214,842 research outputs found
Phase Retrieval by Linear Algebra
The null vector method, based on a simple linear algebraic concept, is
proposed as a solution to the phase retrieval problem.
In the case with complex Gaussian random measurement matrices, a
non-asymptotic error bound is derived, yielding an asymptotic regime of
accurate approximation comparable to that for the spectral vector method
Phase diagram of two-species Bose-Einstein condensates in an optical lattice
The exact macroscopic wave functions of two-species Bose-Einstein condensates
in an optical lattice beyond the tight-binding approximation are studied by
solving the coupled nonlinear Schrodinger equations. The phase diagram for
superfluid and insulator phases of the condensates is determined analytically
according to the macroscopic wave functions of the condensates, which are seen
to be traveling matter waves.Comment: 13 pages, 2 figure
An advanced meshless method for time fractional diffusion equation
Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations
A node-based smoothed conforming point interpolation method (NS-CPIM) for elasticity problems
This paper formulates a node-based smoothed conforming point interpolation method (NS-CPIM) for solid mechanics. In the proposed NS-CPIM, the higher order conforming PIM shape functions (CPIM) have been constructed to produce a continuous and piecewise quadratic displacement field over the whole problem domain, whereby the smoothed strain field was obtained through smoothing operation over each smoothing domain associated with domain nodes. The smoothed Galerkin weak form was then developed to create the discretized system equations. Numerical studies have demonstrated the following good properties: NS-CPIM (1) can pass both standard and quadratic patch test; (2) provides an upper bound of strain energy; (3) avoid the volumetric locking; (4) provides the higher accuracy than those in the node-based smoothed schemes of the original PIMs
Stability of jammed packings I: the rigidity length scale
In 2005, Wyart et al. (Europhys. Lett., 72 (2005) 486) showed that the low
frequency vibrational properties of jammed amorphous sphere packings can be
understood in terms of a length scale, called l*, that diverges as the system
becomes marginally unstable. Despite the tremendous success of this theory, it
has been difficult to connect the counting argument that defines l* to other
length scales that diverge near the jamming transition. We present an alternate
derivation of l* based on the onset of rigidity. This phenomenological approach
reveals the physical mechanism underlying the length scale and is relevant to a
range of systems for which the original argument breaks down. It also allows us
to present the first direct numerical measurement of l*.Comment: 8 pages, 5 figure
Investigation of a novel elastic-mechanical wheel transmission under light duty conditions
A novel 'Elastic Engagement and Friction Coupled' (EEFC) mechanical transmission has been proposed recently in which the power is transmitted through elastic tines on the surfaces of the driving and driven wheels. This study introduces new variations of EEFC mechanical wheel transmission ( broadly emulating a gear-pair) with small contact areas for use under light duty conditions. Because a drive of this type inevitably has a strong statistical component, theoretical analysis of the geometrical and mechanical relationships has been attempted by using linear modeling and empirical weightings. Several simple forms of the EEFC wheel transmission are tested under limiting ( slip) conditions for transmission force and transmission coefficients against normal load. Normalized standard deviation of these parameters is used to summarize noise performance. Models and experiments are in reasonable agreement, suggesting that the model parameters reflect important design considerations. EEFC transmissions appear well suited to force regimes of a few tenths of a newton and to have potential for use in, for example, millimetre-scale robots
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Robust filtering for stochastic genetic regulatory networks with time-varying delay
This is the post print version of the article. The official published version can be obtained from the link - Copyright 2009 Elsevier LtdThis paper addresses the robust filtering problem for a class of linear genetic regulatory networks (GRNs) with stochastic disturbances, parameter uncertainties and time delays. The parameter uncertainties are assumed to reside in a polytopic region, the stochastic disturbance is state-dependent described by a scalar Brownian motion, and the time-varying delays enter into both the translation process and the feedback regulation process. We aim to estimate the true concentrations of mRNA and protein by designing a linear filter such that, for all admissible time delays, stochastic disturbances as well as polytopic uncertainties, the augmented state estimation dynamics is exponentially mean square stable with an expected decay rate. A delay-dependent linear matrix inequality (LMI) approach is first developed to derive sufficient conditions that guarantee the exponential stability of the augmented dynamics, and then the filter gains are parameterized in terms of the solution to a set of LMIs. Note that LMIs can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the U.K. under Grants BB/C506264/1 and 100/EGM17735, an International Joint Project sponsored by the Royal Society of the U.K., the Research Grants Council of Hong Kong under Grant HKU 7031/06P, the National Natural Science Foundation of China under Grant 60804028, and the Alexander von Humboldt Foundation of Germany
Doping of graphene by a Au(111) substrate: Calculation strategy within the local density approximation and a semiempirical van der Waals approach
We have performed a density functional study of graphene adsorbed on Au(111)
surface using both a local density approximation and a semiempirical van der
Waals approach proposed by Grimme, known as the DFT-D2 method. Graphene
physisorbed on metal has the linear dispersion preserved in the band-structure,
but the Fermi level of the system is shifted with respect to the conical points
which results in a doping effect. We show that the type and amount of doping
depends not only on the choice of the exchange-correlation functional used in
the calculations, but also on the supercell geometry that models the physical
system. We analyzed how the factors such as the in-plane cell parameter and
interlayer spacing in gold influence the Fermi level shift and we found that
even a small variation in these parameters may cause a transition from p-type
to n-type doping. We have selected a reasonable set of model parameters and
obtained that graphene is either undoped or at most slightly p-type doped on
the clean Au(111) surface, which seems to be in line with experimental
findings. On the other hand, modifications of the substrate lattice may induce
larger doping up to 0.30-0.40 eV depending on the graphene-metal adsorption
distance. The sensitivity of the graphene-gold interface to the structural
parameters may allow to tune doping across the samples which could lead to
possible applications in graphene-based electronic devices. We believe that the
present remarks can be also useful for other studies based on the periodic DFT
Theory of point contact spectroscopy in electron-doped cuprates
In the hole-doped -wave cuprate superconductor, due to the
midgap surface state (MSS), a zero bias conductance peak (ZBCP) is widely
observed in [110] interface point contact spectroscopy (PCS). However, ZBCP of
this geometry is rarely observed in the electron-doped cuprates, even though
their pairing symmetry is still likely the -wave. We argue
that this is due to the coexistence of antiferromagnetic (AF) and the
superconducting (SC) orders. Generalizing the Blonder-Tinkham-Klapwijk (BTK)
formula to include an AF coupling, it is shown explicitly that the MSS is
destroyed by the AF order. The calculated PCS is in good agreement with the
experiments.Comment: 5 pages, 2 figures. Replaced with published versio
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