相关论文: Kramers-Kronig Relations for Nonlinear Rheology: 1…
The frequency dependence of third-harmonic medium amplitude oscillatory shear (MAOS) modulus $G_{33}^{*}(\omega)$ provides insight into material behavior and microstructure in the asymptotically nonlinear regime. Motivated by the difficulty…
Kramers-Kronig (KK) relations are usually invoked for causal response functions, but their precise status for non-Markovian quantum memory kernels is less explicit. We separate three Laplace-domain objects: the Nakajima-Zwanzig memory…
The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of…
A new mathematical representation for nonlinear viscoelasticity is presented based on application of the Volterra series expansion to the general nonlinear relationship between shear stress and shear strain history. This theoretical and…
We present multiply subtractive Kramers-Kronig (MSKK) relations for the moments of arbitrary order harmonic generation susceptibility. Using experimental data on third-harmonic wave from polysilane, we show that singly subtractive…
The Kramers-Kronig relations describe a pair of integral transforms relating the real and imaginary components of an analytic function in the complex plane. These relations are particularly useful in extracting refractive index…
We derive a general theory of linear coupling and Kerr nonlinear coupling between modes of dielectric optical resonators from first principles. The treatment is not specific to a particular geometry or choice of mode basis, and can…
It is known that the amplification factor, defined as the ratio of the lensed to the unlensed waveform in the frequency domain, satisfies the Kramers-Kronig (KK) relation, which connects the real and imaginary parts of the amplification…
Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to…
We present the first analysis of harmonic generation data where the full potential of the generalized nonlinear Kramers-Kronig (K-K) relations and sum rules is exploited. We consider two published sets of wide spectral range experimental…
A seemingly obvious extension of the weak equivalence principle, in which all matter must respond to Post-Newtonian gravitational fields, such as Lense-Thirring and radiation fields, in a composition-independent way, is considered in light…
The condition for a negative index of refraction with respect to the vacuum index is established in terms of permittivity and permeability susceptibilities. It is found that the imposition of analyticity to satisfy the Kramers-Kronig…
Analytic and passivity properties of reflection and transmission coefficients of thin-film multilayered stacks are investigated. Using a rigorous formalism based on the inverse Helmholtz operator, properties associated to causality…
The nonlinear oscillator model allows a basic understanding of all nonlinear processes and can be adopted to analyse optical vibrational modes and electronic transition in molecules and crystals, in order to derive general properties of…
We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically-nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. We model this setting using a nonlinear…
Granger causal inference is a contentious but widespread method used in fields ranging from economics to neuroscience. The original definition addresses the notion of causality in time series by establishing functional dependence…
Commonsense causality reasoning (CCR) aims at identifying plausible causes and effects in natural language descriptions that are deemed reasonable by an average person. Although being of great academic and practical interest, this problem…
The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent…
This paper is devoted to the study and the obtaining of the general relation between the real part and the imaginary part of the magnetic susceptibility function in the Laplace domain. This new theoretical technique is general, and can be…
Pairwise comparisons are widely used in decision analysis, preference modeling, and evaluation problems. In many practical situations, the observed comparison matrix is not reciprocal. This lack of reciprocity is often treated as a defect…