Search results for "nonlinear"
showing 10 items of 3684 documents
Harmonic generation in all-dielectric metasurfaces
2023
Nonlinear light generation is a key phenomenon in many optical systems. Recently, the field of nonlinear optics has moved to the miniaturization of conventional bulky components. Among all the new platforms that have been proposed, dielectric nanoscale resonators represent excellent candidates for light generation and manipulation. When arranged in periodic arrays, such high refractive index scattering components become an artificial material called metasurface. Several approaches for designing platforms with enhanced optical nonlinearities at moderate pump intensities have been proposed. In this chapter, we review the most recent results on second- and third-order nonlinear processes in hi…
Mathematical modeling of oral absorption and bioavailability of a fluoroquinolone after its precipitation in the gastrointestinal tract
2013
The objective was to characterize the in vivo absorption and bioavailability (BA) of a low solubility, high permeability fluoroquinolone (CNV97101) that precipitates in the gastrointestinal (GI) tract by mathematical modeling approach. In situ rat intestinal perfusion studies were performed to characterize the absorption mechanism. The oral fraction absorbed in vivo was lower than the predicted based on the in situ intestinal permeability. Two additional routes of administration, intraduodenal (ID) and intraperitoneal (IP) were investigated to explore if precipitation in stomach and subsequent partial re-dissolution were the causes of the lower in vivo BA. Ex vivo precipitation studies with…
The role of humidity in associations of high temperature with mortality: A multicountry, multicity study
2019
BACKGROUND: There is strong experimental evidence that physiologic stress from high temperatures is greater if humidity is higher. However, heat indices developed to allow for this have not consistently predicted mortality better than dry-bulb temperature. OBJECTIVES: We aimed to clarify the potential contribution of humidity an addition to temperature in predicting daily mortality in summer by using a large multicountry dataset. METHODS: In 445 cities in 24 countries, we fit a time-series regression model for summer mortality with a distributed lag nonlinear model (DLNM) for temperature (up to lag 3) and supplemented this with a range of terms for relative humidity (RH) and its interaction…
SIMULATING SPIN MODELS ON GPU: A TOUR
2012
The use of graphics processing units (GPUs) in scientific computing has gathered considerable momentum in the past five years. While GPUs in general promise high performance and excellent performance per Watt ratios, not every class of problems is equally well suitable for exploiting the massively parallel architecture they provide. Lattice spin models appear to be prototypic examples of problems suitable for this architecture, at least as long as local update algorithms are employed. In this review, I summarize our recent experience with the simulation of a wide range of spin models on GPU employing an equally wide range of update algorithms, ranging from Metropolis and heat bath updates,…
Spatially localized solutions of the Hammerstein equation with sigmoid type of nonlinearity
2016
Abstract We study the existence of fixed points to a parameterized Hammerstein operator H β , β ∈ ( 0 , ∞ ] , with sigmoid type of nonlinearity. The parameter β ∞ indicates the steepness of the slope of a nonlinear smooth sigmoid function and the limit case β = ∞ corresponds to a discontinuous unit step function. We prove that spatially localized solutions to the fixed point problem for large β exist and can be approximated by the fixed points of H ∞ . These results are of a high importance in biological applications where one often approximates the smooth sigmoid by discontinuous unit step function. Moreover, in order to achieve even better approximation than a solution of the limit proble…
Dimension bounds in monotonicity methods for the Helmholtz equation
2019
The article [B. Harrach, V. Pohjola, and M. Salo, Anal. PDE] established a monotonicity inequality for the Helmholtz equation and presented applications to shape detection and local uniqueness in inverse boundary problems. The monotonicity inequality states that if two scattering coefficients satisfy $q_1 \leq q_2$, then the corresponding Neumann-to-Dirichlet operators satisfy $\Lambda(q_1) \leq \Lambda(q_2)$ up to a finite-dimensional subspace. Here we improve the bounds for the dimension of this space. In particular, if $q_1$ and $q_2$ have the same number of positive Neumann eigenvalues, then the finite-dimensional space is trivial. peerReviewed
The discretized harmonic oscillator: Mathieu functions and a new class of generalized Hermite polynomials
2003
We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansa…
Serrin-Type Overdetermined Problems: an Alternative Proof
2008
We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely the Hessian equations. In the case of the Poisson equation, our proof is alternative to the proofs proposed by Serrin (moving planes) and by Weinberger. Moreover, our proof makes no direct use of the maximum principle while it sheds light on a relation between the Serrin problem and the isoperimetric inequality.
On the Symmetry of Solutions to a k-Hessian Type Equation
2013
Abstract In this note we prove that if u is a negative solution to a nonlinear elliptic equation involving a Hessian operator, and u is zero on the boundary of a ball, then u is radially symmetric and increasing along the radii.
Apertureless scanning near-field optical microscopy: a comparison between homodyne and heterodyne approaches
2006
International audience; In coherent homodyne apertureless scanning near-field optical microscopy (ASNOM) the background field cannot be fully suppressed because of the interference between the different collected fields, making the images difficult to interpret. We show that implementing the heterodyne version of ASNOM allows one to overcome this issue. We present a comparison between homodyne and heterodyne ASNOM through near-field analysis of gold nanowells, integrated waveguides, and a single evanescent wave generated by total internal reflection. The heterodyne approach allows for the control of the interferometric effect with the background light. In particular, the undesirable backgro…