Elastic properties of mono- and polydisperse two-dimensional crystals of hard--core repulsive Yukawa particles

Monte Carlo simulations of mono-- and polydisperse two--dimensional crystals are reported. The particles in the studied system, interacting through hard--core repulsive Yukawa potential, form a solid phase of hexagonal lattice. The elastic properties of crystalline Yukawa systems are determined in the $NpT$ ensemble with variable shape of the periodic box. Effects of the Debye screening length ($\kappa^{-1}$), contact value of the potential ($\epsilon$), and the size polydispersity of particles on elastic properties of the system are studied. The simulations show that the polydispersity of particles strongly influences the elastic properties of the studied system, especially on the shear modulus. It is also found that the elastic moduli increase with density and their growth rate depends on the screening length. Shorter screening length leads to faster increase of elastic moduli with density and decrease of the Poisson's ratio. In contrast to its three-dimensional version, the studied system is non-auxetic, i.e. shows positive Poisson's ratio

Elastic properties of cubic crystals: Every's versus Blackman's diagram

Blackman's diagram of two dimensionless ratios of elastic constants is frequently used to correlate elastic properties of cubic crystals with interatomic bondings. Every's diagram of a different set of two dimensionless variables was used by us for classification of various properties of such crystals. We compare these two ways of characterization of elastic properties of cubic materials and consider the description of various groups of materials, e.g. simple metals, oxides, and alkali halides. With exception of intermediate valent compounds, the correlation coefficients for Every's diagrams of various groups of materials are greater than for Blackaman's diagrams, revealing the existence of a linear relationship between two dimensionless Every's variables. Alignment of elements and compounds along lines of constant Poisson's ratio $\nu(,\textbf{m})$, ($\textbf{m}$ arbitrary perpendicular to ) is observed. Division of the stability region in Blackman's diagram into region of complete auxetics, auxetics and non-auxetics is introduced. Correlations of a scaling and an acoustic anisotropy parameter are considered.Comment: 8 pages, 9 figures, presented on The Ninth International School on Theoretical Physics "Symmetry and Structural Properties of Condensed Matter", 5 - 12 September 2007, Myczkowce, Polan

Corrosion properties of Ca65-xMg17.5Zn17.5+x (x = 0, 2.5, 5) alloys

The aim of the paper is to study the effect of zinc addition on the corrosion behavior of Ca65–xMg17.5Zn17.5+x (x = 0, 2.5, 5 at.%) alloys in simulated physiological fluids at 37°C. The electrochemical measurements allowed to determine a corrosion potential, which showed a positive shift from –1.60 V for Ca65Mg17.5Zn17.5 alloy to –1.58 V for Ca60Mg17.5Zn22.5 alloy, adequately. The more significant decrease of hydrogen evolution was noticed for Ca60Mg17.5Zn22.5 alloy (22.4 ml/cm2) than for Ca62.5Mg17.5Zn20 and Ca65Mg17.5Zn17.5 samples (29.9 ml/cm2 and 46.4 ml/cm2), consequently. The corrosion products after immersion tests in Ringer’s solution during 1 h were identified by X-ray diffraction and X-ray photoelectron spectroscopy as calcium, magnesium oxides, carbonates, hydroxides and calcium hydrate

Spectral asymmetry for bag boundary conditions

We give an expression, in terms of boundary spectral functions, for the spectral asymmetry of the Euclidean Dirac operator in two dimensions, when its domain is determined by local boundary conditions, and the manifold is of product type. As an application, we explicitly evaluate the asymmetry in the case of a finite-length cylinder, and check that the outcome is consistent with our general result. Finally, we study the asymmetry in a disk, which is a non-product case, and propose an interpretation.Comment: Some minor changes. To appear in Journal of Physics A: Mathematical and Genera

Experimental evaluation of sub-sampling IQ detection for low-level RF control in particle accelerator systems

The low-level radio frequency (LLRF) control system is one of the fundamental parts of a particle accelerator, ensuring the stability of the electro-magnetic (EM) field inside the resonant cavities. It leverages on the precise measurement of the field by in-phase/quadrature (IQ) detection of an RF probe signal from the cavities, usually performed using analogue downconversion. This approach requires a local oscillator (LO) and is subject to hardware non-idealities like mixer nonlinearity and long-term temperature drifts. In this work, we experimentally evaluate IQ detection by direct sampling for the LLRF system of the Polish free electron laser (PolFEL) now under development at the National Centre for Nuclear Research (NCBJ) in Poland. We study the impact of the sampling scheme and of the clock phase noise for a 1.3-GHz input sub-sampled by a 400-MSa/s analogue-to-digital converter (ADC), estimating amplitude and phase stability below 0.01% and nearly 0.01◦, respectively. The results are in line with state-of-the-art implementations, and demonstrate the feasibility of direct sampling for GHz-range LLRF systems

Novel Features Arising in the Maximally Random Jammed Packings of Superballs

Dense random packings of hard particles are useful models of granular media and are closely related to the structure of nonequilibrium low-temperature amorphous phases of matter. Most work has been done for random jammed packings of spheres, and it is only recently that corresponding packings of nonspherical particles (e.g., ellipsoids) have received attention. Here we report a study of the maximally random jammed (MRJ) packings of binary superdisks and monodispersed superballs whose shapes are defined by |x_1|^2p+...+|x_2|^2p<=1 with d = 2 and 3, respectively, where p is the deformation parameter with values in the interval (0, infinity). We find that the MRJ densities of such packings increase dramatically and nonanalytically as one moves away from the circular-disk and sphere point. Moreover, the disordered packings are hypostatic and the local arrangements of particles are necessarily nontrivially correlated to achieve jamming. We term such correlated structures "nongeneric". The degree of "nongenericity" of the packings is quantitatively characterized by determining the fraction of local coordination structures in which the central particles have fewer contacting neighbors than average. We also show that such seemingly special packing configurations are counterintuitively not rare. As the anisotropy of the particles increases, the fraction of rattlers decreases while the minimal orientational order increases. These novel characteristics result from the unique rotational symmetry breaking manner of the particles.Comment: 20 pages, 8 figure

New boundary conditions for integrable lattices

New boundary conditions for integrable nonlinear lattices of the XXX type, such as the Heisenberg chain and the Toda lattice are presented. These integrable extensions are formulated in terms of a generic XXX Heisenberg magnet interacting with two additional spins at each end of the chain. The construction uses the most general rank 1 ansatz for the 2x2 L-operator satisfying the reflection equation algebra with rational r-matrix. The associated quadratic algebra is shown to be the one of dynamical symmetry for the A1 and BC2 Calogero-Moser problems. Other physical realizations of our quadratic algebra are also considered.Comment: 22 pages, latex, no figure

Phase Transitions of Soft Disks in External Periodic Potentials: A Monte Carlo Study

The nature of freezing and melting transitions for a system of model colloids interacting by a DLVO potential in a spatially periodic external potential is studied using extensive Monte Carlo simulations. Detailed finite size scaling analyses of various thermodynamic quantities like the order parameter, its cumulants etc. are used to map the phase diagram of the system for various values of the reduced screening length $\kappa a_{s}$ and the amplitude of the external potential. We find clear indication of a reentrant liquid phase over a significant region of the parameter space. Our simulations therefore show that the system of soft disks behaves in a fashion similar to charge stabilized colloids which are known to undergo an initial freezing, followed by a re-melting transition as the amplitude of the imposed, modulating field produced by crossed laser beams is steadily increased. Detailed analysis of our data shows several features consistent with a recent dislocation unbinding theory of laser induced melting