Dynamical Multiple-Timestepping Methods for Overcoming the Half-Period Time Step Barrier

Current molecular dynamic simulations of biomolecules using multiple time steps to update the slowingly changing force are hampered by an instability occuring at time step equal to half the period of the fastest vibrating mode. This has became a critical barrier preventing the long time simulation of biomolecular dynamics. Attemps to tame this instability by altering the slowly changing force and efforts to damp out this instability by Langevin dynamics do not address the fundamental cause of this instability. In this work, we trace the instability to the non-analytic character of the underlying spectrum and show that a correct splitting of the Hamiltonian, which render the spectrum analytic, restores stability. The resulting Hamiltonian dictates that in additional to updating the momentum due to the slowly changing force, one must also update the position with a modified mass. Thus multiple-timestepping must be done dynamically.Comment: 10 pages, 2 figures, submitted to J. Chem. Phy

Fourth Order Gradient Symplectic Integrator Methods for Solving the Time-Dependent Schr\"odinger Equation

We show that the method of splitting the operator ${\rm e}^{\epsilon(T+V)}$ to fourth order with purely positive coefficients produces excellent algorithms for solving the time-dependent Schr\"odinger equation. These algorithms require knowing the potential and the gradient of the potential. One 4th order algorithm only requires four Fast Fourier Transformations per iteration. In a one dimensional scattering problem, the 4th order error coefficients of these new algorithms are roughly 500 times smaller than fourth order algorithms with negative coefficient, such as those based on the traditional Ruth-Forest symplectic integrator. These algorithms can produce converged results of conventional second or fourth order algorithms using time steps 5 to 10 times as large. Iterating these positive coefficient algorithms to 6th order also produced better converged algorithms than iterating the Ruth-Forest algorithm to 6th order or using Yoshida's 6th order algorithm A directly.Comment: 11 pages, 2 figures, submitted to J. Chem. Phy

Gradient Symplectic Algorithms for Solving the Radial Schrodinger Equation

The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators are well known for their excellent conservation properties. The class of {\it gradient} symplectic algorithms is particularly suited for solving harmonic oscillator dynamics. By use of Suzuki's rule for decomposing time-ordered operators, these algorithms can be easily applied to the Schrodinger equation. We demonstrate the power of this class of gradient algorithms by solving the spectrum of highly singular radial potentials using Killingbeck's method of backward Newton-Ralphson iterations.Comment: 19 pages, 10 figure

Variable frequency microwave (VFM) processing facilities and application in processing thermoplastic matrix composites

Microwave processing of materials is a relatively new technology advancement alternative that provides new approaches for enhancing material properties as well as economic advantages through energy savings and accelerated product development. Factors that hinder the use of microwaves in materials processing are declining, so that prospect for the development of this technology seem to be very promising. The two mechanisms of orientation polarisation and interfacial space charge polarisation, together with dc conductivity, form the basis of high frequency heating. Clearly, advantages in utilising microwave technologies for processing materials include penetration radiation, controlled electric field distribution and selective and volumetric heating. However, the most commonly used facilities for microwave processing materials are of fixed frequency, e.g. 2.45 GHz. This paper presents a state-of-the-art review of microwave technologies, processing methods and industrial applications, using variable frequency microwave (VFM) facilities. This is a new alternative for microwave processing

Low-momentum ring diagrams of neutron matter at and near the unitary limit

We study neutron matter at and near the unitary limit using a low-momentum ring diagram approach. By slightly tuning the meson-exchange CD-Bonn potential, neutron-neutron potentials with various $^1S_0$ scattering lengths such as $a_s=-12070fm$ and $+21fm$ are constructed. Such potentials are renormalized with rigorous procedures to give the corresponding $a_s$-equivalent low-momentum potentials $V_{low-k}$, with which the low-momentum particle-particle hole-hole ring diagrams are summed up to all orders, giving the ground state energy $E_0$ of neutron matter for various scattering lengths. At the limit of $a_s\to \pm \infty$, our calculated ratio of $E_0$ to that of the non-interacting case is found remarkably close to a constant of 0.44 over a wide range of Fermi-momenta. This result reveals an universality that is well consistent with the recent experimental and Monte-Carlo computational study on low-density cold Fermi gas at the unitary limit. The overall behavior of this ratio obtained with various scattering lengths is presented and discussed. Ring-diagram results obtained with $V_{low-k}$ and those with $G$-matrix interactions are compared.Comment: 9 pages, 7 figure

The home team advantage gives football referees something to ruminate about

Observation suggests that referees significantly contribute to the home team advantage in football. The atmosphere created by the home team fans is thought to be the major contributing factor, but the extent of this influence is dependent on the referee. The Decision-Specific Reinvestment Scale was developed to identify those individuals susceptible to disrupted decision making under pressure as a result of their tendency to overinvolve consciousness in decision making (Decision Reinvestment) or as a result of their tendency to ruminate upon poor decisions made in the past (Decision Rumination). We asked qualified referees to make a series of video-based decisions to examine whether the home team advantage effect was associated with a high or low tendency for Decision Reinvestment or Decision Rumination. We showed that referees categorized as high Decision Ruminators disproportionately made decisions in favour of the home team. The tendency to ruminate upon poor decisions may help explain some of the variance in the home team advantage effect shown by different referees. We conclude that aspects of personality should be considered in the development of training programs designed to improve and standardise football refereeing.published_or_final_versio

Effective algebraic degeneracy

We prove that any nonconstant entire holomorphic curve from the complex line C into a projective algebraic hypersurface X = X^n in P^{n+1}(C) of arbitrary dimension n (at least 2) must be algebraically degenerate provided X is generic if its degree d = deg(X) satisfies the effective lower bound: d larger than or equal to n^{{(n+1)}^{n+5}}

Humoral autoimmunity after solid organ transplantation: Germinal ideas may not be natural

Non-HLA antibody responses following solid organ transplantation have become increasingly emphasised, with several large clinical series suggesting that such responses contribute to late graft failure. Many of the responses described recognise both recipient and donor moieties of the target antigen and thus represent auto-, rather than allo-immunity. Within this rapidly evolving field, many questions remain unanswered: what triggers the response; how innate and adaptive humoral autoimmunity integrate; and most pressingly, how autoimmunity contributes to graft damage and its relationship to other effector mechanisms of graft rejection. This review summarises recent clinical and experimental studies of humoral autoimmunity in transplant rejection, and considers some of the answers to these questions