Scaling laws for the 2d 8-state Potts model with Fixed Boundary Conditions

We study the effects of frozen boundaries in a Monte Carlo simulation near a first order phase transition. Recent theoretical analysis of the dynamics of first order phase transitions has enabled to state the scaling laws governing the critical regime of the transition. We check these new scaling laws performing a Monte Carlo simulation of the 2d, 8-state spin Potts model. In particular, our results support a pseudo-critical beta finite-size scaling of the form beta(infinity) + a/L + b/L^2, instead of beta(infinity) + c/L^d + d/L^{2d}. Moreover, our value for the latent heat is 0.294(11), which does not coincide with the latent heat analytically derived for the same model if periodic boundary conditions are assumed, which is 0.486358...Comment: 10 pages, 3 postscript figure

Light levitated geostationary cylindrical orbits are feasible

This paper discusses a new family of non-Keplerian orbits for solar sail spacecraft displaced above or below the Earth's equatorial plane. The work aims to prove the assertion in the literature that displaced geostationary orbits exist, possibly to increase the number of available slots for geostationary communications satellites. The existence of displaced non-Keplerian periodic orbits is ¯rst shown analytically by linearization of the solar sail dynamics around a geostationary point. The full displaced periodic solution of the non-linear equations of motion is then obtained using a Hermite-Simpson collocation method with inequality path constraints. The initial guess to the collocation method is given by the linearized solution and the inequality path constraints are enforced as a box around the linearized solution. The linear and nonlinear displaced periodic orbits are also obtained for the worst-case Sun-sail orientation at the solstices. Near-term and high-performance sails can be displaced between 10 km and 25 km above the Earth's equatorial plane during the summer solstice, while a perforated sail can be displaced above the usual station-keeping box (75 £ 75 km) of nominal geostationary satellites. Light-levitated orbit applications to Space Solar Power are also considered

Secrecy content of two-qubit states

We analyze the set of two-qubit states from which a secret key can be extracted by single-copy measurements plus classical processing of the outcomes. We introduce a key distillation protocol and give the corresponding necessary and sufficient condition for positive key extraction. Our results imply that the critical error rate derived by Chau, Phys. Rev. A {\bf 66}, 060302 (2002), for a secure key distribution using the six-state scheme is tight. Remarkably, an optimal eavesdropping attack against this protocol does not require any coherent quantum operation.Comment: 5 pages, RevTe

The Phases and Triviality of Scalar Quantum Electrodynamics

The phase diagram and critical behavior of scalar quantum electrodynamics are investigated using lattice gauge theory techniques. The lattice action fixes the length of the scalar (``Higgs'') field and treats the gauge field as non-compact. The phase diagram is two dimensional. No fine tuning or extrapolations are needed to study the theory's critical behovior. Two lines of second order phase transitions are discovered and the scaling laws for each are studied by finite size scaling methods on lattices ranging from $6^4$ through $24^4$. One line corresponds to monopole percolation and the other to a transition between a ``Higgs'' and a ``Coulomb'' phase, labelled by divergent specific heats. The lines of transitions cross in the interior of the phase diagram and appear to be unrelated. The monopole percolation transition has critical indices which are compatible with ordinary four dimensional percolation uneffected by interactions. Finite size scaling and histogram methods reveal that the specific heats on the ``Higgs-Coulomb'' transition line are well-fit by the hypothesis that scalar quantum electrodynamics is logarithmically trivial. The logarithms are measured in both finite size scaling of the specific heat peaks as a function of volume as well as in the coupling constant dependence of the specific heats measured on fixed but large lattices. The theory is seen to be qualitatively similar to $\lambda\phi^{4}$. The standard CRAY random number generator RANF proved to be inadequateComment: 25pages,26figures;revtex;ILL-(TH)-94-#12; only hardcopy of figures availabl

A Validation of the p-SLLOD Equations of Motion for Homogeneous Steady-state Flows

A validation of the p-SLLOD equations of motion for nonequilibrium molecular dynamics simulation under homogeneous steady-state flow is presented. We demonstrate that these equations generate the correct center-of-mass trajectory of the system, are completely compatible with (and derivable from) Hamiltonian dynamics, satisfy an appropriate energy balance, and require no fictitious external force to generate the required homogeneous flow. It is also shown that no rigorous derivation of the SLLOD equations exists to date

String tension in gonihedric 3D Ising models

For the 3D gonihedric Ising models defined by Savvidy and Wegner the bare string tension is zero and the energy of a spin interface depends only on the number of bends and self-intersections, in antithesis to the standard nearest-neighbour 3D Ising action. When the parameter kappa weighting the self-intersections is small the model has a first order transition and when it is larger the transition is continuous. In this paper we investigate the scaling of the renormalized string tension, which is entirely generated by fluctuations, using Monte Carlo simulations This allows us to obtain an estimate for the critical exponents alpha and nu using both finite-size-scaling and data collapse for the scaling function.Comment: Latex + postscript figures. 8 pages text plus 7 figures, spurious extra figure now removed

Precise Analysis of Polymer Rotational Dynamics

Through the analysis of individual chain dynamics alongside the corresponding molecular structures under shear via nonequilibrium molecular dynamics simulations of C178H358 linear and short-chain branched polyethylene melts under shear flow, we observed that the conventional method based on the chain end-to-end vector (and/or the gyration tensor of chain) is susceptible to quantitatively inaccurate measurements and often misleading information in describing the rotational dynamics of polymers. Identifying the flaw as attributed to strong irregular Brownian fluctuations inherent to the chain ends associated with their large free volume and strong molecular collisions, we propose a simple, robust way based on the chain center-to-center vector connecting the two centers of mass of the bisected chain, which is shown to adequately describe polymer rotational dynamics without such shortcomings. We present further consideration that the proposed method can be useful in accurately measuring the overall chain structure and dynamics of polymeric materials with various molecular architectures, including branched and ring polymers.open

A novel interplanetary communications relay

A case study of a potential Earth-Mars interplanetary communications relay, designed to ensure continuous communications, is detailed. The relay makes use of orbits based on artificial equilibrium points via the application of continuous low thrust, which allows a spacecraft to hover above the orbital plane of Mars and thus ensure communications when the planet is occulted with respect to the Earth. The artificial equilibria of two different low-thrust propulsion technologies are considered: solar electric propulsion, and a solar sail/solar electric propulsion hybrid. In the latter case it is shown that the combination of sail and solar electric propulsion may prove advantageous, but only under specific circumstances of the relay architecture suggested. The study takes into account factors such as the spacecraft's power requirements and communications band utilized to determine the mission and system architecture. A detailed contingency analysis is considered for recovering the relay after increasing periods of spacecraft motor failure, and combined with a consideration for how best to deploy the relay spacecraft to maximise propellant reserves and mission duration

Multiple copy 2-state discrimination with individual measurements

We address the problem of non-orthogonal two-state discrimination when multiple copies of the unknown state are available. We give the optimal strategy when only fixed individual measurements are allowed and show that its error probability saturates the collective (lower) bound asymptotically. We also give the optimal strategy when adaptivity of individual von Neumann measurements is allowed (which requires classical communication), and show that the corresponding error probability is exactly equal to the collective one for any number of copies. We show that this strategy can be regarded as Bayesian updating.Comment: 5 pages, RevTe