f Gravity and gravitational singularities

TRAUTMAN has postulated1 that the usual space−time singularity occurring in classical cosmological models and in the gravitational collapse of massive objects could be averted if intrinsic spin effects are incorporated into general relativity by adding torsion terms to the usual Einstein field equations, that is through the Einstein−Cartan theory. Invoking a primordial magnetic field for aligning all the individual nuclear spins he shows that his universe consisting of 1080 aligned neutrons collapses to a minimum radius of the order of 1 cm with a corresponding matter density of 1055 g cm-3.

f Gravity and gravitational singularities

TRAUTMAN has postulated1 that the usual space−time singularity occurring in classical cosmological models and in the gravitational collapse of massive objects could be averted if intrinsic spin effects are incorporated into general relativity by adding torsion terms to the usual Einstein field equations, that is through the Einstein−Cartan theory. Invoking a primordial magnetic field for aligning all the individual nuclear spins he shows that his universe consisting of 1080 aligned neutrons collapses to a minimum radius of the order of 1 cm with a corresponding matter density of 1055 g cm-3.

Quantum capacitance in bilayer graphene nanoribbon

We address a physically based analytical model of quantum capacitance (C-Q) in a bilayer graphene nanoribbon (BGN) under the application of an external longitudinal static bias. We demonstrate that as the gap (Delta) about the Dirac point increases, a phenomenological population inversion of the carriers in the two sets of subbands occurs. This results in a periodic and composite oscillatory behavior in the C-Q with the channel potential, which also decreases with increase in Delta. We also study the quantum size effects on the C-Q, which signatures heavy spatial oscillations due to the occurrence of van Hove singularities in the total density-of-states function of both the sets of subbands. All the mathematical results as derived in this paper converge to the corresponding well-known solution of graphene under certain limiting conditions and this compatibility is an indirect test of our theoretical formalism. (C) 2012 Elsevier By. All rights reserved.

Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane

We examine the large-order behavior of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from renormalization-group invariance. The expansion is first written as an effective series in powers of the one-loop coupling, and its leading singularities in the Borel plane are shown to be identical to those of the standard ``contour-improved'' expansion. Applying the technique of conformal mappings for the analytic continuation in the Borel plane, we define a class of improved expansions, which implement both the renormalization-group invariance and the knowledge about the large-order behavior of the series. Detailed numerical studies of specific models for the Adler function indicate that the new expansions have remarkable convergence properties up to high orders. Using these expansions for the determination of the strong coupling from the hadronic width of the tau lepton we obtain, with a conservative estimate of the uncertainty due to the nonperturbative corrections, alpha(s)(M-tau(2)) = 0.3189(-0.0151)(+0.0173), which translates to alpha(s)(M-Z(2)) = 0.1184(-0.0018)(+0.0021). DOI: 10.1103/PhysRevD.87.014008

Time resolved terahertz spectroscopy of low frequency electronic resonances and optical pump-induced terahertz photoconductivity in reduced graphene oxide membrane

Towards ultrafast optoelectronic applications of single and a few layer reduced graphene oxide (RGO), we study time domain terahertz spectroscopy and optical pump induced changes in terahertz conductivity of self-supported RGO membrane in the spectral window of 0.5-3.5 THz. The real and imaginary parts of conductivity spectra clearly reveal low frequency resonances, attributed to the energy gaps due to the van Hove singularities in the density of states flanking the Dirac points arising due to the relative rotation of the graphene layers. Further, optical pump induced terahertz conductivity is positive, pointing to the dominance of intraband scattering processes. The relaxation dynamics of the photo-excited carriers consists of three cooling pathways: the faster (similar to 450 fs) one due to optical phonon emission followed by disorder mediated large momentum and large energy acoustic phonon emission with a time constant of a few ps (called the super-collision mechanism) and a very large time (similar to 100 ps) arising from the deep trap states. The frequency dependence of the dynamic conductivity at different delay times is analyzed in term of Drude-Smith model. (C) 2014 Published by Elsevier Ltd.

Rotating Beams and Nonrotating Beams With Shared Eigenpair

In this paper, we look for rotating beams whose eigenpair (frequency and mode-shape) is the same as that of uniform nonrotating beams for a particular mode. It is found that, for any given mode, there exist flexural stiffness functions (FSFs) for which the jth mode eigenpair of a rotating beam, with uniform mass distribution, is identical to that of a corresponding nonrotating uniform beam with the same length and mass distribution. By putting the derived FSF in the finite element analysis of a rotating cantilever beam, the frequencies and mode-shapes of a nonrotating cantilever beam are obtained. For the first mode, a physically feasible equivalent rotating beam exists, but for higher modes, the flexural stiffness has internal singularities. Strategies for addressing the singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test-functions for rotating beam codes and for targeted destiffening of rotating beams.

Dynamics after a sweep through a quantum critical point

The coherent quantum evolution of a one-dimensional many-particle system after slowly sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and nonintegrable regimes. It is known from previous work that universal power laws of the sweep rate appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two different scaling behaviors of the entanglement entropy and a relaxation that is power law in time rather than exponential. The final state of evolution after the quench is not characterized by any effective temperature, and the Loschmidt echo converges algebraically for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.

Singularity and controllability analysis of parallel manipulators and closed-loop mechanisms

This paper presents a study of kinematic and force singularities in parallel manipulators and closed-loop mechanisms and their relationship to accessibility and controllability of such manipulators and closed-loop mechanisms, Parallel manipulators and closed-loop mechanisms are classified according to their degrees of freedom, number of output Cartesian variables used to describe their motion and the number of actuated joint inputs. The singularities in the workspace are obtained by considering the force transformation matrix which maps the forces and torques in joint space to output forces and torques ill Cartesian space. The regions in the workspace which violate the small time local controllability (STLC) and small time local accessibility (STLA) condition are obtained by deriving the equations of motion in terms of Cartesian variables and by using techniques from Lie algebra.We show that for fully actuated manipulators when the number ofactuated joint inputs is equal to the number of output Cartesian variables, and the force transformation matrix loses rank, the parallel manipulator does not meet the STLC requirement. For the case where the number of joint inputs is less than the number of output Cartesian variables, if the constraint forces and torques (represented by the Lagrange multipliers) become infinite, the force transformation matrix loses rank. Finally, we show that the singular and non-STLC regions in the workspace of a parallel manipulator and closed-loop mechanism can be reduced by adding redundant joint actuators and links. The results are illustrated with the help of numerical examples where we plot the singular and non-STLC/non-STLA regions of parallel manipulators and closed-loop mechanisms belonging to the above mentioned classes. (C) 2000 Elsevier Science Ltd. All rights reserved.

An Efficient Robust Algorithm for the Surface-Potential Calculation of Independent DG MOSFET

Although the recently proposed single-implicit-equation-based input voltage equations (IVEs) for the independent double-gate (IDG) MOSFET promise faster computation time than the earlier proposed coupled-equations-based IVEs, it is not clear how those equations could be solved inside a circuit simulator as the conventional Newton-Raphson (NR)-based root finding method will not always converge due to the presence of discontinuity at the G-zero point (GZP) and nonremovable singularities in the trigonometric IVE. In this paper, we propose a unique algorithm to solve those IVEs, which combines the Ridders algorithm with the NR-based technique in order to provide assured convergence for any bias conditions. Studying the IDG MOSFET operation carefully, we apply an optimized initial guess to the NR component and a minimized solution space to the Ridders component in order to achieve rapid convergence, which is very important for circuit simulation. To reduce the computation budget further, we propose a new closed-form solution of the IVEs in the near vicinity of the GZP. The proposed algorithm is tested with different device parameters in the extended range of bias conditions and successfully implemented in a commercial circuit simulator through its Verilog-A interface.

Electrochemical tuning and mechanical resilience of single-wall carbon nanotubes

Single-wall carbon nanotubes (SWNTs) are fascinating systems exhibiting many novel physical properties. In this paper, we give a brief review of the structural, electronic, vibrational, and mechanical properties of carbon nanotubes. In situ resonance Raman scattering of SWNTs investigated under electrochemical biasing demonstrates that the intensity of the radial breathing mode varies significantly in a nonmonotonic manner as a function of the cathodic bias voltage, but does not change appreciably under anodic bias. These results can be quantitatively understood in terms of the changes in the energy gaps between the 1 D van Hove singularities in the electron density of states, arising possibly due to the alterations in the overlap integral of pi bonds between the p-orbitals of the adjacent carbon atoms. In the second part of this paper, we review our high-pressure X-ray diffraction results, which show that the triangular lattice of the carbon nanotube bundles continues to persist up to similar to10 GPa. The lattice is seen to relax just before the phase transformation, which is observed at similar to10 GPa. Further, our results display the reversibility of the 2D lattice symmetry even after compression up to 13 GPa well beyond the 5 GPa value observed recently. These experimental results explicitly validate the predicted remarkable mechanical resilience of the nanotubes.

Rotating beams and non-rotating beams with shared eigenpair for pinned-free boundary condition

In this paper we look for a rotating beam, with pinned-free boundary conditions, whose eigenpair (frequency and mode-shape) is same as that of a uniform non-rotating beam for a particular mode. It is seen that for any given mode, there exists a flexural stiffness function (FSF) for which the ith mode eigenpair of a rotating beam with uniform mass distribution, is identical to that of a corresponding non-rotating beam with same length and mass distribution. Inserting these derived FSF's in a finite element code for a rotating pinned-free beam, the frequencies and mode shapes of a non-rotating pinned-free beam are obtained. For the first mode, a physically realistic equivalent rotating beam is possible, but for higher modes, the FSF has internal singularities. Strategies for addressing these singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test functions for rotating beam codes and also for targeted destiffening of rotating beams.

Wheeler-Feynman absorber revisited: a useful technique to calculate decay rates and lifetimes in small scale optical systems

The Wheeler-Feynman (WF) absorber theory of radiation though no more of interest in explaining self interaction of an electron, can be very useful in today's research in small scale optical systems. The significance of the WF absorber is the use of time-symmetrical solution of Maxwell's equations as opposed to only the retarded solution. The radiative coupling of emitters to nano wires in the near field and change in their lifetimes due to small mode volume enclosures have been elucidated with the retarded solutions before. These solutions have also been shown to agree with quantum electrodynamics, thus allowing for classical electromagnetic approaches in such problems. It is here assumed that the radiative coupling of the emitter with a body is in proportion to its contribution to the classical force of radiative reaction as derived in the WF absorber theory. Representing such nano structures as a partial WF absorber acting on the emitter makes the computations considerably easier than conventional electromagnetic solutions for full boundary conditions.

Isolated singularities of polyharmonic operator in even dimension

We consider the equation Delta(2)u = g(x, u) >= 0 in the sense of distribution in Omega' = Omega\textbackslash {0} where u and -Delta u >= 0. Then it is known that u solves Delta(2)u = g(x, u) + alpha delta(0) - beta Delta delta(0), for some nonnegative constants alpha and beta. In this paper, we study the existence of singular solutions to Delta(2)u = a(x) f (u) + alpha delta(0) - beta Delta delta(0) in a domain Omega subset of R-4, a is a nonnegative measurable function in some Lebesgue space. If Delta(2)u = a(x) f (u) in Omega', then we find the growth of the nonlinearity f that determines alpha and beta to be 0. In case when alpha = beta = 0, we will establish regularity results when f (t) <= Ce-gamma t, for some C, gamma > 0. This paper extends the work of Soranzo (1997) where the author finds the barrier function in higher dimensions (N >= 5) with a specific weight function a(x) = |x|(sigma). Later, we discuss its analogous generalization for the polyharmonic operator.

Shock propagation in gas dynamics: explicit form of higher order compatibility conditions

With the use of tensor analysis and the method of singular surfaces, an infinite system of equations can be derived to study the propagation of curved shocks of arbitrary strength in gas dynamics. The first three of these have been explicitly given here. This system is further reduced to one involving scalars only. The choice of dependent variables in the infinite system is quite important, it leads to coefficients free from singularities for all values of the shock strength.