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Inflation, Cosmic Perturbations and Non-Gaussianities

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Communications in Theoretical Physics 2014年第7期61卷 109-166页

作者：王一 Kavli Institute for the Physics and Mathematics of the Universe Todai Institutes for Advanced Study University of Tokyo Centre for Theoretical Cosmology DAMTP University of Cambridge

We review the theory of inflationary perturbations. Perturbations at both linear and nonlinear orders are reviewed. We also review a variety of inflation models, emphasizing their signatures on cosmic perturbations.

关键词： inflation cosmic perturbation gravitational wave non-Gaussianity

Asymptotic solvers for ordinary differential equations with multiple frequencies

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Science China Mathematics 2015年第11期58卷 2279-2300页

作者： CONDON Marissa DEAO Alfredo GAO Jing ISERLES Arieh School of Electronic Engineering Dublin City University Departmento de Matematicas Universidad Carlos III de Madrid School of Mathematics and Statistics Xi'an Jiaotong University damtp Centre for Mathematical SciencesUniversity of Cambridge

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms,focusing on the case of multiple,non-commensurate frequencies.We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question.Numerical examples illustrate the effectiveness of the method.

关键词：常微分方程频率渐近解渐近展开振荡参数数值算例 ing

QUADRATURE METHODS FOR HIGHLY OSCILLATORY SINGULAR INTEGRALS

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Journal of Computational Mathematics 2021年第2期39卷 227-260页

作者： Jing Gao Marissa Condon Arieh Iserles Benjamin Gilvey Jon Trevelyan School of Mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049China School of Electronic Engineering Dublin City UniversityIreland damtp Centre for Mathematical SciencesUniversity of CambridgeUK Department of Engineering Durham UniversityUK

We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates the run-time for wave-enriched boundary integral formulations for wave scattering,and many of these exhibit singularities.We show that the asymptotic behaviour of the integral depends on the integrand and its derivatives at the singular point of the integrand,the stationary points and the endpoints of the integral.A truncated asymptotic expansion achieves an error that decays faster for increasing frequency.Based on the asymptotic analysis,a Filon-type method is constructed to approximate the integral.Unlike an asymptotic expansion,the Filon method achieves high accuracy for both small and large frequency.Complex-valued quadrature involves interpolation at the zeros of polynomials orthogonal to a complex weight function.Numerical results indicate that the complex-valued Gaussian quadrature achieves the highest accuracy when the three methods are compared.However,while it achieves higher accuracy for the same number of function evaluations,it requires signi cant additional cost of computation of orthogonal polynomials and their zeros.

关键词： Numerical quadrature Singular highly oscillatory integrals Asymptotic analysis Boundary Element Method Plane wave enrichment Partition of Unity

Improved Retrieval of Sea Ice Thickness and Density from Laser Altimeter

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Atmospheric and Climate Sciences 2014年第5期4卷 907-918页

作者： Vera Djepa Department of Applied Mathematics and Theoretical Physics (damtp) Cambridge University Cambridge UK

The sensitivity of weather and climate system to sea ice thickness (SIT) in the Arctic is recognised from various studies. Decrease of SIT will affect atmospheric circulation, temperature, precipitation and wind speed in the Arctic and remotely. Ice thermodynamics and dynamic properties depend strongly on ice and snow thickness. The heat transfer through ice critically depends on ice thickness. Long term accurate SIT records with corresponding uncertainties are required for improved seasonal weather forecast and estimate of the sea ice mass balance. Satellite radar and Laser Altimeter (LA) provide long term records of sea ice freeboard. Assuming isostatic equilibrium, SIT is retrieved from the freeboard, extracted from radar altimeter (RA) or LA, where the snow depth, density, ice and water density are input variables in the equation for hydrostatic equilibrium to derive SIT from LA or RA. Different input variables (snow depth, density, ice and water density) with unknown accuracy have been applied from various authors to retrieve SIT and Sea Ice Draft (SID) from RA or LA, leading to not comparative results. Sea ice density dependence on ice type, thermodynamic properties and freeboard is confirmed with different studies. Sensitivity analyses confirm the great impact of sea ice density, snow depth and density on accuracy of the retrieved SIT and the importance of inserting variable ice density (VID) in the equation for hydrostatic equilibrium for more accurate SIT retrieval, weather and climate forecast. The impact of sea ice density and snow depth and density on retrieved SIT from the freeboard derived from LA and RA have been analyzed in this study using the equation for hydrostatic equilibrium, statistical and sensitivity analyses. An algorithm is developed to convert the freeboard, derived from LA in SIT, inserting VID in the equation for hydrostatic equilibrium. The algorithm is validated with field, laboratory studies and collocated SIT retrieved from RA on board Envisat. The accuracy of the developed algor

关键词： Sea Ice Thickness Radar Altimeter Laser Altimeter Sea Ice Density Freeboard Arctic

Loss of Exchange Symmetry in Multiqubit States under Ising Chain Evolution

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Chinese Physics Letters 2011年第2期28卷 39-42页

作者： Sudha B.G.Divyamani A.R.Usha Devi Department of Physics Kuvempu UniversityShankaraghattaShimoga-577451India damtp Centre for Mathematical SciencesWilberforce RoadCambridgeCB3OWAUK Department of Physics Bangalore UniversityBangalore-560056India Inspire Institute Inc. McLeanVA 22101USA.

Keeping in view of importance of exchange symmetry aspects in studies on spin squeezing of multiqubit states,we show that the one-dimensional Ising Hamiltonian with nearest neighbor interactions does not retain the exchange symmetry of initially symmetric multiqubit states.Specifically we show that among 4-qubit states obeying exchange symmetry,all states except W class(and their linear combination)lose their symmetry under time evolution with Ising Hamiltonian.Attributing the loss of symmetry of the initially symmetric states to rotational asymmetry of the one-dimensional Ising Hamiltonian with more than 3 qubits,we indicate that all N-qubit states(N>5)obeying permutation symmetry lose their symmetry after time evolution with Ising Hamiltonian.

关键词： symmetry Ising qubit

State Transition Induced by Self-Steepening and Self Phase-Modulation

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Chinese Physics Letters 2014年第1期31卷 33-36页

作者： He Jing-Song Xu Shu-Wei M. S. Ruderman R. Erdélyi Department of Mathematics Ningbo University Ningbo 315211 damtp University of Cambridge Cambridge CB3 0WA UK School of Mathematics University of Science and Technology of China Hefei 230026 Solar Physics and Space Plasma Research Centre University of Sheffield Sheffield S3 7RH UK

We present a rational solution for a mixed nonlinear Schr6dinger （MNLS） equation. This solution has two free parameters, a and b, representing the contributions of self-steepening and self phase-modulation （SPM） of an associated physical system, respectively. It describes five soliton states： a paired bright-bright soliton, a single soliton, a paired bright-grey soliton, a paired bright-black soliton, and a rogue wave state. We show that the transition among these live states is induced by self-steepening and SPM through tuning the values of a and b. This is a unique and potentially fundamentally important phenomenon in a physical system described by the MNLS eauation.

关键词： Solitons

Observational constraints on running vacuum model

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Chinese Physics C 2019年第2期43卷 132-137页

作者：张进军 Chung-Chi Lee 耿朝强 School of Physics and Information Engineering Shanxi Normal University damtp Centre for Mathematical Sciences University of Cambridge Department of Physics National Tsing Hua University National Center for Theoretical Sciences

We investigate the power spectra of the CMB temperature and matter density in the running vacuum model(RVM) with the time-dependent cosmological constant of A=3 vH^2+ Λ_0, where H is the Hubble parameter. In this model, dark energy decreases in time and decays to both matter and radiation. By using the Markov chain Monte Carlo method, we constrain the model parameter v as well as the cosmological observables. Explicitly, we obtain v ≤1.54× 10^(-4)(68% confidence level) in the RVM with the best-fit χ_(RVM)~2 =13968.8, which is slightly smaller thanχ_(ΛCDM)~2= 13969.8 in the ΛCDM model of v = 0.

关键词： matter power spectrum running vacuum model CMB temperature spectrum cosmological constant

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带剪切作用的海洋扩散型温盐驱动对流湍流

带剪切作用的海洋扩散型温盐驱动对流湍流