Search results for "Ellipsoid"

Robust control of uncertain multi-inventory systems via linear matrix inequality

2008

We consider a continuous time linear multi inventory system with unknown demands bounded within ellipsoids and controls bounded within ellipsoids or polytopes. We address the problem of "-stabilizing the inventory since this implies some reduction of the inventory costs. The main results are certain conditions under which "-stabilizability is possible through a saturated linear state feedback control. All the results are based on a Linear Matrix Inequalities (LMIs) approach and on some recent techniques for the modeling and analysis of polytopic systems with saturations.

Morphological determination of the phototrophic community composition of biological soil crusts in coastal sand dunes in northern Germany

2022

This dataset comprises the microbial community composition of biological soil crusts in north-German sand dunes. For this we obtained enrichment cultures of phototrophic microorganisms, by placing fragments of biocrusts of the same Petri dishes as used for sequencing, in Petri dishes with Bold Basal (1N BBM) agarized medium (Bischoff and Bold 1963). Cultures were grown under standard laboratory conditions: with a 12-hour alteration of light and dark phases and irradiation of 25 μmol photons m-2 s-1 at a temperature 20 ± 5 ºС. Microscopic study of these raw cultures began in the third week of cultivation. Morphological examinations were performed using Olympus BX53 light microscope with Noma…

Solid-solid phase transition in hard ellipsoids

2009

We present a computer simulation study of the crystalline phases of hard ellipsoids of revolution. A previous study [P. Pfleiderer and T. Schilling, Phys. Rev. E 75, 020402 (2007)]. showed that for aspect ratios a/bor=3 the previously suggested stretched-fcc phase [D. Frenkel and B. Mulder, Mol. Phys. 55, 1171 (1985)] is unstable with respect to a simple monoclinic phase with two ellipsoids of different orientations per unit cell (SM2). In order to study the stability of these crystalline phases at different aspect ratios and as a function of density we have calculated their free energies by thermodynamic integration. The integration path was sampled by an expanded ensemble method in which …

Understanding the global structure of two-level quantum systems with relaxation: Vector fields organized through the magic plane and the steady-state…

2013

Simple monoclinic crystal phase in suspensions of hard ellipsoids

2006

We present a computer simulation study on the crystalline phases of hard ellipsoids of revolution. For aspect ratios $\ensuremath{\geqslant}3$ the previously suggested stretched-fcc phase [Frenkel and Mulder, Mol. Phys. 55, 1171 (1985)] is replaced by a different crystalline phase. Its unit cell contains two ellipsoids with unequal orientations. The lattice is simple monoclinic. The angle of inclination of the lattice, $\ensuremath{\beta}$, is a very soft degree of freedom, while the two right angles are stiff. For one particular value of $\ensuremath{\beta}$, the close-packed version of this crystal is a specimen of the family of superdense packings recently reported [Donev et al., Phys. R…

Mode coupling theory for molecular liquids: What can we learn from a system of hard ellipsoids?

1999

Molecular fluids show rich and complicated dynamics close to the glass transition. Some of these observations are related to the fact that translational and orientational degrees of freedom couple in nontrivial ways. A model system which can serve as a paradigm to understand these couplings is a system of hard ellipsoids of revolution. To test this we compare at the ideal glass transition the static molecular correlators of a linear A-B Lennard-Jones molecule obtained from a molecular dynamics simulation with a selected fluid of hard ellipsoids for which the static correlators have been obtained using Percus-Yevick theory. We also demonstrate that the critical non-ergodicity parameters obta…

Anisotropy in strain gradient elasticity: Simplified models with different forms of internal length and moduli tensors

2018

Abstract Anisotropy of centro-symmetric (first) strain gradient elastic materials is addressed and the role there played by the dual gradient directions (i.e. directions of strain gradient and of double stress lever arm) is investigated. Anisotropy manifests itself not only through the classical fourth-rank elasticity tensor C (21 independent constants) in the form of moduli anisotropy, but also through a sixth-rank elasticity tensor B (171 independent constants) in a unified non-separable form as compound internal length/moduli anisotropy. Depending on the microstructure properties, compound anisotropy may also manifest itself in a twofold separable form through a decoupled tensor B = L C …

Overdamped dynamics of paramagnetic ellipsoids in a precessing magnetic field

2009

We report on the dynamical behavior of paramagnetic ellipsoidal particles dispersed in water and floating above a flat plane when subjected to an external precessing magnetic field. When the magnetic field and the long axis of the particles are on the same plane, two clear regimes are distinguished in which the particles follow the magnetic modulation synchronously or asynchronously. Both regimes are also observed when the field precesses at an angle $\ensuremath{\vartheta}l90\ifmmode^\circ\else\textdegree\fi{}$ with respect to the normal to the confining plane, while the transition frequency increases with decreasing precession angle. We combine experimental observations with a theoretical…

Electron-gas clusters: the ultimate jellium model

1995

The local spin-density approximation is used to calculate ground- and isomeric-state geometries of jellium clusters with 2 to 22 electrons. The positive background charge of the model is completely deformable, both in shape and in density. The model has no input parameters. The resulting shapes of the clusters exhibit breaking of axial and inversion symmetries; in general the shapes are far from ellipsoidal. Those clusters which lack inversion symmetry are extremely soft against odd-multipole deformations. Some clusters can be interpreted as molecules built from magic clusters. The deformation produces a gap at the Fermi level. This results in a regular odd-even staggering of the total ener…

Dynamics of Uniaxial Hard Ellipsoids

2007

We study the dynamics of monodisperse hard ellipsoids via a new event-driven molecular dynamics algorithm as a function of volume fraction $\phi$ and aspect ratio $X_0$. We evaluate the translational $D_{trans}$ and the rotational $D_{rot}$ diffusion coefficient and the associated isodiffusivity lines in the $\phi-X_0$ plane. We observe a decoupling of the translational and rotational dynamics which generates an almost perpendicular crossing of the $D_{trans}$ and $D_{rot}$ isodiffusivity lines. While the self intermediate scattering function exhibits stretched relaxation, i.e. glassy dynamics, only for large $\phi$ and $X_0 \approx 1$, the second order orientational correlator $C_2(t)$ sho…