Principal component analysis - an efficient tool for variable stars diagnostics

We present two diagnostic methods based on ideas of Principal Component Analysis and demonstrate their efficiency for sophisticated processing of multicolour photometric observations of variable objects.Comment: 8 pages, 4 figures. Published alread

Plus-minus construction leads to perfect invisibility

Recent theoretical advances applied to metamaterials have opened new avenues to design a coating that hides objects from electromagnetic radiation and even the sight. Here, we propose a new design of cloaking devices that creates perfect invisibility in isotropic media. A combination of positive and negative refractive indices, called plus-minus construction, is essential to achieve perfect invisibility (i.e., no time delay and total absence of reflection). Contrary to the common understanding that between two isotropic materials having different refractive indices the electromagnetic reflection is unavoidable, our method shows that surprisingly the reflection phenomena can be completely eliminated. The invented method, different from the classical impedance matching, may also find electromagnetic applications outside of cloaking devices, wherever distortions are present arising from reflections.Comment: 24 pages, 10 figure

Sheath parameters for non-Debye plasmas: simulations and arc damage

This paper describes the surface environment of the dense plasma arcs that damage rf accelerators, tokamaks and other high gradient structures. We simulate the dense, non-ideal plasma sheath near a metallic surface using Molecular Dynamics (MD) to evaluate sheaths in the non-Debye region for high density, low temperature plasmas. We use direct two-component MD simulations where the interactions between all electrons and ions are computed explicitly. We find that the non-Debye sheath can be extrapolated from the Debye sheath parameters with small corrections. We find that these parameters are roughly consistent with previous PIC code estimates, pointing to densities in the range $10^{24} - 10^{25}\mathrm{m}^{-3}$. The high surface fields implied by these results could produce field emission that would short the sheath and cause an instability in the time evolution of the arc, and this mechanism could limit the maximum density and surface field in the arc. These results also provide a way of understanding how the "burn voltage" of an arc is generated, and the relation between self sputtering and the burn voltage, while not well understood, seems to be closely correlated. Using these results, and equating surface tension and plasma pressure, it is possible to infer a range of plasma densities and sheath potentials from SEM images of arc damage. We find that the high density plasma these results imply and the level of plasma pressure they would produce is consistent with arc damage on a scale 100 nm or less, in examples where the liquid metal would cool before this structure would be lost. We find that the sub-micron component of arc damage, the burn voltage, and fluctuations in the visible light production of arcs may be the most direct indicators of the parameters of the dense plasma arc, and the most useful diagnostics of the mechanisms limiting gradients in accelerators.Comment: 8 pages, 16 figure

Casimir force between planes as a boundary finite size effect

The ground state energy of a boundary quantum field theory is derived in planar geometry in D+1 dimensional spacetime. It provides a universal expression for the Casimir energy which exhibits its dependence on the boundary conditions via the reflection amplitudes of the low energy particle excitations. We demonstrate the easy and straightforward applicability of the general expression by analyzing the free scalar field with Robin boundary condition and by rederiving the most important results available in the literature for this geometry.Comment: 10 pages, 2 eps figures, LaTeX2e file. v2: A reference is added, some minor modifications made to clarify the text. v3: 9 pages, 3 eps figures, LaTeX2e file, revtex style. Paper throughly restructured and rewritten. Much more details are given, but essential results and conclusions are unchanged. Version accepted for publicatio

On the maximal number of real embeddings of spatial minimally rigid graphs

The number of embeddings of minimally rigid graphs in $\mathbb{R}^D$ is (by definition) finite, modulo rigid transformations, for every generic choice of edge lengths. Even though various approaches have been proposed to compute it, the gap between upper and lower bounds is still enormous. Specific values and its asymptotic behavior are major and fascinating open problems in rigidity theory. Our work considers the maximal number of real embeddings of minimally rigid graphs in $\mathbb{R}^3$. We modify a commonly used parametric semi-algebraic formulation that exploits the Cayley-Menger determinant to minimize the {\em a priori} number of complex embeddings, where the parameters correspond to edge lengths. To cope with the huge dimension of the parameter space and find specializations of the parameters that maximize the number of real embeddings, we introduce a method based on coupler curves that makes the sampling feasible for spatial minimally rigid graphs. Our methodology results in the first full classification of the number of real embeddings of graphs with 7 vertices in $\mathbb{R}^3$, which was the smallest open case. Building on this and certain 8-vertex graphs, we improve the previously known general lower bound on the maximum number of real embeddings in $\mathbb{R}^3$

Photonic Clusters

We show through rigorous calculations that dielectric microspheres can be organized by an incident electromagnetic plane wave into stable cluster configurations, which we call photonic molecules. The long-range optical binding force arises from multiple scattering between the spheres. A photonic molecule can exhibit a multiplicity of distinct geometries, including quasicrystal-like configurations, with exotic dynamics. Linear stability analysis and dynamical simulations show that the equilibrium configurations can correspond with either stable or a type of quasi-stable states exhibiting periodic particle motion in the presence of frictional dissipation.Comment: 4 pages, 3 figure

Longitudinal chirality, enhanced non-reciprocity, and nano-scale planar one-way guiding

When a linear chain of plasmonic nano-particles is exposed to a transverse DC magnetic field, the chain modes are elliptically polarized, in a single plane parallel to the chain axis; hence, a novel longitudinal plasmon-rotation is created. If, in addition, the chain geometry possesses longitudinal rotation, e.g. by using ellipsoidal particles that rotate in the same plane as the plasmon rotation, strong non-reciprocity is created. The structure possesses a new kind of chirality--the longitudinal chirality--and supports one-way guiding. Since all particles rotate in the same plane, the geometry is planar and can be fabricated by printing leaf-like patches on a single plane. Furthermore, the magnetic field is significantly weaker than in previously reported one-way guiding structures. These properties are examined for ideal (lossless) and for lossy chains.Comment: to appear in PR

The moving boundary problem in the presence of a dipole magnetic field

An exact analytic solution is obtained for a uniformly expanding, neutral, infinitely conducting plasma sphere in an external dipole magnetic field. The electrodynamical aspects related to the radiation and transformation of energy were considered as well. The results obtained can be used in analyzing the recent experimental and simulation data.Comment: 17 pages, 1 figure, Submitted to J. Phys. A, Math. and Genera

Electronic Properties of Graphene in a Strong Magnetic Field

We review the basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strong perpendicular magnetic field. One of its most salient features is the relativistic quantum Hall effect the observation of which has been the experimental breakthrough in identifying pseudo-relativistic massless charge carriers as the low-energy excitations in graphene. The effect may be understood in terms of Landau quantization for massless Dirac fermions, which is also the theoretical basis for the understanding of more involved phenomena due to electronic interactions. We present the role of electron-electron interactions both in the weak-coupling limit, where the electron-hole excitations are determined by collective modes, and in the strong-coupling regime of partially filled relativistic Landau levels. In the latter limit, exotic ferromagnetic phases and incompressible quantum liquids are expected to be at the origin of recently observed (fractional) quantum Hall states. Furthermore, we discuss briefly the electron-phonon coupling in a strong magnetic field. Although the present review has a dominating theoretical character, a close connection with available experimental observation is intended.Comment: 56 pages, 27 figures; published version with minor corrections and updated reference

High-resolution images of five radio quasars at early cosmological epochs

Context: Until now, there have only been seven quasars at z>4.5 whose the high-resolution radio structure had been studied in detail with Very Long Baseline Interferometry (VLBI) imaging. Aims: We almost double the number of VLBI-imaged quasars at these high redshifts with the aim of studying their redshift-dependent structural and physical properties in a larger sample. Methods: We observed five radio quasars (J0813+3508, J1146+4037, J1242+5422, J1611+0844, and J1659+2101) at 4.5<z<5 with the European VLBI Network (EVN) at 1.6 GHz on 29 October 2008 and at 5 GHz on 22 October 2008. The angular resolution achieved ranges from 1.5 to 25 milli-arcseconds (mas), depending on the observing frequency, the position angle in the sky, and the source's celestial position. Results: The sources are all somewhat extended on mas scales, but compact enough to be detected at both frequencies. With one exception of a flat-spectrum source (J1611+0844), their compact emission is characterised by a steep radio spectrum. We found no evidence of Doppler-boosted radio emission in the quasars in our sample. The radio structure of one of them (J0813+3508) is extended to ~7", which corresponds to 43 kpc projected linear size. Many of the highest redshift compact radio sources are likely to be young, evolving objects, far-away cousins of the powerful gigahertz peaked-spectrum (GPS) and compact steep-spectrum (CSS) sources that populate the Universe at lower redshifts.Comment: 7 pages, 2 figures, accepted for Astronomy & Astrophysic