Contributed Talks (alphabetically ordered following the speaker’s surname)
Hansj¨o rg Albrecherc罗是哪个国家
Reinhold Kainhofer
Robert F.Tichy
Department of Mathematics
Graz University of Technology
Steyrergas30/II高云翔电视剧
A-8010Graz,Austria
e-mail:albrecher@tugraz.at
www.cis.TUGraz.at/matha
Title
Simulation Methods in Ruin Models
with Non-linear Dividend Barriers1
Abstract
In this paper we consider a collective risk rerve process of an insurance portfolio char-acterized by a homogeneous Poisson claim number process,a constant premiumflow and independent and identically distributed claims.In the prence of a non-linear dividend bar-rier strategy and interest on the free rerve we derive equations for the probability of ruin and the expected prent value of dividend payments which give ri to veral numerical number-theoretic solution techniques.For various claim size distributions and a parabolic barrier numerical tests and comparisons of the techniques are performed.
立定跳远技巧训练方法
In particular,the efficiency gain obtained by implementing low-discrepancy quences instead of pudorandom quences is investigated.
1Rearch supported by the Austrian Science Foundation Project S-8308MAT
James B.Anderson
Department of Chemistry
Pennsylvania State University
University Park,Pennsylvania16802
e-mail:jba@psu.edu
random.chem.psu.edu
Title
Quantum Monte Carlo:
Direct Calculation of Corrections to Trial Wave Functions and Their Energies
Abstract
We will discuss an improved Monte Carlo method for calculating the differenceδbetween
a true wavefunctionΨand an analytic trial wavefunctionΨ0.The method also produces
a correction to the expectation value of the energy for the trial function.Applications to veral sample problems as well as to the water molecule will be described.
河北景区We have described previously a quantum Monte Carlo(QMC)method for the direct cal-culation of corrections to trial wavefunctions[1-3].Our improved method is much simpler
to u.Like its predecessors the improved method gives(forfixed nodes)the differenceδbetween a true wavefunctionΨand a trial wavefunctionΨ0,but it gives in addition the
difference between the true energy E and the expectation value of the energy E var for the trial wavefunction.
The statistical or sampling errors associated with the Monte Carlo procedures as well as any systematic errors occur only in the corrections.Thus,very accurate wavefunctions and energies may be corrected with very simple calculations.
For systems with nodes the nodes are unchanged.The wavefunctions and energies for the systems are corrected to thefixed-node values-tho corresponding to the exact solutions
for thefixed nodes of the trial wavefunctions.
The method has the very desirable features of:good wavefunction in/better d energy in/better energy out.
The ground state of the helium atom provides a simple example.We ud as a trial wavefunc-tion the189-term Hylleraas function described by Schwartz[4]which is accurate to about10 digits.The true energy is known to at least13digits from the analytic variational calculation
of Freund,Huxtable,and Morgan[5]with a more complex trial function.
The expectation value for the trial function is−2.903724376180(0)hartrees.The calculated correction is−0.000000000856(2)hartrees which gives a corrected value of−2.903724377036(2) hartrees.This may be compared with the known value of−2.903724377034(0)hartrees.
The water molecule prents the problem of nodes in the wavefunction as well as a much higher dimensionality.In this ca the nodes arefixed in position by the u offixed-node QMC procedures[6]and the resulting energy obtained is thefixed-node energy for the nodes
of the trial wavefunction.As in anyfixed-node calculation the energy obtained is a variational
upper bound to the true energy,and if the nodes are wrong the energy will be higher than the true en
ergy.
The trial function for this ca was a simple SCF function,consisting of a single10x10 determinant of LCAO-MO terms of Slater-type orbitals without any Jastrow or other explicit electron correlation terms.The expectation value of the energy for the trial function and the fixed-node QMC energy were determined independently by standard methods.
In this ca the initial energy is−75.560hartrees,the calculated correction is−0.599hartrees, and the corrected value is−76.169(10)hartrees.This may be compared with the indepen-dently calculated value of−76.170(10)hartrees.
Earlierfixed-node QMC calculations for systems of ten or more electrons have ud single-determinant trial wavefunctions with Jastrow terms.With the improved correction procedure the need for accurate expectation values for the trial function requires eliminating the Jastrow terms,but it may make practical the u of many more determinants in the trial function. This is likely to give improved node locations and lead to much lower node location errors. The sign problem of quantum Monte Carlo for large systems would not be eliminated but it might be significantly reduced.
[1]J.B.Anderson and B.H.Freihaut,J.Comput.Phys.31,425(1979).
与春天有关的成语
[2]J.B.Anderson,J.Chem.Phys.73,3897(1980).
[3]J.B.Anderson,M.Mella,and A.Luechow,in Recent Advances in Quantum Monte Carlo Methods,(W.A.Lester,Jr.,Ed.,World Scientific,Singapore)1997,pp.21-38.
[4]C.Schwartz,Phys.Rev.128,1146(1962).
[5]D.E.Freund,B.D.Huxtable,and J.D.Morgan III,Phys.Rev.A29,980(1984).
[6]J.B.Anderson,J.Chem.Phys.63,1499(1975).
James B.Anderson1
Lyle N.Long2
1Department of Chemistry
2Department of Aerospace Engineering
Pennsylvania State University
University Park,Pennsylvania16802
e-mail:jba@psu.edu约束的反义词
random.chem.psu.edu
Title
雄安新区定位The Simulation of Detonations
笔芯表情包Abstract
The Direct Simulation Monte Carlo(DSMC)method(1,2)has been found remarkably suc-cessful for predicting and understanding a number of difficult problems in rarefied gas dynam-ics.Extension to chemical reaction systems has provided a very powerful tool for reacting gas mixtures with non-Maxwellian velocity distributions,with non-Boltzmann state distribu-tions,with coupled gas-dynamic and reaction effects,with concentration gradients,and with many other effects difficult or impossible to treat in any other way.Examples of systems which may be treated includeflames and explosions,shock waves and detonations,reactions and energy transfer in lar cavities,upper atmosphere reactions,and many,many others.In this paper we will discuss the application of the DSMC method to the problem of detonations, a classic and extreme example of the coupling of gas
dynamics and chemical kinetics. Although a Monte Carlo simulation of a gas was described by Lord Kelvin in1901(3),it was not until the1960’s that the u of such simulations became practical for solving problems in thefield of rarefied gas dynamics.The combination of an efficient sampling method by Bird(1)in1963with high speed computers made possible the nearly exact simulation of a number of systems that had earlier been impossible to analyze.The current generation of computers makes it possible to consider much more ambitious applications:tho in which chemical reactions are important.
A detonation wave travels at supersonic speed in a reactive gas mixture and is driven by the energy relead in exothermic reaction within the wave.The modern theory of detonations begins with the work of Chapman and of Jouguet about1900,and their work has been extended by a number of others,in particular by Zeldovich(4),von Neumann(5),and D¨o ring(6).The three arrived independently at an expression,the ZVD expression,giving the velocity of a detonation wave as the velocity of sound in the completely burned gas when the shock wave precedes the reaction.
In order to simplify our DSMC calculations and to clarify the results by eliminating extrane-ous effects,we considered the special ca of the reaction of A+M→B+M in which the mass of A,B,and M are equal.The gas were specified as ideal and calorically perfect with constant heat capacities.T
he cross-ctions for reaction were specified as simple functions of collision energy corresponding to Arrhenius behavior.Calculations were carried out for a variety of conditions-covering a wide range of exothermicities and reaction rate parameters.
The simulations provide complete details of the properties of the system as they vary across the detonation wave.A variety of interesting results have been obtained.Temperature, density,and reaction-rate peaks may be parated.Temperature and density maxima depend strongly on reaction rate.The thickness of the reaction zone depends strongly on conditions. The results provide vere tests for some of the earlier theoretical models of detonations.
(1)G.A.Bird,Phys.Fluids6,1518(1963).
(2)G.A.Bird,Molecular Gas Dynamics and the Direct Simulation of Gasflows,Clarendon Press,Oxford,1994.
(3)Lord Kelvin,Phil.Mag.(London)2,1(1901).
(4)Y.B.Zeldovich,J.Exptl.Theoret.Phys.(U.S.S.R.)10,542(1940).
(5)J.von Neumann,O.S.R.D.Rept.No.549(1942).
(6)W.D¨o ring,Ann.Physik43,421(1943).
