One-dimensional global attractor for strongly damped wave equations

We consider the dynamical behavior of the strongly damped wave equations under homogeneous Neumann boundary condition. By the property of limit set of asymptotic autonomous differential equations, we prove that in certain parameter region, the system has a one-dimensional global attractor, which is a periodic horizontal curve.     

A class of subgrid-scale models preserving the symmetry group of Navier–Stokes equations

Navier–Stokes equations (NS) admit transformations which transform a solution to another solution (galilean transformation, scaling transformation, …). They also admit viscosity dependent transformations which transform a solution to a solution of another NS with different viscosity. These particular transformations are called symmetries of NS. Each of them has a physical role (such as conservation laws, …). A consistent turbulence model should then remain invariant under these symmetry transformations. Unfortunately, this is not the case of several models.In this article, a class of subgrid-scale models preserving the symmetries of NS is built. This class is then refined such that the models respect the second law of thermodynamics. One of the simplest models of the class is tested to the flow in a ventilated room. Better results than those provided by Smagorinsky and dynamic models are obtained.     

On new forms of motive differential equations of a mechanical system relative to non-inertial frame

Based on D'Alembert's principle of a mechanical system relative to non-inertial frame and by introducing the concept of the generalized inertial potential, new forms of differential equations of motion of a mechanical system with holonomic and the non-holonomic constraints relative to the non-inertial frame are obtained. The merits and demerits between our method and the Newtonian dynamic method as well as the analytic dynamic method are discussed comparatively. Finally, two examples are given to illustrate the application of the motive differential equations in the new forms.     

Initial value problem for first-order integro-differential equation of Volterra type on time scales

In this paper, we combine the monotone iterative technique with fixed point theory to investigate the extremal solutions of nonlinear integro-differential equations on time scales. Several important lemmas and existence criteria are obtained.     

On the Riemann–Hilbert problem of the matrix Lakshmanan–Porsezian–Daniel system with a $$4\times4$$ AKNS-type matrix Lax pair

Theoretical and Mathematical Physics - The initial-boundary value problems for the matrix Lakshmanan–Porsezian–Daniel system are studied by utilizing the Fokas unified transform...     

Syntheses,Structures and Photocurrent Response Properties of Two Crystals Based on Tetrathiafulvalene Derivatives

In this paper, two compounds [Zn_2~(2+)(2,6-bis(4'-pyridyl)-TTF)(TPA)_2~(2-)](1) and [Cd~(2+)(2,6(7)-bis(4'-pyridyl)-TTF)(TPA)~(2-)(H_2O)_2](TTF = tetrathiafulvalene, TPA = terephthalic acid)(2) were synthesized by using solvothermal method and characterized by single-crystal X-ray. The purity of the two compounds was confirmed by their PXRD data. We also tested the photocurrent responses of these two compounds, and found they could generate photocurrent signal when exposed to light, but the photocurrent intensity of compound 2 is significantly greater than that of 1. From the crystal structure analysis, the possible reason for this phenomenon is that 2 has a more compact ligand arrangement than 1, leading to a higher carrier density and easier excitation.     

Simultaneous chromatic dispersion monitoring,extinction ratio enhancement and wavelength conversion using four-wave mixing

This paper presents a multi-functional all-optical device performs simultaneous chromatic dispersion (CD) monitoring, extinction ratio (ER) improvement and tunable wavelength conversion using four-wave mixing (FWM) in a single piece of highly nonlinear optical fiber (HNLF). The multi-functional ability arises from the nonlinear power transfer function (PTF) between the input signal and the output idler wave, which not only maps the CD information of the signal onto the average power of idler wave, but also transfers the data information to the idler wave with ER enhancement, making the device compact and cost effective. Furthermore within the wavelength tuning range the monitoring sensitivity and output ER can be much higher compared to all optical monitors and regenerators proposed before. Numerical simulations are then used to demonstrate the efficiency of this method.     

Exact solutions to a coupled modified KdV equations with non-uniformity terms

The bilinear form of a coupled modified KdV equations with non-uniformity terms is given and a few soliton solutions are obtained. Furthermore, the multisoliton of the coupled system is expressed by Pfaffian.     

The study of energy bands in nucleus ~(102)Zr

Theoretical calculations of the energy bands in nucleus 102 Zr are carried out by taking the projected shell model approach, which has reproduced the experimental data. In addition, by analyzing band-head energies, corresponding configurations of yrast band, quasi-particle rotational bands and side bands, we have worked out the microscopic formation mechanism of axially symmetric deformation bands: The low-excitation deformation bands are attributed to the high-j intruder states 1g 7/2 and 1h 11/2 in the N=...     

Photolyses of mammalian carboxy-hemoglobin studied by photoacoustic calorimetry

The enthalpy and conformational volume changes in the photolyses of carboxy-hemoglobin (HbCO) of human, bovine, pig, horse and rabbit are investigated by photoacoustic calorimetry. Considering the time scales of the exciting laser pulse and the receiving ultrasound transducers (PVDF films and PZT ceramics), as well as the reaction lifetimes in the photolysis processes of HbCO, the measured results are related to the geminate recombination and tertiary relaxation in photolyses of HbCO. Moreover, the quantum yields of the five mammals are also measured by laser pump-probe technique. The results show that the dynamic parameters, such as enthalpy and conformational volume changes, differ between the processes of the geminate recombination and tertiary relaxation. Also, the dynamic parameters differ among the five mammals although some of them may be consistent with each other.