arXiv subjects

Alex Travesset

Publications and source records attributed to Alex Travesset.

32 records · Page 2Linked to original sources

arXiv2006

Ground state of a large number of particles on a frozen topography

Problems consisting in finding the ground state of particles interacting with a given potential constrained to move on a particular geometry are surprisingly difficult. Explicit solutions have been found for small numbers of particles by the use of numerical methods in some particular cases such as particles on a sphere and to a much lesser extent on a torus. In this paper we propose a general solution to the problem in the opposite limit of a very large number of particles M by expressing the energy as an expansion in M whose coefficients can be minimized by a geometrical ansatz. The solution is remarkably universal with respect to the geometry and the interaction potential. Explicit solutions for the sphere and the torus are provided. The paper concludes with several predictions that could be verified by further theoretical or numerical work.

cond-mat.stat-mech↗

arXiv2005

Monovalent counterion distributions at highly charged water interfaces: Proton-transfer and Poisson-Boltzmann theory

Surface sensitive synchrotron-X-ray scattering studies reveal the distributions of monovalent ions next to highly charged interfaces. A lipid phosphate (dihexadecyl hydrogen-phosphate) was spread as a monolayer at the air-water interface, containing CsI at various concentrations. Using anomalous reflectivity off and at the $L_3$ Cs$^+$ resonance, we provide, for the first time, spatial counterion distributions (Cs$^+$) next to the negatively charged interface over a wide range of ionic concentrations. We argue that at low salt concentrations and for pure water the enhanced concentration of hydroniums H$_3$O$^+$ at the interface leads to proton-transfer back to the phosphate group by a high contact-potential, whereas high salt concentrations lower the contact-potential resulting in proton-release and increased surface charge-density. The experimental ionic distributions are in excellent agreement with a renormalized-surface-charge Poisson-Boltzmann theory without fitting parameters or additional assumptions.

cond-mat.soft↗

arXiv2005

Crystalline Particle Packings on a Sphere with Long Range Power Law Potentials

The original Thomson problem of "spherical crystallography" seeks the ground state of electron shells interacting via the Coulomb potential; however one can also study crystalline ground states of particles interacting with other potentials. We focus here on long range power law interactions of the form 1/r^gamma (0 < γ< 2), with the classic Thomson problem given by gamma=1. At large R/a, where R is the sphere radius and a is the particle spacing, the problem can be reformulated as a continuum elastic model that depends on the Young's modulus of particles packed in the plane and the universal (independent of the pair potential) geometrical interactions between disclination defects. The energy of the continuum model can be expressed as an expansion in powers of the total number of particles, M sim (R/a)^2, with coefficients explicitly related to both geometric and potential-dependent terms. For icosahedral configurations of twelve 5-fold disclinations, the first non-trivial coefficient of the expansion agrees with explicit numerical evaluation for discrete particle arrangements to 4 significant digits; the discrepancy in the 5th digit arises from a contribution to the energy that is sensitive to the particular icosadeltahedral configuration and that is neglected in the continuum calculation. In the limit of a very large number of particles, an instability toward grain boundaries can be understood in terms of a "Debye{--}Huckel" solution, where dislocations have continuous Burgers' vector "charges". Discrete dislocations in grain boundaries for intermediate particle numbers are discussed as well.

cond-mat.soft↗

arXiv2003

Curvature-Induced Defect Unbinding in Toroidal Geometries

Toroidal templates such as vesicles with hexatic bond orientational order are discussed. The total energy including disclination charges is explicitly computed for hexatic order embedded in a toroidal geometry. Related results apply for tilt or nematic order on the torus in the one Frank constant approximation. Although there is no topological necessity for defects in the ground state, we find that excess disclination defects are nevertheless energetically favored for fat torii or moderate vesicle sizes. Some experimental consequences are discussed.

cond-mat.soft↗

arXiv2002

Crystalline Order on a Sphere and the Generalized Thomson Problem

We attack generalized Thomson problems with a continuum formalism which exploits a universal long range interaction between defects depending on the Young modulus of the underlying lattice. Our predictions for the ground state energy agree with simulations of long range power law interactions of the form 1/r^{gamma} (0 < gamma < 2) to four significant digits. The regime of grain boundaries is studied in the context of tilted crystalline order and the generality of our approach is illustrated with new results for square tilings on the sphere.

cond-mat.soft↗

arXiv2001

The formation of vortex loops (strings) in continuous phase transitions

The formation of vortex loops (global cosmic strings) in an O(2) linear sigma model in three spatial dimensions is analyzed numerically. For over-damped Langevin dynamics we find that defect production is suppressed by an interaction between correlated domains that reduces the effective spatial variation of the phase of the order field. The degree of suppression is sensitive to the quench rate. A detailed description of the numerical methods used to analyze the model is also reported.

cond-mat.stat-mech↗

arXiv2001

The Geometrical Structure of 2d Bond-Orientational Order

We study the formulation of bond-orientational order in an arbitrary two dimensional geometry. We find that bond-orientational order is properly formulated within the framework of differential geometry with torsion. The torsion reflects the intrinsic frustration for two-dimensional crystals with arbitrary geometry. Within a Debye-Huckel approximation, torsion may be identified as the density of dislocations. Changes in the geometry of the system cause a reorganization of the torsion density that preserves bond-orientational order. As a byproduct, we are able to derive several identities involving the topology, defect density and geometric invariants such as Gaussian curvature. The formalism is used to derive the general free energy for a 2D sample of arbitrary geometry, both in the crystalline and hexatic phases. Applications to conical and spherical geometries are briefly addressed.

cond-mat.stat-mech↗

arXiv2001

Universality Classes of Self-Avoiding Fixed-Connectivity Membranes

We present an analysis of extensive large-scale Monte Carlo simulations of self-avoiding fixed-connectivity membranes for sizes (number of faces) ranging from 512 to 17672 (triangular) plaquettes. Self-avoidance is implemented via impenetrable plaquettes. We simulate the impenetrable plaquette model in both three and four bulk dimensions. In both cases we find the membrane to be flat for all temperatures: the size exponent in three dimensions is nu=0.95(5) (Hausdorff dimension d_H=2.1(1)). The single flat phase appears, furthermore, to be equivalent to the large bending rigidity phase of non-self-avoiding fixed-connectivity membranes - the roughness exponent in three dimensions is xi=0.63(4). This suggests that there is a unique universality class for flat fixed-connectivity membranes without attractive interactions. Finally we address some theoretical and experimental implications of our work.

cond-mat.stat-mech↗

arXiv2000

The Statistical Mechanics of Membranes

The fluctuations of two-dimensional extended objects membranes is a rich and exciting field with many solid results and a wide range of open issues. We review the distinct universality classes of membranes, determined by the local order, and the associated phase diagrams. After a discussion of several physical examples of membranes we turn to the physics of crystalline (or polymerized) membranes in which the individual monomers are rigidly bound. We discuss the phase diagram with particular attention to the dependence on the degree of self-avoidance and anisotropy. In each case we review and discuss analytic, numerical and experimental predictions of critical exponents and other key observables. Particular emphasis is given to the results obtained from the renormalization group epsilon-expansion. The resulting renormalization group flows and fixed points are illustrated graphically. The full technical details necessary to perform actual calculations are presented in the Appendices. We then turn to a discussion of the role of topological defects whose liberation leads to the hexatic and fluid universality classes. We finish with conclusions and a discussion of promising open directions for the future.

cond-mat.soft↗

arXiv1999

Interacting Topological Defects on Frozen Topographies

We propose and analyze an effective free energy describing the physics of disclination defects in particle arrays constrained to move on an arbitrary two-dimensional surface. At finite temperature the physics of interacting disclinations is mapped to a Laplacian Sine-Gordon Hamiltonian suitable for numerical simulations. We then specialize to the case of a spherical crystal at zero temperature. The ground state is analyzed as a function of the ratio of the defect core energy to the Young's modulus. We argue that the core energy contribution becomes less and less important in the limit R >> a, where R is the radius of the sphere and a is the particle spacing. For large core energies there are twelve disclinations forming an icosahedron. For intermediate core energies unusual finite-length grain boundaries are preferred. The complicated regime of small core energies, appropriate to the limit R/a goes to infinity, is also addressed. Finally we discuss the application of our results to the classic Thomson problem of finding the ground state of electrons distributed on a two-sphere.

cond-mat.stat-mech↗

arXiv1998

The Quantum Hall effect, Skyrmions and Anomalies

We discuss the properties of Skyrmions in the Fractional Quantum Hall effect (FQHE). We begin with a brief description of the Chern-Simons-Landau-Ginzburg description of the FQHE, which provides the framework in which to understand a new derivation of the properties of FQHE Skyrmions (S. Baez, A.P. Balachandran, A. Stern and A. Travesset cond-mat/9712151) from anomaly and edge considerations.

cond-mat.mes-hall↗

arXiv1998

The tubular phase of self-avoiding anisotropic crystalline membranes

We analyze the tubular phase of self-avoiding anisotropic crystalline membranes. A careful analysis using renormalization group arguments together with symmetry requirements motivates the simplest form of the large-distance free energy describing fluctuations of tubular configurations. The non-self-avoiding limit of the model is shown to be exactly solvable. For the full self-avoiding model we compute the critical exponents using an epsilon-expansion about the upper critical embedding dimension for general internal dimension D and embedding dimension d. We then exhibit various methods for reliably extrapolating to the physical point (D=2,d=3). Our most accurate estimates are nu=0.62 for the Flory exponent and zeta=0.80 for the roughness exponent.

cond-mat.soft↗

arXiv1997

Monte Carlo Renormalization Group calculation in $λϕ^4_3$

We start by discussing some theoretical issues of renormalization group transformations and Monte Carlo renormalization group technique. A method to compute the anomalous dimension is proposed and investigated. As an application, we find excellent values for critical exponents in $λϕ^4_3$. Some technical questions regarding the hybrid algorithm and strong coupling expansions, used to compute the critical couplings of the canonical surface, are also briefly discussed.

hep-lat↗

arXiv1997

O(N) models within the local potential approximation

Using Wegner-Houghton equation, within the Local Potential Approximation, we study critical properties of O(N) vector models. Fixed Points, together with their critical exponents and eigenoperators, are obtained for a large set of values of N, including N=0 and N\to\infty. Polchinski equation is also treated. The peculiarities of the large N limit, where a line of Fixed Points at d=2+2/n is present, are studied in detail. A derivation of the equation is presented together with its projection to zero modes.

hep-th↗