We present a review of experimental data on the nonlinear optical properties of thermotropic and lyotropic liquid crystals probed by the Z-scan technique. Depending on the time scale, different processes originate a nonlinear optical response. Particularly, at nanosecond range, the physical processes associated with the nonlinear response in thermotropics are not completely understood. In lyotr...

In order to account for low temperature heat propagation phenomena in crystals of sodium fluoride and bismuth, we employ a thermodynamic model for rigid materials involving a vector-field internal state variable. The model is either wavelike or diffusive, depending on the temperature regime considered.

Given the measurement of temperature at a fixed time θ > 0 and the measurement of temperature in a subregion of the physical domain, we investigate the simultaneous reconstruction of the initial temperature and heat radiative coefficient in a heat conductive system. The stability of the inverse problem is first established, and then the numerical reconstruction is mainly studied. The reconstruc...

Low temperature and low frequency properties of a spin-boson model are investigated within a super operator and Liouville space formulation. The leading contributions are identified with the help of projection operators projecting onto the equilibrium state. The quantities of interest are expressed in terms of weighted bath propagators and static linear and nonlinear susceptibilities. In partic...

It is commonly acknowledged that ecosystem responses to global climate change are nonlinear. However, patterns of the nonlinearity have not been well characterized on ecosystem carbon and water processes. We used a terrestrial ecosystem (TECO) model to examine nonlinear patterns of ecosystem responses to changes in temperature, CO2, and precipitation individually or in combination. The TECO mod...

This paper deals with a theoretical mathematical analysis of one-dimensional solidification problem, in which kinetic undercooling is incorporated into the This temperature condition at the interface. A model problem with nonlinear kinetic law is considered. We prove a local result intimate for the uniqueness of solution of the corresponding free boundary problem.

This paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. A model problem with nonlinear kinetic law is considered. The main result is an existence theorem. The mathematical effects of the kinetic term are discussed

In recent years, a sufficient condition for determining chaotic behaviours of the nonlinear systems has been characterized by the negative Schwarzian derivative (Hacıbekiroǧlu et al, Nonlinear Anal.: Real World Appl. 10, 1270 (2009)). In this work, the Schwarzian derivative has been calculated for investigating the quantum chaotic transition points in the high-temperature superconducting frame ...

Knowledge of the most suitable environmental conditions for an organism growth and development is a prerequisite for developing mass rearing technology. The temperature requirements for development and the optimal range of temperatures for growth and reproduction of Coleomegilla maculata De Geer were studied. The development time of individual C. maculata larvae was determined at 18, 21, 24, 27...

Thermal conduction is an important energy transfer and damping mechanism in astrophysical flows. Fourier’s law, in which the heat flux is proportional to the negative temperature gradient, leading to temperature diffusion, is a well-known empirical model of thermal conduction. However, entropy diffusion has emerged as an alternative thermal conduction model, despite not ensuring the monotonicit...