7,660 research outputs found

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

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

Type-based amortised resource analysis following Hofmann and Jostāwhere resources are associated with individual elements of data structures and doled out to the programmer under a linear typing disciplineāhave 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

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

The perfect fluid cosmology in the 1+d+D dimensional Kaluza-Klein spacetimes
for an arbitrary barotropic equation of state $p= n \rho$ 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 $n=1$ we
exactly solve the Wheeler-DeWitt equation when the $d$ 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 $d$ spaces and the
compact $D$ spaces will eventually evolve into finite scale functions. For the
second case of $n \approx 1$, 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 $d$ spaces will be expanding forever while the scale function of the
contracting $D$ 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 $D$ 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 $t=\infty$.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

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

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 ĪT
= -2, ĪT
inrx1
= +1, ĪT
inrx2
inrx
= +1 , ĪT
inrx4
inrx3
= +2 and ĪH2/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

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

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

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

- ā¦