Self-Assembly on a Cylinder: A Model System for Understanding the Constraint of Commensurability

A crystal lattice, when confined to the surface of a cylinder, must have a periodic structure that is commensurate with the cylinder circumference. This constraint can frustrate the system, leading to oblique crystal lattices or to structures with a chiral seam known as a "line slip" phase, neither of which are stable for isotropic particles in equilibrium on flat surfaces. In this study, we use molecular dynamics simulations to find the steady-state structure of spherical particles with short-range repulsion and long-range attraction far below the melting temperature. We vary the range of attraction using the Lennard-Jones and Morse potentials and find that a shorter-range attraction favors the line-slip. We develop a simple model based only on geometry and bond energy to predict when the crystal or line-slip phases should appear, and find reasonable agreement with the simulations. The simplicity of this model allows us to understand the influence of the commensurability constraint, an understanding that might be extended into the more general problem of self-assembling particles in strongly confined spaces.Comment: 12 pages, 9 figures. Submitted for publication, 201

Nonlinear Schroedinger Equation in the Presence of Uniform Acceleration

We consider a recently proposed nonlinear Schroedinger equation exhibiting soliton-like solutions of the power-law form $e_q^{i(kx-wt)}$, involving the $q$-exponential function which naturally emerges within nonextensive thermostatistics [$e_q^z \equiv [1+(1-q)z]^{1/(1-q)}$, with $e_1^z=e^z$]. Since these basic solutions behave like free particles, obeying $p=\hbar k$, $E=\hbar \omega$ and $E=p^2/2m$ ($1 \le q<2$), it is relevant to investigate how they change under the effect of uniform acceleration, thus providing the first steps towards the application of the aforementioned nonlinear equation to the study of physical scenarios beyond free particle dynamics. We investigate first the behaviour of the power-law solutions under Galilean transformation and discuss the ensuing Doppler-like effects. We consider then constant acceleration, obtaining new solutions that can be equivalently regarded as describing a free particle viewed from an uniformly accelerated reference frame (with acceleration $a$) or a particle moving under a constant force $-ma$. The latter interpretation naturally leads to the evolution equation $i\hbar \frac{\partial}{\partial t}(\frac{\Phi}{\Phi_0}) = - \frac{1}{2-q}\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} [(\frac{\Phi}{\Phi_0})^{2-q}] + V(x)(\frac{\Phi}{\Phi_0})^{q}$ with $V(x)=max$. Remarkably enough, the potential $V$ couples to $\Phi^q$, instead of coupling to $\Phi$, as happens in the familiar linear case ($q=1$).Comment: 4 pages, no figure

Helioseismic holography of simulated sunspots: magnetic and thermal contributions to travel times

Wave propagation through sunspots involves conversion between waves of acoustic and magnetic character. In addition, the thermal structure of sunspots is very different than that of the quiet Sun. As a consequence, the interpretation of local helioseismic measurements of sunspots has long been a challenge. With the aim of understanding these measurements, we carry out numerical simulations of wave propagation through sunspots. Helioseismic holography measurements made from the resulting simulated wavefields show qualitative agreement with observations of real sunspots. We use additional numerical experiments to determine, separately, the influence of the thermal structure of the sunspot and the direct effect of the sunspot magnetic field. We use the ray approximation to show that the travel-time shifts in the thermal (non-magnetic) sunspot model are primarily produced by changes in the wave path due to the Wilson depression rather than variations in the wave speed. This shows that inversions for the subsurface structure of sunspots must account for local changes in the density. In some ranges of horizontal phase speed and frequency there is agreement (within the noise level in the simulations) between the travel times measured in the full magnetic sunspot model and the thermal model. If this conclusion proves to be robust for a wide range of models, it would suggest a path towards inversions for sunspot structure.Comment: Accepted for publication in The Astrophysical Journa

Anharmonic effects in magnetoelastic chains

We describe a new mechanism leading to the formation of rational magnetization plateau phases, which is mainly due to the anharmonic spin-phonon coupling. This anharmonicity produces plateaux in the magnetization curve at unexpected values of the magnetization without explicit magnetic frustration in the Hamiltonian and without an explicit breaking of the translational symmetry. These plateau phases are accompanied by magneto-elastic deformations which are not present in the harmonic case.Comment: 5 pages, 3 figure

Order Parameter Flow in the SK Spin-Glass I: Replica Symmetry

We present a theory to describe the dynamics of the Sherrington- Kirkpatrick spin-glass with (sequential) Glauber dynamics in terms of deterministic flow equations for macroscopic parameters. Two transparent assumptions allow us to close the macroscopic laws. Replica theory enters as a tool in the calculation of the time- dependent local field distribution. The theory produces in a natural way dynamical generalisations of the AT- and zero-entropy lines and of Parisi's order parameter function $P(q)$. In equilibrium we recover the standard results from equilibrium statistical mechanics. In this paper we make the replica-symmetric ansatz, as a first step towards calculating the order parameter flow. Numerical simulations support our assumptions and suggest that our equations describe the shape of the local field distribution and the macroscopic dynamics reasonably well in the region where replica symmetry is stable.Comment: 41 pages, Latex, OUTP-94-29S, 14 figures available in hardcop

Constraints on θ_(13) from a three-flavor oscillation analysis of reactor antineutrinos at KamLAND

We present new constraints on the neutrino oscillation parameters Δm^2_(21), θ_(12), and θ_(13) from a three flavor analysis of solar and KamLAND data. The KamLAND data set includes data acquired following a radiopurity upgrade and amounts to a total exposure of 3.49 x 10^(32) target-proton-year. Under the assumption of CPT invariance, a two-flavor analysis (θ_(13) = 0) of the KamLAND and solar data yields the best-fit values tan^2θ_(12) = 0.444^(+0.036)_(-0.030) and Δm^2_(21) = 7.50^(+0.19)_(-0.20) x 10^(-5) eV^2; a three-flavor analysis with θ13 as a free parameter yields the best-fit values tan^2θ_(12) = 0.452^(+0.035)_(-0.033), Δm^2_(21) = 7.50^(+0.19)_(-0.20) x 10^(-5) eV^2, and sin^2θ_(13) = 0.020^(+0.016)_(-0.016). This θ_(13) interval is consistent with other recent work combining the CHOOZ, atmospheric and long-baseline accelerator experiments. We also present a new global θ_(13) analysis, incorporating the CHOOZ, atmospheric, and accelerator data, which indicates sin^2θ_(13) = 0.009^(+0.013)-_(0.007). A nonzero value is suggested, but only at the 79% C.L

Statistical transmutation in doped quantum dimer models

We prove a "statistical transmutation" symmetry of doped quantum dimer models on the square, triangular and kagome lattices: the energy spectrum is invariant under a simultaneous change of statistics (i.e. bosonic into fermionic or vice-versa) of the holes and of the signs of all the dimer resonance loops. This exact transformation enables to define duality equivalence between doped quantum dimer Hamiltonians, and provides the analytic framework to analyze dynamical statistical transmutations. We investigate numerically the doping of the triangular quantum dimer model, with special focus on the topological Z2 dimer liquid. Doping leads to four (instead of two for the square lattice) inequivalent families of Hamiltonians. Competition between phase separation, superfluidity, supersolidity and fermionic phases is investigated in the four families.Comment: 3 figure

Apparatus for measuring charged particle beam

An apparatus to measure the incident charged particle beam flux while effectively eliminating losses to reflection and/or secondary emission of the charged particle beam being measured is described. It comprises a sense cup through which the charged particle beam enters. A sense cone forms the rear wall of the interior chamber with the cone apex adjacent the entry opening. An outer case surrounds the sense cup and is electrically insulated therefrom. Charged particles entering the interior chamber are trapped and are absorbed by the sense cup and cone and travel through a current measuring device to ground

Discrete approximations to vector spin models

We strengthen a result of two of us on the existence of effective interactions for discretised continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretising continuous-spin models, and show that, except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions.Comment: 12 page