The fast sampling algorithm for Lie-Trotter products

A fast algorithm for path sampling in path integral Monte Carlo simulations is proposed. The algorithm utilizes the Levy-Ciesielski implementation of Lie-Trotter products to achieve a mathematically proven computational cost of n*log_2(n) with the number of time slices n, despite the fact that each path variable is updated separately, for reasons of optimality. In this respect, we demonstrate that updating a group of random variables simultaneously results in loss of efficiency.Comment: 4 pages, 1 figure; fast rejection from Phys. Rev. Letts; transfered to PRE as a Rapid Communication. Eq. 6 to 10 contained some inconsistencies that have been repaired in the present version; A sample code implementing the algorithm for LJ clusters is available from the author upon reques

Thermo-mechanical compatibility of CFRP versus steel reinforcement for concrete at high temperature

Optimization of the design of concrete structures has become a driver for the use of nonconventional reinforcing materials. One example of this is the emerging use of non-corrosive, highstrength, and lightweight carbon fibre reinforced polymer (CFRP) prestressing tendons. It is widely known that the bond between FRP reinforcing tendons and concrete deteriorates at elevated temperature due to a combination of factors. Lateral thermal expansion of FRP reinforcing tendons at elevated temperature has been shown to have consequences for the bond performance of these systems. This paper presents the results of an experimental study carried out to assess the occurrence of heat-induced longitudinal splitting cracks in concrete specimens reinforced with CFRP or steel prestressing tendons. A novel testing methodology, namely a Heat-Transfer Rate Inducing System (H-TRIS), is used to subject specimens to thermal loading which replicates that experienced by equivalent specimens in a standard fire resistance test. A comparison between CFRP and steel tendons is made, and the occurrence of longitudinal splitting cracks is evaluated in terms of the time to occurrence and thermal gradient within the concrete. Results are compared against an available analytical model

Features of gravity-Yang-Mills hierarchies in d-dimensions

Higher dimensional, direct analogues of the usual d=4 Einstein--Yang-Mills (EYM) systems are studied. These consist of the gravitational and Yang-Mills hierarchies in d=4p dimensional spacetimes, both consisting of 2p-form curvature terms only. Regular and black hole solutions are constructed in $2p+2\le d \le 4p$, in which dimensions the total mass-energy is finite, generalising the familiar Bartnik-McKinnon solutions in EYM theory for p=1. In d=4p, this similarity is complete. In the special case of d=2p+1, just beyond the finite energy range of d, exact solutions in closed form are found. Finally, d=2p+1 purely gravitational systems, whose solutions generalise the static d=3 BTZ solutions, are discussed.Comment: 19 pages, 9 figure

Thermodynamics and equilibrium structure of Ne_38 cluster: Quantum Mechanics versus Classical

The equilibrium properties of classical LJ_38 versus quantum Ne_38 Lennard-Jones clusters are investigated. The quantum simulations use both the Path-Integral Monte-Carlo (PIMC) and the recently developed Variational-Gaussian-Wavepacket Monte-Carlo (VGW-MC) methods. The PIMC and the classical MC simulations are implemented in the parallel tempering framework. The VGW method is used to locate and characterize the low energy states of Ne_38, which are then further refined by PIMC calculations. Unlike the classical case, the ground state of Ne_38 is a liquid-like structure. Among the several liquid-like states with energies below the two symmetric states (O_h and C_5v), the lowest two exhibit strong delocalization over basins associated with at least two classical local minima. Because the symmetric structures do not play an essential role in the thermodynamics of Ne_38, the quantum heat capacity is a featureless curve indicative of the absence of any structural transformations. Good agreement between the two methods, VGW and PIMC, is obtained.Comment: 13 pages, 9 figure

Two repelling random walks on Z\mathbb Z

We consider two interacting random walks on $\mathbb{Z}$ such that the transition probability of one walk in one direction decreases exponentially with the number of transitions of the other walk in that direction. The joint process may thus be seen as two random walks reinforced to repel each other. The strength of the repulsion is further modulated in our model by a parameter $\beta \geq 0$. When $\beta = 0$ both processes are independent symmetric random walks on $\mathbb{Z}$, and hence recurrent. We show that both random walks are further recurrent if $\beta \in (0,1]$. We also show that these processes are transient and diverge in opposite directions if $\beta > 2$. The case $\beta \in (1,2]$ remains widely open. Our results are obtained by considering the dynamical system approach to stochastic approximations.Comment: 17 pages. Added references and corrected typos. Revised the argument for the convergence to equilibria of the vector field. Improved the proof for the recurrence when beta belongs to (0,1); leading to the removal of a previous conjectur

WHO BENEFITS FROM FUNDS OF HEDGE FUNDS? A CRITIQUE OF ALTERNATIVE ORGANIZATIONAL STRUCTURES IN THE HEDGE FUND INDUSTRY (I)

This paper provides a critique of alternative organizational structures in the hedge fund industry. Our critique is facilitated by several stylized models describing alternative industry structures. The models include: (1) An insideonly hedge fund model; (2) A straddling hedge fund model; (3) A straddling “feeder” fund of funds (FOF) hedge fund model; (4) A stand-alone outside hedge fund; and (5) An outside “feeder” FOF hedge fund model. Our discussion of these models, which centers on benefits vs. fundamental problems related to illiquidity, information asymmetry, and conflicts of interest, leads to several hypotheses about the differential characteristics and return performance of both individual hedge funds and FOFs.Hedge funds, Funds of funds, Illiquidity, Information asymmetry, Conflicts of interest, Adjacency risk, Contagion, Return performance