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David Ruiz - One of the best experts on this subject based on the ideXlab platform.
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A general existence result for the Toda system on Compact Surfaces
Advances in Mathematics, 2015Co-Authors: Luca Battaglia, Aleks Jevnikar, Andrea Malchiodi, David RuizAbstract:In this paper we consider the following Toda system of equations on a Compact Surface: {−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−Δu1=−4π∑j=1mα1,j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−Δu2=−4π∑j=1mα2,j(δpj−1), which is motivated by the study of models in non-abelian Chern–Simons theory. Here h1,h2h1,h2 are smooth positive functions, ρ1,ρ2ρ1,ρ2 two positive parameters, pipi points of the Surface and α1,i,α2,jα1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation −Δu=ρ1(heu∫ΣheudVg−1)−ρ2(he−u∫Σhe−udVg−1), which arises in fluid dynamics.
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On the Leray-Schauder degree of the Toda system on Compact Surfaces
Proceedings of the American Mathematical Society, 2015Co-Authors: Andrea Malchiodi, David RuizAbstract:In this paper we consider the following Toda system of equations on a Compact Surface: { −∆u1 = 2ρ1 (h1e1 − 1)− ρ2 (h2e2 − 1) , −∆u2 = 2ρ2 (h2e2 − 1)− ρ1 (h1e1 − 1) . Here h1, h2 are smooth positive functions and ρ1, ρ2 two positive parameters. In this note we compute the Leray-Schauder degree mod Z2 of the problem for ρi ∈ (4πk, 4π(k+ 1)) (k ∈ N). Our main tool is a theorem of Krasnoselskii and Zabreiko on the degree of maps symmetric with respect to a subspace. This result yields new existence results as well as a new proof of previous results in literature.
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On the Leray-Schauder degree of the Toda system on Compact Surfaces
arXiv: Analysis of PDEs, 2013Co-Authors: Andrea Malchiodi, David RuizAbstract:In this paper we consider the so-called Toda system of equations on a Compact Surface. In particular, we discuss the parity of the Leray-Schauder degree of that problem. Our main tool is a theorem of Krasnoselskii and Zabreiko on the degree of maps symmetric with respect to a subspace. This result yields new existence results as well as a new proof of previous results in literature.
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A general existence result for the Toda system on Compact Surfaces
arXiv: Analysis of PDEs, 2013Co-Authors: Luca Battaglia, Aleks Jevnikar, Andrea Malchiodi, David RuizAbstract:In this paper we consider the Toda system of equations on a Compact Surface, which is motivated by the study of models in non-abelian Chern-Simons theory. We prove a general existence result using variational methods. The same analysis applies to a mean field equation which arises in fluid dynamics.
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A variational Analysis of the Toda System on Compact Surfaces
Communications on Pure and Applied Mathematics, 2012Co-Authors: Andrea Malchiodi, David RuizAbstract:In this paper we consider the following Toda system of equations on a Compact Surface: We will give existence results by using variational methods in a noncoercive case. A key tool in our analysis is a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u1 and u2. © 2012 Wiley Periodicals, Inc.
Partha Pratim Sahu - One of the best experts on this subject based on the ideXlab platform.
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A Compact Surface Plasmonics Polariton Quantum Entanglement Device
Plasmonics, 2019Co-Authors: Partha Pratim SahuAbstract:Large-scale quantum integrated circuit requires its basic component at nanoscale beyond the diffraction limit. To obtain nanodimensional quantum operation, we introduce two Surface plasmonic polariton (SPP) mode interference couplers as a fundamental component. The Handel-Ou-Mandel (HOM) interference of the coupler of 50:50 splitting ratio provides high-fidelity quantum entanglement. It also enhances the visibility in quantum regime in comparison to that in classical regime. The degradation of fidelity due to small deviation of waveguide width is lower than that of a SPP mode directional coupler. Our results promise to achieve the complexity of quantum plasmonic circuit with high fabrication tolerances.
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theoretical investigation of all optical switch based on Compact Surface plasmonic two mode interference coupler
Journal of Lightwave Technology, 2016Co-Authors: Partha Pratim SahuAbstract:In this paper, an optical controlled Surface plasmonic two mode interference (SPTMI) structure based on silicon waveguide has been proposed for all optical switching. We have shown cross and bar state switching characteristics depending on additional phase between the excited SPP modes propagating through the silicon core obtained due to refractive index modulation of GaAsInP cladding with incidence of optical pulse of width ~1 ps. It is also seen that the coupling length of the proposed device is ~33 times Compact than that of the existing multimode interference-directional coupler. The deviation of crosstalk of the SPTMI switch with increase of fabrication tolerances (±δw) is also almost to that of previously reported all optical switch.
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Compact Surface plasmonic waveguide component for integrated optical processor
International Conference on Optics and Photonics 2015, 2015Co-Authors: Nilima Gogoi, Partha Pratim SahuAbstract:A Compact Surface plasmonic two mode interference waveguide component having silicon core and silver and GaAsInP side cladding is proposed for optical processor elements. Coupling operation is obtained by using index modulation of GaAsInP cladding with applied optical pulse.
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all optical Compact Surface plasmonic two mode interference device for optical logic gate operation
Applied Optics, 2015Co-Authors: Nilima Gogoi, Partha Pratim SahuAbstract:In this paper, we have proposed an ultra-Compact Surface plasmonic two-mode interference (SPTMI) coupler having a silicon core, silver upper and lower cladding, and GaAsInP left and right cladding for basic logic gate operations. By modulating the refractive index of the GaAsInP cladding with incidence of optical pulse energy, we have shown coupling characteristics depending on additional phase change ΔΦ(E) between the excited Surface plasmon polariton modes propagating through the silicon core. By using applied optical pulse dependent coupling behavior of the proposed SPTMI device, the operations of NOT, AND, and OR logic gates are shown. It is also seen that the coupling length of the proposed device is 32.3 times more Compact than that of a multimode interference-directional coupler.
Andrea Malchiodi - One of the best experts on this subject based on the ideXlab platform.
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A topological join construction and the Toda system on Compact Surfaces of arbitrary genus
Analysis & PDE, 2015Co-Authors: Aleks Jevnikar, Sadok Kallel, Andrea MalchiodiAbstract:We consider a Toda system of Liouville equations defined on a Compact Surface which arises as a model for non-abelian Chern-Simons vortices. For the first time the range of parameters $\rho_1 \in (4k\pi , 4(k+1)\pi)$, $k \in \mathbb{N}$, $\rho_2 \in (4\pi, 8\pi )$ is studied with a variational approach on Surfaces with arbitrary genus. We provide a general existence result by means of a new improved Moser-Trudinger type inequality and introducing a topological join construction in order to describe the interaction of the two components.
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A general existence result for the Toda system on Compact Surfaces
Advances in Mathematics, 2015Co-Authors: Luca Battaglia, Aleks Jevnikar, Andrea Malchiodi, David RuizAbstract:In this paper we consider the following Toda system of equations on a Compact Surface: {−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−Δu1=−4π∑j=1mα1,j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−Δu2=−4π∑j=1mα2,j(δpj−1), which is motivated by the study of models in non-abelian Chern–Simons theory. Here h1,h2h1,h2 are smooth positive functions, ρ1,ρ2ρ1,ρ2 two positive parameters, pipi points of the Surface and α1,i,α2,jα1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation −Δu=ρ1(heu∫ΣheudVg−1)−ρ2(he−u∫Σhe−udVg−1), which arises in fluid dynamics.
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Existence and non-existence results for the SU(3) singular Toda system on Compact Surfaces
arXiv: Analysis of PDEs, 2015Co-Authors: Luca Battaglia, Andrea MalchiodiAbstract:We consider the SU(3) Toda system on a Compact Surface. We give both existence and non-existence results under some conditions on the parameters. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohozaev identities.
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On the Leray-Schauder degree of the Toda system on Compact Surfaces
Proceedings of the American Mathematical Society, 2015Co-Authors: Andrea Malchiodi, David RuizAbstract:In this paper we consider the following Toda system of equations on a Compact Surface: { −∆u1 = 2ρ1 (h1e1 − 1)− ρ2 (h2e2 − 1) , −∆u2 = 2ρ2 (h2e2 − 1)− ρ1 (h1e1 − 1) . Here h1, h2 are smooth positive functions and ρ1, ρ2 two positive parameters. In this note we compute the Leray-Schauder degree mod Z2 of the problem for ρi ∈ (4πk, 4π(k+ 1)) (k ∈ N). Our main tool is a theorem of Krasnoselskii and Zabreiko on the degree of maps symmetric with respect to a subspace. This result yields new existence results as well as a new proof of previous results in literature.
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On the Leray-Schauder degree of the Toda system on Compact Surfaces
arXiv: Analysis of PDEs, 2013Co-Authors: Andrea Malchiodi, David RuizAbstract:In this paper we consider the so-called Toda system of equations on a Compact Surface. In particular, we discuss the parity of the Leray-Schauder degree of that problem. Our main tool is a theorem of Krasnoselskii and Zabreiko on the degree of maps symmetric with respect to a subspace. This result yields new existence results as well as a new proof of previous results in literature.
Gunter Gauglitz - One of the best experts on this subject based on the ideXlab platform.
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Compact Surface plasmon resonance transducers with spectral readout for biosensing applications
Sensors and Actuators B-chemical, 1999Co-Authors: Ivo Stemmler, Andreas Brecht, Gunter GauglitzAbstract:Abstract Surface plasmon resonance (SPR) has become an important tool in sensing applications. The most abundant set-up records Surface plasmon excitation for monochromatic light as a function of the angle of incidence. This requires imaging systems and makes the overall set-up bulky. An alternative is spectrally resolved SPR, which allows to separate sensor and signal analysis. One approach is based on the excitation of Surface plasmon waves on the Surface of a declad optical fibre. This allows an elegant probe-type geometry, but is less desirable under manufacturing and liquid handling aspects. We have investigated the possibility to develop Compact SPR-probes combining spectral SPR and a planar sensor geometry. Two miniaturised set-ups were compared to a classical optical-bench device. Performance was assessed by use of the devices as a refractometer. Results were confirmed by two bioassays: (i) by a protein multilayer system consisting of a biotin-albumin-conjugate and polystreptavidin; and (ii) by monitoring the interaction of thrombin and an immobilised thrombin-inhibitor. All set-ups showed good long term stability. Noise values from refractometry were in good agreement with bioassays, for the classical set-up, but increased noise levels were observed for the miniaturised set-ups indicating a requirement for improved mechanical device stability.
James J. Little - One of the best experts on this subject based on the ideXlab platform.
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IROS - Environment modeling with stereo vision
2004 IEEE RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566), 2004Co-Authors: D. Murray, James J. LittleAbstract:We consider the problem of creating Compact Surface-based environment models from stereo vision images taken from a stereo-camera equipped mobile robot. The stereo images can be quite complex and correlation stereo suffers from considerable noise at ranges over a few metres. We construct the environment models by segmenting the scene viewed from a stereo camera into rectangular planar Surfaces through the use of the patchlets Surface element data structure. Patchlets are the projection of the stereo pixels onto detected Surfaces in the scene. They have position, orientation, size and sensor-based confidence measures. The confidence measures allow proper weighting of patchlet parameters when aggregating patchlets into larger Surfaces.
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Environment modeling with stereo vision
2004 IEEE RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566), 2004Co-Authors: D. Murray, James J. LittleAbstract:We consider the problem of creating Compact Surface-based environment models from stereo vision images taken from a stereo-camera equipped mobile robot. The stereo images can be quite complex and correlation stereo suffers from considerable noise at ranges over a few metres. We construct the environment models by segmenting the scene viewed from a stereo camera into rectangular planar Surfaces through the use of the patchlets Surface element data structure. Patchlets are the projection of the stereo pixels onto detected Surfaces in the scene. They have position, orientation, size and sensor-based confidence measures. The confidence measures allow proper weighting of patchlet parameters when aggregating patchlets into larger Surfaces.