arXiv subjects

S. Sridhar

Publications and source records attributed to S. Sridhar.

At least 55 records · Page 3Linked to original sources

arXiv2009

Slow m=1 instabilities of softened gravity Keplerian discs

We present the simplest model that permits a largely analytical exploration of the m=1 counter-rotating instability in a "hot" nearly Keplerian disc of collisionless self-gravitating matter. The model consists of a two-component softened gravity disc, whose linear modes are analysed using WKB. The modes are slow in the sense that their (complex) frequency is smaller than the Keplerian orbital frequency by a factor which is of order the ratio of the disc mass to the mass of the central object. Very simple analytical expressions are derived for the precession frequencies and growth rates of local modes; it is shown that a nearly Keplerian disc must be unrealistically hot to avoid an overstability. Global modes are constructed for the case of zero net rotation.

astro-ph.GA↗

arXiv2009

Anomalous drift of spiral waves in heterogeneous excitable media

We study the drift of spiral waves in a simple model of heterogeneous excitable medium, having gradients in local excitability or cellular coupling. For the first time, we report the anomalous drift of spiral waves towards regions having higher excitability, in contrast to all earlier observations in reaction-diffusion models of excitable media. Such anomalous drift can promote the onset of complex spatio-temporal patterns, e.g., those responsible for life-threatening arrhythmias in the heart.

nlin.PS↗

arXiv2009

Shear dynamo problem: Quasilinear kinematic theory

Large-scale dynamo action due to turbulence in the presence of a linear shear flow is studied. Our treatment is quasilinear and kinematic but is non perturbative in the shear strength. We derive the integro-differential equation for the evolution of the mean magnetic field, by systematic use of the shearing coordinate transformation and the Galilean invariance of the linear shear flow. For non helical turbulence the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves. This is valid for any Galilean-invariant velocity field, independent of its dynamics. Hence the shear-current assisted dynamo is essentially absent, although large-scale non helical dynamo action is not ruled out.

astro-ph↗

arXiv2008

Nanoengineering of a Negative-Index Binary-Staircase Lens for the Optics Regime

We show that a binary-staircase optical element can be engineered to exhibit an effective negative index of refraction, thereby expanding the range of optical properties theoretically available for future optoelectronic devices. The mechanism for achieving a negative-index lens is based on exploiting the periodicity of the surface corrugation. By designing and nanofabricating a plano-concave binary-staircase lens in the InP/InGaAsP platform, we have experimentally demonstrated at 1.55 microns that such negative-index concave lenses can focus plane waves. The beam propagation in the lens was studied experimentally and was in excellent agreement with the three-dimensional finite-difference time-domain numerical simulations.

physics.optics↗

arXiv2008

Nanowire waveguide made from extremely anisotropic metamaterials

Exact solutions are obtained for all the modes of wave propagation along an anisotropic cylindrical waveguide. Closed-form expressions for the energy flow on the waveguide are also derived. For extremely anisotropic waveguide where the transverse permittivity is negative while the longitudinal permittivity is positive, only transverse magnetic (TM) and hybrid modes will propagate on the waveguide. At any given frequency the waveguide supports an infinite number of eigenmodes. Among the TM modes, at most only one mode is forward wave. The rest of them are backward waves which can have very large effective index. At a critical radius, the waveguide supports degenerate forward- and backward-wave modes with zero group velocity. These waveguides can be used as phase shifters and filters, and as optical buffers to slow down and trap light.

physics.optics↗

arXiv2007

Controlling spatiotemporal chaos in excitable media using an array of control points

The dynamics of activation waves in excitable media can give rise to spiral turbulence, the resulting spatiotemporal chaos being associated with empirical biological phenomena such as life-threatening disturbances in the natural rhythm of the heart. In this paper, we propose a spatially extended but non-global scheme using an array of control points for terminating such spatiotemporally chaotic excitations. A low-amplitude control signal is applied sequentially at each point on the array, resulting in a traveling wave of excitation in the underlying medium which drives away the turbulent activity. Our method is robust even in the presence of significant heterogeneities in the medium, which have often been an impediment to the success of other control schemes.

nlin.CD↗

arXiv2007

Superlens imaging theory for anisotropic nanostructured metamaterials with broadband all-angle negative refraction

We show that a metamaterial consisting of aligned metallic nanowires in a dielectric matrix has strongly anisotropic optical properties. For filling ratio f<1/2, the composite medium shows two surface plasmon resonances (SPRs): the transverse and longitudinal SPR with wavelengths lambda_t lambda_l, the longitudinal SPR, the material exhibits Re epsilon_l<0, Re epsilon_t>0, relative to the nanowires axis, enabling the achievement of broadband all-angle negative refraction and superlens imaging. An imaging theory of superlens made of these media is established. High performance systems made with Au, Ag or Al nanowires in nanoporous templates are designed and predicted to work from the infrared up to ultraviolet frequencies.

cond-mat.mtrl-sci↗

arXiv2007

Controlling spatiotemporal chaos and spiral turbulence in excitable media: A review

Excitable media are a generic class of models used to simulate a wide variety of natural systems including cardiac tissue. Propagation of excitation waves in this medium results in the formation of characteristic patterns such as rotating spiral waves. Instabilities in these structures may lead to spatiotemporal chaos through spiral turbulence, which has been linked to clinically diagnosed conditions such as cardiac fibrillation. Usual methods for controlling such phenomena involve very large amplitude perturbations and have several drawbacks. There have been several recent attempts to develop low-amplitude control procedures for spatiotemporal chaos in excitable media which are reviewed in this paper. The control schemes have been broadly classified by us into three types: (i) global, (ii) non-global spatially-extended and (iii) local, depending on the way the control signal is applied, and we discuss the merits and drawbacks for each.

nlin.CD↗

arXiv2007

Alternative approach to all-angle negative refraction in two-dimensional photonic crystals

We show that with an appropriate surface modification, a slab of photonic crystal can be made to allow wave transmission within the band gap. Furthermore, negative refraction and all-angle-negative-refraction (AANR) can be achieved by this surface modification in frequency windows that were not realized before in two-dimensional photonic crystals [C. Luo et al, Phys. Rev. B 65, 201104 (2002)]. This approach to AANR leads to new applications in flat lens imaging. Previous flat lens using photonic crystals requires object-image distance u+v less than or equal to the lens thickness d, u+v d. Our approach can be used to design flat lens with u+v=sd with s>>1, thus being able to image large and/or far away objects. Our results are confirmed by FDTD simulations.

cond-mat.other↗

arXiv2007

A new mechanism for negative refraction and focusing using selective diffraction from surface corrugation

Refraction at a smooth interface is accompanied by momentum transfer normal to the interface. We show that corrugating an initially smooth, totally reflecting, non-metallic interface provides a momentum kick parallel to the surface, which can be used to refract light negatively or positively. This new mechanism of negative refraction is demonstrated by visible light and microwave experiments on grisms (grating-prisms). Single-beam all-angle-negative-refraction is achieved by incorporating a surface grating on a flat multilayered material. This negative refraction mechanism is used to create a new optical device, a grating lens. A plano-concave grating lens is demonstrated to focus plane microwaves to a point image. These results show that customized surface engineering can be used to achieve negative refraction even though the bulk material has positive refractive index. The surface periodicity provides a tunable parameter to control beam propagation leading to novel optical and microwave devices.

cond-mat.other↗

arXiv2006

Imbalanced Strong MHD Turbulence

We present a phenomenological model of imbalanced MHD turbulence in an incompressible magnetofluid. The steady-state cascades, of waves traveling in opposite directions along the mean magnetic field, carry unequal energy fluxes to small length scales, where they decay due to viscous and resistive dissipation. The inertial-range scalings are well-understood when both cascades are weak. We study the case when both cascades are, in a sense, strong. The inertial-range of this imbalanced cascade has the following properties: (i) the ratio of the r.m.s. Elsasser amplitudes is independent of scale, and is equal to the ratio of the corresponding energy fluxes; (ii) in common with the balanced strong cascade, the energy spectra of both Elsasser waves are of the anisotropic Kolmogorov form, with their parallel correlation lengths equal to each other on all scales, and proportional to the two-thirds power of the transverse correlation length; (iii) the equality of cascade time and waveperiod (critical balance) that characterizes the strong balanced cascade does not apply to the Elsasser field with the larger amplitude. Instead, the more general criterion that always applies to both Elsasser fields is that the cascade time is equal to the correlation time of the straining imposed by oppositely-directed waves. Our results are particularly relevant for turbulence in the solar wind. Spacecraft measurements have established that, in the inertial range of solar wind turbulence, waves travelling away from the sun have higher amplitudes than those travelling towards it. Result (i) allows us to infer the turbulent flux ratios from the amplitude ratios, thus providing insight into the origin of the turbulence.

astro-ph↗

arXiv2006

Negative refraction and plano-concave lens focusing in one-dimensional photonic crystals

Negative refraction is demonstrated in one-dimensional (1D) dielectric photonic crystals (PCs) at microwave frequencies. Focusing by plano-concave lens made of 1D PC due to negative refraction is also demonstrated. The frequency-dependent negative refractive indices, calculated from the experimental data matches very well with those determined from band structure calculations. The easy fabrication of one-dimensional photonic crystals may open the door for new applications.

cond-mat.other↗

arXiv2006

Folded Fields as the Source of Extreme Radio-Wave Scattering in the Galactic Center

A strong case has been made that radio waves from sources within about half a degree of the Galactic Center undergo extreme diffractive scattering. However, problems arise when standard (``Kolmogorov'') models of electron density fluctuations are employed to interpret the observations of scattering in conjunction with those of free-free radio emission. Specifically, the outer scale of a Kolmogorov spectrum of electron density fluctuations is constrained to be so small that it is difficult to identify an appropriate astronomical setting. Moreover, an unacceptably high turbulent heating rate results if the outer scale of the velocity field coincides with that of the density fluctuations. We propose an alternative model based on folded magnetic field structures that have been reported in numerical simulations of small-scale dynamos. Nearly isothermal density variations across thin current sheets suffice to account for the scattering. There is no problem of excess turbulent heating because the outer scale for the velocity fluctuations is much larger than the widths of the current sheets. We speculate that interstellar magnetic fields could possess geometries that reflect their origins: fields maintained by the galactic dynamo could have large correlation lengths, whereas those stirred by local energetic events might exhibit folded structures.

astro-ph↗

arXiv2006

Duality between quantum and classical dynamics for integrable billiards

We establish a duality between the quantum wave vector spectrum and the eigenmodes of the classical Liouvillian dynamics for integrable billiards. Signatures of the classical eigenmodes appear as peaks in the correlation function of the quantum wave vector spectrum. A semiclassical derivation and numerical calculations are presented in support of the results. These classical eigenmodes can be observed in physical experiments through the auto-correlation of the transmission coefficient of waves in quantum billiards. Exact classical trace formulas of the resolvent are derived for the rectangle, equilateral triangle, and circle billiards. We also establish a correspondence between the classical periodic orbit length spectrum and the quantum spectrum for integrable polygonal billiards.

nlin.SI↗

arXiv2005

Flat lens without optical axis: Theory of imaging

We derive a general theory for imaging by a flat lens without optical axis. We show that the condition for imaging requires a material having elliptic dispersion relations with negative group refraction, equivalent to an effective anisotropic refractive index n(theta). Imaging can be achieved with both negative (n<0) and positive (n>0) refractive indices. The Veselago-Pendry lens is a special case with isotropic negative refractive index of n(theta)=-1. Realizations of the imaging conditions using anisotropic media and inhomogeneous media, particularly photonic crystals, are discussed. Numerical examples of imaging and requirements for sub-wavelength imaging are also presented.

cond-mat.other↗

arXiv2005

Focusing by Plano-Concave lens using Negative Refraction

We demonstrate focusing of a plane microwave by a plano-concave lens fabricated from a photonic crystal (PhC) having negative refractive index and left-handed electromagnetic properties. An inverse experiment, in which a plane wave is produced from a source placed at the focal point of the lens is also reported. A frequency dependent negative refractive index, is obtained for the lens from the experimental data which matches well with that determined from band structure calculations.

cond-mat.other↗

arXiv2004

Microwave photonic crystal with tailor-made negative refractive index

Negative refraction and left-handed electromagnetism in a metallic photonic crystal (PC) wedge are demonstrated in free space for both transverse magnetic and electric mode propagation. The experimental results are in excellent agreement with numerical calculations based on the band structure with no fit parameters used in modeling. The results demonstrate precision control on the design and fabrication of the PC to achieve tailor-made refractive indices between -0.6 and +1.

cond-mat.other↗

arXiv2004

Correlations among the Riemann zeros: Invariance, resurgence, prophecy and self-duality

We present a conjecture describing new long range correlations among the Riemann zeros leading to 3 principal features: (i) The spectral auto-correlation is invariant w.r.t. the averaging window. (ii) Resurgence occurs wherein the lowest zeros appear in all auto-correlations. (iii) Suitably defined correlations lead to predictions (prophecy) of new zeros. This conjecture is supported by analytical arguments and confirmed by numerical calculations using 10^{22} zeros computed by Odlyzko. The results lead to a self-duality of the Riemann spectrum similar to the quantum-classical duality observed in billiards.

nlin.CD↗