low energies (<3 keV), the blackbody component shows a significant presence in our continuum model. We report evidence for the possible presence of two independent sets of CRSFs with fundamentals at similar to 11 and similar to 15 keV. These two sets of CRSFs could arise from spatially distinct emitting regions. We also find evidence for variations in the line equivalent widths, with the 11 keV CRSF weakening and the 15 keV line strengthening with decreasing luminosity. Finally, we propose that the reason for the earlier observed anticorrelation of line energy with luminosity could be due to modelling of these two independent line sets (similar to 11 and similar to 15 keV) as a single CRSF.

DOES THE CHEMOTHERMAL INSTABILITY HAVE ANY ROLE IN THE FRAGMENTATION OF PRIMORDIAL GAS

The collapse of the primordial gas in the density regime similar to 10(8)-10(10) cm(-3) is controlled by the three-body H-2 formation process, in which the gas can cool faster than free-fall time-a condition proposed as the chemothermal instability. We investigate how the heating and cooling rates are affected during the rapid transformation of atomic to molecular hydrogen. With a detailed study of the heating and cooling balance in a 3D simulation of Pop III collapse, we follow the chemical and thermal evolution of the primordial gas in two dark matter minihalos. The inclusion of sink particles in modified Gadget-2 smoothed particle hydrodynamics code allows us to investigate the long-term evolution of the disk that fragments into several clumps. We find that the sum of all the cooling rates is less than the total heating rate after including the contribution from the compressional heating (pdV). The increasing cooling rate during the rapid increase of the molecular fraction is offset by the unavoidable heating due to gas contraction. We conclude that fragmentation occurs because H-2 cooling, the heating due to H-2 formation and compressional heating together set a density and temperature structure in the disk that favors fragmentation, not the chemothermal instability.

Anomalous transport at weak coupling

We evaluate the contribution of chiral fermions in d = 2, 4, 6, chiral bosons, a chiral gravitino like theory in d = 2 and chiral gravitinos in d = 6 to all the leading parity odd transport coefficients at one loop. This is done by using finite temperature field theory to evaluate the relevant Kubo formulae. For chiral fermions and chiral bosons the relation between the parity odd transport coefficient and the microscopic anomalies including gravitational anomalies agree with that found by using the general methods of hydrodynamics and the argument involving the consistency of the Euclidean vacuum. For the gravitino like theory in d = 2 and chiral gravitinos in d = 6, we show that relation between the pure gravitational anomaly and parity odd transport breaks down. From the perturbative calculation we clearly identify the terms that contribute to the anomaly polynomial, but not to the transport coefficient for gravitinos. We also develop a simple method for evaluating the angular integrals in the one loop diagrams involved in the Kubo formulae. Finally we show that charge diffusion mode of an ideal 2 dimensional Weyl gas in the presence of a finite chemical potential acquires a speed, which is equal to half the speed of light.