7,660 research outputs found

    Fourth Order Algorithms for Solving the Multivariable Langevin Equation and the Kramers Equation

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    We develop a fourth order simulation algorithm for solving the stochastic Langevin equation. The method consists of identifying solvable operators in the Fokker-Planck equation, factorizing the evolution operator for small time steps to fourth order and implementing the factorization process numerically. A key contribution of this work is to show how certain double commutators in the factorization process can be simulated in practice. The method is general, applicable to the multivariable case, and systematic, with known procedures for doing fourth order factorizations. The fourth order convergence of the resulting algorithm allowed very large time steps to be used. In simulating the Brownian dynamics of 121 Yukawa particles in two dimensions, the converged result of a first order algorithm can be obtained by using time steps 50 times as large. To further demostrate the versatility of our method, we derive two new classes of fourth order algorithms for solving the simpler Kramers equation without requiring the derivative of the force. The convergence of many fourth order algorithms for solving this equation are compared.Comment: 19 pages, 2 figure

    Amortised resource analysis with separation logic

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    Type-based amortised resource analysis following Hofmann and Jost—where resources are associated with individual elements of data structures and doled out to the programmer under a linear typing discipline—have been successful in providing concrete resource bounds for functional programs, with good support for inference. In this work we translate the idea of amortised resource analysis to imperative languages by embedding a logic of resources, based on Bunched Implications, within Separation Logic. The Separation Logic component allows us to assert the presence and shape of mutable data structures on the heap, while the resource component allows us to state the resources associated with each member of the structure. We present the logic on a small imperative language with procedures and mutable heap, based on Java bytecode. We have formalised the logic within the Coq proof assistant and extracted a certified verification condition generator. We demonstrate the logic on some examples, including proving termination of in-place list reversal on lists with cyclic tails

    On the construction of high-order force gradient algorithms for integration of motion in classical and quantum systems

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    A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic algorithms are first derived up to the eighth order by direct decompositions of exponential propagators and further collected using an advanced composition scheme to obtain the algorithms of higher orders. Contrary to the scheme by Chin and Kidwell [Phys. Rev. E 62, 8746 (2000)], where high-order algorithms are introduced by standard iterations of a force-gradient integrator of order four, the present method allows to reduce the total number of expensive force and its gradient evaluations to a minimum. At the same time, the precision of the integration increases significantly, especially with increasing the order of the generated schemes. The algorithms are tested in molecular dynamics and celestial mechanics simulations. It is shown, in particular, that the efficiency of the new fourth-order-based algorithms is better approximately in factors 5 to 1000 for orders 4 to 12, respectively. The results corresponding to sixth- and eighth-order-based composition schemes are also presented up to the sixteenth order. For orders 14 and 16, such highly precise schemes, at considerably smaller computational costs, allow to reduce unphysical deviations in the total energy up in 100 000 times with respect to those of the standard fourth-order-based iteration approach.Comment: 23 pages, 2 figures; submitted to Phys. Rev.

    Quantum Perfect-Fluid Kaluza-Klein Cosmology

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    The perfect fluid cosmology in the 1+d+D dimensional Kaluza-Klein spacetimes for an arbitrary barotropic equation of state p=nρp= n \rho is quantized by using the Schutz's variational formalism. We make efforts in the mathematics to solve the problems in two cases. For the first case of the stiff fluid n=1n=1 we exactly solve the Wheeler-DeWitt equation when the dd space is flat. After the superposition of the solutions we analyze the Bohmian trajectories of the final-stage wave-packet functions and show that the flat dd spaces and the compact DD spaces will eventually evolve into finite scale functions. For the second case of n1n \approx 1, we use the approximated wavefunction in the Wheeler-DeWitt equation to find the analytic forms of the final-stage wave-packet functions. After analyzing the Bohmian trajectories we show that the flat dd spaces will be expanding forever while the scale function of the contracting DD spaces would not become zero within finite time. Our investigations indicate that the quantum effect in the quantum perfect-fluid cosmology could prevent the extra compact DD spaces in the Kaluza-Klein theory from collapsing into a singularity or that the "crack-of-doom" singularity of the extra compact dimensions is made to occur at t=t=\infty.Comment: Latex 18 pages, add section 2 to introduce the quantization of perfect flui

    A new broken U(1)-symmetry in extreme type-II superconductors

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    A phase transition within the molten phase of the Abrikosov vortex system without disorder in extreme type-II superconductors is found via large-scale Monte-Carlo simulations. It involves breaking a U(1)-symmetry, and has a zero-field counterpart, unlike vortex lattice melting. Its hallmark is the loss of number-conservation of connected vortex paths threading the entire system {\it in any direction}, driving the vortex line tension to zero. This tension plays the role of a generalized ``stiffness'' of the vortex liquid, and serves as a probe of the loss of order at the transition, where a weak specific heat anomaly is found.Comment: 5 pages, 3 figure

    Kinetic Model and Simulation Analysis for Propane Dehydrogenation in an Industrial Moving Bed Reactor

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    A kinetic model for propane dehydrogenation in an industrial moving bed reactor is developed based on the reported reaction scheme. The kinetic parameters and activity constant are fine tuned with several sets of balanced plant data. Plant data at different operating conditions is applied to validate the model and the results show a good agreement between the model predictions and plant observations in terms of the amount of main product, propylene produced. The simulation analysis of key variables such as inlet temperature of each reactor (T ) and hydrogen to total hydrocarbon ratio (H2/THC) affecting process performance is performed to identify the operating condition to maximize the production of propylene. Within the range of operating conditions applied in the present studies, the operating condition to maximize the propylene production at the same weighted average inlet temperature (WAIT) is ΔT = -2, ΔT inrx1 = +1, ΔT inrx2 inrx = +1 , ΔT inrx4 inrx3 = +2 and ΔH2/THC= -0.02. Under this condition, the surplus propylene produced is 7.07 tons/day as compared with base case

    Measurement of the two-photon absorption cross-section of liquid argon with a time projection chamber

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    This paper reports on laser-induced multiphoton ionization at 266 nm of liquid argon in a time projection chamber (LAr TPC) detector. The electron signal produced by the laser beam is a formidable tool for the calibration and monitoring of next-generation large-mass LAr TPCs. The detector that we designed and tested allowed us to measure the two-photon absorption cross-section of LAr with unprecedented accuracy and precision: sigma_ex=(1.24\pm 0.10stat \pm 0.30syst) 10^{-56} cm^4s{-1}.Comment: 15 pages, 9 figure

    A Forward-Design Approach to Increase the Production of Poly-3-Hydroxybutyrate in Genetically Engineered Escherichia coli

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    Biopolymers, such as poly-3-hydroxybutyrate (P(3HB)) are produced as a carbon store in an array of organisms and exhibit characteristics which are similar to oil-derived plastics, yet have the added advantages of biodegradability and biocompatibility. Despite these advantages, P(3HB) production is currently more expensive than the production of oil-derived plastics, and therefore, more efficient P(3HB) production processes would be desirable. In this study, we describe the model-guided design and experimental validation of several engineered P(3HB) producing operons. In particular, we describe the characterization of a hybrid phaCAB operon that consists of a dual promoter (native and J23104) and RBS (native and B0034) design. P(3HB) production at 24 h was around six-fold higher in hybrid phaCAB engineered Escherichia coli in comparison to E. coli engineered with the native phaCAB operon from Ralstonia eutropha H16. Additionally, we describe the utilization of non-recyclable waste as a low-cost carbon source for the production of P(3HB)

    An Assessment of Risk of Iodine Deficiency Among Pregnant Women in Sarawak, Malaysia

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    Previous findings from a state-wide Iodine Deficiency Disorders (IDD) study among pregnant women (PW) in Sarawak indicated that PW are at risk of IDD and further assessment is needed. This paper describes the methodology used in conducting this study for an assessment of risk of iodine deficiency among pregnant women in Sarawak, Malaysia. A total of 30 maternal child health care clinics (MCHCs) were selected using probability proportional to population size (PPS) sampling technique. The PW sample size was calculated based on 95% confidence interval (CI), relative precision of 5%, design effect of 2, anticipated IDD prevalence of 65.0% and non-response rate of 20%. Thus, the total sample size required was 750 (25 respondents per selected MCHC). The WHO Expanded Programme on Immunization (EPI) surveys approach was used to randomly select the first respondent and subsequent respondents were chosen until the required number of PW was met. The required data were obtained through: face-to-face interviews (socio-demographic and food frequency questionnaire), clinical assessments (thyroid size, and hyper/hypothyroidism) and biochemical analysis (urine and blood serum). A total of 677 PW responded in the study with a response rate of 90.2%. Majority of the PW were at second gravida, aged 25-29 years old and of Malay ethnicity. The methodology used in this study was based on International guidelines which may provide state's estimates. All the necessary steps were taken into consideration to ensure valid and reliable findings on current iodine status among PW
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