- 标题
- 摘要
- 关键词
- 实验方案
- 产品
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Correlation imaging in inverse scattering is tomography on probability distributions
摘要： Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be recovered from empirical correlations between amplitude measurements of the leading singularities, detected in the exterior of a region where the potential is almost surely supported. The result is then applied to show that if two sufficiently regular random fields yield the same correlations, they have identical laws as function-valued random variables.
关键词： random potential,scattering,inverse problems,partial differential equations
更新于2025-09-23 15:23:52
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Toward a Precision Ophthalmology: Targeting the Retina
摘要： Efficacious drug delivery to the posterior chamber of the eye is a very challenging problem due to the many physiological barriers that protect the eye against the entry of exogenous substances. To avoid, or to limit, the action of these barriers several drug delivery routes are being investigated and used in clinical ophthalmology. To assist medical and pharmaceutical research, mathematical modeling of the release kinetics assumes a crucial role. In this paper three-dimensional computational models that simulate drug delivery from two different biodegradable polymeric platforms---intravitreal and transscleral---are presented. The models consist of coupled systems of partial differential equations linked by interface conditions, where the properties of the drug, of the implant, and of the eye tissues are taken into account. Peak concentrations and residence times are compared for the two delivery routes. Particular attention is devoted to the modeling of the blood retinal barrier (BRB). The influence of retinal diseases, represented by parameters that characterize the permeation through the BRB, is analyzed. Numerical simulations that illustrate the differences in the behavior of drug released from intravitreal and transscleral implants are included. The numerical results are compared with available experimental data.
关键词： partial differential equations,well-posedness,numerical simulation,drug delivery,retina
更新于2025-09-23 15:21:21
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Nano-wrinkles, compactons, and wrinklons associated with laser-induced Rayleigha??Taylor instability: I. Bubble environment
摘要： We study dynamics, structure and organization of the new paradigm of wavewrinkle structures associated with multipulse laser-induced RayleighTaylor (RT) instability in the plane of a target surface in the circumferential zone (C-zone) of the spot. Irregular target surface, variation of the fluid layer thickness and of the fluid velocity affect the nonlinearity and dispersion. The fluid layer inhomogeneity establishes local domains arranged (organized) in the ?domain network?. The traveling wavewrinkles become solitary waves and latter on become transformed into stationary soliton wavewrinkle patterns. Their morphology varies in the radial direction ofaussian-like spot ranging from the compacton-like solitons to the aperiodic rectangular waves (with rounded top surface) and to the periodic ones. These wavewrinkles may be successfully juxtapositioned with the exact solution of the nonlinear differential equations formulated in the KadomtsevPetviashvili sense taking into account the fluid conditions in particular domain. The cooling wave that starts at the periphery by the end of the pulse causes sudden increase of density and surface tension: the wavewrinkle structures become unstable what causes their break-up. The onset of solidification causes formation of an elastic sheet which starts to shrink generating lateral tension on the wavewrinkles. The focusing of energy at the constrained boundary causes the formation of wrinklons as the new elementary excitation of the elastic sheets.
关键词： solitary waves,nonlinear waves,Compactons,RayleighTaylor instability,wrinklons,lasermatter interaction,partial differential equations
更新于2025-09-23 15:19:57
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[IEEE 2019 International Seminar on Electron Devices Design and Production (SED) - Prague, Czech Republic (2019.4.23-2019.4.24)] 2019 International Seminar on Electron Devices Design and Production (SED) - Thermal model of Zeeman ring laser
摘要： This paper is concerned with modeling of networks with an extremely large number of components using partial differential equations (PDEs). This modeling method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N, the number of components in the network. As N goes to in?nity, the sequence converges to a continuum limit, which is the solution of a certain PDE. We provide suf?cient conditions for the convergence and characterize the rate of convergence. As an application, we model large wireless sensor networks by PDEs. While traditional Monte Carlo simulation for extremely large networks is practically infeasible, PDEs can be solved with reasonable computation overhead using well-established mathematical tools.
关键词： Markov processes,network modeling,partial differential equations,Modeling
更新于2025-09-19 17:13:59
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Modeling and stabilization of current-controlled piezo-electric beams with dynamic electromagnetic field
摘要： Piezoelectric materials can be controlled with current (or charge) as the electrical input, instead of voltage. The main purpose of this paper is to derive the governing equations for a current-controlled piezo-electric beam and to investigate stabilizability. The magnetic permeability in piezo-electric materials is generally neglected in models. However, it has a significant qualitative effect on properties of the control system such as stabilizability. Besides the consideration of current control, there are several new aspects to the model. Most importantly, a fully dynamic magnetic model is included. Also, electrical potential and magnetic vector potential are chosen to be quadratic-through thickness to include the induced effects of the electromagnetic field. Hamilton’s principle is used to derive a boundary value problem that models a single piezo-electric beam actuated by a current (or charge) source at the electrodes. Two sets of decoupled system of partial differential equations are obtained; one for stretching of the beam and another one for bending motion. Since current (or charge) controller only affects the stretching motion, attention is focused on control of the stretching equations in this paper. It is shown that the Lagrangian of the beam is invariant under certain transformations. A Coulomb type gauge condition is used. This gauge condition decouples the electrical potential equation from the equations of the magnetic potential. A semigroup approach is used to prove that the Cauchy problem is well-posed. Unlike voltage actuation, a bounded control operator in the natural energy space is obtained. The paper concludes with analysis of stabilizability and comparison with other actuation approaches and models.
关键词： Piezoelectric,distributed parameter system,charge actuation,current actuation,induced voltage,partial differential equations,control,stabilization,electromotive force
更新于2025-09-19 17:13:59
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[IEEE 2019 IEEE 58th Conference on Decision and Control (CDC) - Nice, France (2019.12.11-2019.12.13)] 2019 IEEE 58th Conference on Decision and Control (CDC) - Design and implementation of a backstepping controller for regulating temperature in 3D printers based on selective laser sintering
摘要： In this paper we investigate the preheating temperature control problem in 3D printers based on the selective laser sintering (SLS) technology. We formulate the process as a temporal sequence of diffusion partial differential equations (PDEs), where each of these PDEs represent the temperature distribution of the layers and the control variable appears at one of the boundary conditions. We propose a full-state feedback control law, an state observer and the associated output feedback control law for the boundary input. The associated output feedback controller ensures the exponential stability of the estimation error in the L2 norm. The theoretical results were tested through numerical simulations and experiments. These results are promising as a method for industrial implementation of the backstepping controller.
关键词： 3D printers,backstepping control,selective laser sintering,temperature control,partial differential equations
更新于2025-09-19 17:13:59
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Time Domain Traveling Wave Model of a Hybrid Laser for Silicon Photonics Applications
摘要： Integration of lasers sources in Silicon Photonics (SiPh), realised trough different techniques, became very appealing for applications in the ever growing field of intra/inter chip data data interconnects and optical communications. We implemented a Time Domain Traveling Wave (TDTW) model based on a set of Partial Differential Equations (PDE) for the slowly varying envelope of the electric field, the medium polarization and the charge carriers density in order to describe the dynamics of a new generation of hybrid laser based on III-V Reflective Semiconductor Optical Amplifier (RSOA) and SiPh external mirror with narrow effective reflectivity bandwidth (< 10GHz) similar to that considered in [2, 3]. The effect of the SiPh mirror can be taken into account by cascading the transmission matrices associated with all its passive sections (namely spot-size-conveter, phase control sections, ring resonators etc...) and including the result in frequency dependent boundary conditions for the PDE problem. Differently from standard rate equation models for semiconductor lasers, our approch correctly reproduce the RSOA gain/refractive index dependence from frequency and carriers density that represent peculiar features of radiation-matter interaction in semiconductor media and play a fundamental role in determining the hybrid laser dynamical behaviour. After computing the TW (Traveling wave) solutions for typical narrow reflectivity bandwidth designs, we numerically showed how for realistic values of the linewidth enhancement factor α (namely α > 2) stable single frequency lasing emission not always occurs at the reflectivity peak (TW0 solution in Fig. 1), but on the red part of the SiPh mirror reflectivity resonance curve around the point of maximum reflectivity slope (TW1 solution in Fig. 1a and Fig. 1b). The fact that this point also coincides with that of minimum optical linewidth, where negative feedback regime reduces instantaneous frequencies fluctuations, and the additional numerical evidence that the interval of TW stability decreases with increasing output power indicate that phase-amplitude coupling mediated by the α-factor may be at the origin of the observed TW instability. It also follows that by a suitable tuning of a phase section in SiPh circuit it is possible to stabilize hybrid laser emission by placing a TW solution on the point of maximum reflectivity slope.
关键词： hybrid laser,Partial Differential Equations,linewidth enhancement factor,Silicon Photonics,Time Domain Traveling Wave model,Reflective Semiconductor Optical Amplifier
更新于2025-09-12 10:27:22