From bcc to fcc: interplay between oscillating long-range and repulsive short-range forces

This paper supplements and partly extends an earlier publication, Phys. Rev. Lett. 95, 265501 (2005). In $d$-dimensional continuous space we describe the infinite volume ground state configurations (GSCs) of pair interactions \vfi and \vfi+\psi, where \vfi is the inverse Fourier transform of a nonnegative function vanishing outside the sphere of radius $K_0$, and $\psi$ is any nonnegative finite-range interaction of range $r_0\leq\gamma_d/K_0$, where $\gamma_3=\sqrt{6}\pi$. In three dimensions the decay of \vfi can be as slow as $\sim r^{-2}$, and an interaction of asymptotic form $\sim\cos(K_0r+\pi/2)/r^3$ is among the examples. At a dimension-dependent density $\rho_d$ the ground state of \vfi is a unique Bravais lattice, and for higher densities it is continuously degenerate: any union of Bravais lattices whose reciprocal lattice vectors are not shorter than $K_0$ is a GSC. Adding $\psi$ decreases the ground state degeneracy which, nonetheless, remains continuous in the open interval $(\rho_d,\rho_d')$, where $\rho_d'$ is the close-packing density of hard balls of diameter $r_0$. The ground state is unique at both ends of the interval. In three dimensions this unique GSC is the bcc lattice at $\rho_3$ and the fcc lattice at $\rho_3'=\sqrt{2}/r_0^3$.Comment: Published versio

Evolutionary bi-stability in pathogen transmission mode

Many pathogens transmit to new hosts by both infection (horizontal transmission) and transfer to the infected host's offspring (vertical transmission). These two transmission modes require speci®c adap- tations of the pathogen that can be mutually exclusive, resulting in a trade-off between horizontal and vertical transmission. We show that in mathematical models such trade-offs can lead to the simultaneous existence of two evolutionary stable states (evolutionary bi-stability) of allocation of resources to the two modes of transmission. We also show that jumping between evolutionary stable states can be induced by gradual environmental changes. Using quantitative PCR-based estimates of abundance in seed and vege- tative parts, we show that the pathogen of wheat, Phaeosphaeria nodorum, has jumped between two distinct states of transmission mode twice in the past 160 years, which, based on published evidence, we interpret as adaptation to environmental change. The ®nding of evolutionary bi-stability has impli- cations for human, animal and other plant diseases. An ill-judged change in a disease control programme could cause the pathogen to evolve a new, and possibly more damaging, combination of transmission modes. Similarly, environmental changes can shift the balance between transmission modes, with adverse effects on human, animal and plant health

Two-dimensional array of magnetic particles: The role of an interaction cutoff

Based on theoretical results and simulations, in two-dimensional arrangements of a dense dipolar particle system, there are two relevant local dipole arrangements: (1) a ferromagnetic state with dipoles organized in a triangular lattice, and (2) an anti-ferromagnetic state with dipoles organized in a square lattice. In order to accelerate simulation algorithms we search for the possibility of cutting off the interaction potential. Simulations on a dipolar two-line system lead to the observation that the ferromagnetic state is much more sensitive to the interaction cutoff $R$ than the corresponding anti-ferromagnetic state. For $R \gtrsim 8$ (measured in particle diameters) there is no substantial change in the energetical balance of the ferromagnetic and anti-ferromagnetic state and the ferromagnetic state slightly dominates over the anti-ferromagnetic state, while the situation is changed rapidly for lower interaction cutoff values, leading to the disappearance of the ferromagnetic ground state. We studied the effect of bending ferromagnetic and anti-ferromagnetic two-line systems and we observed that the cutoff has a major impact on the energetical balance of the ferromagnetic and anti-ferromagnetic state for $R \lesssim 4$. Based on our results we argue that $R \approx 5$ is a reasonable choice for dipole-dipole interaction cutoff in two-dimensional dipolar hard sphere systems, if one is interested in local ordering.Comment: 8 page

Statistical-mechanical theory of the overall magnetic properties of mesocrystals

The mesocrystal showing both electrorheological and magnetorheological effects is called electro-magnetorheological (EMR) solids. Prediction of the overall magnetic properties of the EMR solids is a challenging task due to the coexistence of the uniaxially anisotropic behavior and structural transition as well as long-range interaction between the suspended particles. To consider the uniaxial anisotropy effect, we present an anisotropic Kirkwood-Fr\"{o}hlich equation for calculating the effective permeabilities by adopting an explicit characteristic spheroid rather than a characteristic sphere used in the derivation of the usual Kirkwood-Fr\"{o}hlich equation. Further, by applying an Ewald-Kornfeld formulation we are able to investigate the effective permeability by including the structural transition and long-range interaction explicitly. Our theory can reduce to the usual Kirkwood-Fr\"{o}hlich equation and Onsager equation naturally. To this end, the numerical simulation shows the validity of monitoring the structure of EMR solids by detecting their effective permeabilities.Comment: 14 pages, 1 figur

Field-induced structure transformation in electrorheological solids

We have computed the local electric field in a body-centered tetragonal (BCT) lattice of point dipoles via the Ewald-Kornfeld formulation, in an attempt to examine the effects of a structure transformation on the local field strength. For the ground state of an electrorheological solid of hard spheres, we identified a novel structure transformation from the BCT to the face-centered cubic (FCC) lattices by changing the uniaxial lattice constant c under the hard sphere constraint. In contrast to the previous results, the local field exhibits a non-monotonic transition from BCT to FCC. As c increases from the BCT ground state, the local field initially decreases rapidly towards the isotropic value at the body-centered cubic lattice, decreases further, reaching a minimum value and increases, passing through the isotropic value again at an intermediate lattice, reaches a maximum value and finally decreases to the FCC value. An experimental realization of the structure transformation is suggested. Moreover, the change in the local field can lead to a generalized Clausius-Mossotti equation for the BCT lattices.Comment: Submitted to Phys. Rev.

Effects of geometric anisotropy on local field distribution: Ewald-Kornfeld formulation

We have applied the Ewald-Kornfeld formulation to a tetragonal lattice of point dipoles, in an attempt to examine the effects of geometric anisotropy on the local field distribution. The various problems encountered in the computation of the conditionally convergent summation of the near field are addressed and the methods of overcoming them are discussed. The results show that the geometric anisotropy has a significant impact on the local field distribution. The change in the local field can lead to a generalized Clausius-Mossotti equation for the anisotropic case.Comment: Accepted for publications, Journal of Physics: Condensed Matte

Electrophoresis of a rod macroion under polyelectrolyte salt: Is mobility reversed for DNA?

By molecular dynamics simulation, we study the charge inversion phenomenon of a rod macroion in the presence of polyelectrolyte counterions. We simulate electrophoresis of the macroion under an applied electric field. When both counterions and coions are polyelectrolytes, charge inversion occurs if the line charge density of the counterions is larger than that of the coions. For the macroion of surface charge density equal to that of the DNA, the reversed mobility is realized either with adsorption of the multivalent counterion polyelectrolyte or the combination of electrostatics and other mechanisms including the short-range attraction potential or the mechanical twining of polyelectrolyte around the rod axis.Comment: 8 pages, 5 figures, Applied Statistical Physics of Molecular Engineering (Mexico, 2003). Journal of Physics: Condensed Matters, in press (2004). Journal of Physics: Condensed Matters, in press (2004

Spatiotemporal Response of Crystals in X-ray Bragg Diffraction

The spatiotemporal response of crystals in x-ray Bragg diffraction resulting from excitation by an ultra-short, laterally confined x-ray pulse is studied theoretically. The theory presents an extension of the analysis in symmetric reflection geometry [1] to the generic case, which includes Bragg diffraction both in reflection (Bragg) and transmission (Laue) asymmetric scattering geometries. The spatiotemporal response is presented as a product of a crystal-intrinsic plane wave spatiotemporal response function and an envelope function defined by the crystal-independent transverse profile of the incident beam and the scattering geometry. The diffracted wavefields exhibit amplitude modulation perpendicular to the propagation direction due to both angular dispersion and the dispersion due to Bragg's law. The characteristic measure of the spatiotemporal response is expressed in terms of a few parameters: the extinction length, crystal thickness, Bragg angle, asymmetry angle, and the speed of light. Applications to self-seeding of hard x-ray free electron lasers are discussed, with particular emphasis on the relative advantages of using either the Bragg or Laue scattering geometries. Intensity front inclination in asymmetric diffraction can be used to make snapshots of ultra-fast processes with femtosecond resolution

Laughlin-Jastrow-correlated Wigner crystal in a strong magnetic field

We propose a new ground state trial wavefunction for a two-dimensional Wigner crystal in a strong perpendicular magnetic field. The wavefunction includes Laughlin-Jastrow correlations between electron pairs, and may be interpreted as a crystal state of composite fermions or composite bosons. Treating the power $m$ of the Laughlin-Jastrow factor as a variational parameter, we use quantum Monte Carlo simulations to compute the energy of these new states. We find that our wavefunctions have lower energy than existing crystalline wavefunctions in the lowest Landau level. Our results are consistent with experimental observations of the filling factor at which the transition between the fractional quantum Hall liquid and the Wigner crystal occurs for electron systems. Exchange contributions to the wavefunctions are estimated quantitatively and shown to be negligible for sufficiently small filling factors