Ocean internal waves interpreted as oscillation travelling waves in consideration of ocean dissipation

Most studies of the synthetic aperture radar remote sensing of ocean internal waves are based on the solitary wave solutions of the Korteweg-de Vries （KdV） equation, and the dissipative term in the KdV equation is not taken into account. However, the dissipative term is very important, both in the synthetic aperture radar images and in ocean models. In this paper, the traveling-wave structure to characterize the ocean internal wave phenomenon is modeled, the results of numerical experiments are advanced, and a theoretical hypothesis of the traveling wave to retrieve the ocean internal wave parameters in the synthetic aperture radar images is introduced.     

Dynamical structure of peptide molecules: Fourier transform microwave spectroscopy and ab initio calculations of N-methylformamide

Rotational spectra of both trans and cis forms of the N-methylformamide normal as well as deuterated (HCONDCH₃, referred to as N-D) species were observed by Fourier transform microwave spectroscopy in the frequency region from 5 to 118 GHz. Samples were prepared in the form of a beam by a pulsed jet valve maintained at 50 °C and were introduced in a high-vacuum cavity cell, with either Ne or Ar as a carrier gas at a backing pressure of 100 kPa. The observed spectra were analyzed to yield molecular parameters including rotational constants and barrier, V₃, to CH₃ internal-rotation: 53.9 (6) and 301 (4) cm⁻¹ for the trans and cis forms of the normal species, respectively, and 41.9 (6) and 309 (4) cm⁻¹ for the trans and cis forms of the N-D species, respectively. Spectra of four trans isotopologues with ¹³C, ¹⁵N, or ¹⁸O singly-substituted in the internal-rotation A state were observed and analyzed to derive the r_s structure of the trans form. For comparison with the experimental data, ab initio calculations were carried out at MP2/6-31G∗∗ level to derive molecular structure, potential barrier to CH₃ internal rotation, and the energy difference between the cis and trans forms. An extensive coupling was found between the CH₃ internal rotation and N-H out-of-plane bending, suggesting that the potential function for the CH₃ internal-rotation deviates considerably from a simple cos(3α) form. The effects of the V₆ term is briefly discussed.     

On the existence,uniqueness and stability of solutions for semi-linear generalized elasticity equation with general damping term

In this paper, we consider a semi-linear generalized hyperbolic boundary value problem associated to the linear elastic equations with general damping term and nonlinearities of variable exponent type. Under suitable conditions, local and global existence theorems are proved. The uniqueness of the solution have been gotten by eliminating some hypotheses that have been imposed by other authors for different particular problems. We show that any solution with nontrivial initial datum becomes stable.     

Rotation rate of a three-wing rotor illuminated by upward-directed focused beam in optical tweezers

The optical torque and the trapping position (focal point) in optical tweezers are analyzed for upward-directed focused laser illumination using a ray optics model, considering that laser light is incident at not only the lower surface but also the side surface of a 3-wing rotor. The viscous drag force due to the pressure and the shearing stress on all surfaces of the rotor is evaluated using computational fluid dynamics. The rotation rate is simulated in water by balancing the optical torque with the drag force, resulting in 500 rpm for an SU-8 rotor with 20 μm diameter at a laser power of 200 mW. The trapping position is estimated to be 7.6 μm in the rotor with an upward-directed laser at 200 mW via an objective lens having a numerical aperture of 1.4. Both the rotation rate and the trapping position agree well with the values obtained in the experiment.     

Electron Energies, Dipole Electric Moments, and Distribution of the Laurdan Molecule over the Conformation States of Methyl Groups

Using the methods of molecular simulation and HyperChem v.5.0 programs (PM3 method), we carried out calculations of the principal spectroscopic characteristics and of the structure of the laurdan molecule in the ground and the first excited electronic states. The thermal static distribution of molecules over various possible orientations of the plane of methyl groups relative to the plane of the naphthalene bicycle was taken into account. The energies and dipole moments of these electronic states have been calculated as functions of the torsion angle of methyl groups. The existence of an additional mechanism of electronic spectrum broadening is shown; it is associated with thermal mismatch of the equilibrium orientations of the rotational fragment of the molecule and with the dependence of the electron transition frequency on the degree of deviation of the angle from the equilibrium value. The dependence of dipole moments on this angle has been found and calculated. This dependence is the strongest for the ground state. The maximum values of dipole moments in the ground and excited states are 4.0 and 7.6 D.     

变质量质点的动能定理与软绳问题

给出变量质点的动能定理和一对反推内力作功的表达式,并由此给出软绳问题的正确解。     

Lusternik-Schnirelmann 定理的推广

本文根据Brouwer映射度的理论和微分拓扑的基本方法推广了Lusternik_Schnirelmann定理     

Elastic constants of lead-bismuth alloys

A study of ultrasonic velocities and internal friction has been carried out in Pb-Bi alloys in the concentration range of 0 to 49.5 atomic % Bi using the composite oscillator technique. From the velocity and density data a set of elastic constants namely, Young’s modulus, rigidity modulus, bulk modulus and Poisson’s ratio are estimated. The results are interpreted in terms of the phase changes occurring in the alloy system. Internal friction is found to be more sensitive than the elastic constants to the phase changes.     

Orientational anisotropic studies by field rotation technique: near zero-field pulsed EPR experiments of pentacene doped in p-terphenyl

We report a new technique to map the orientational anisotropy of paramagnetic systems without physically changing the crystal orientations in near zero-field (NZF) pulsed EPR experiments. By implementing three sets of orthogonal coils around the sample, we are ble to create a magnetic vector up to 2 mT in any three-dimensional orientation in space. In NZF region, the hyperfine tensor elements are comparable to the electronic Zeeman interaction energy, thus very rich spectral patterns can be obtained by "dialing" in a magnetic field vector without moving the sample. The technique further allows us to examine the site symmetry of organic crystals and powdered solids doped with chromophores which can be photo-excited to the triplet state by laser light. The technique is exemplified in the study of pentacene in p-terphenyl crystals.     

Bridging the Length Scales: Micromechanics of Granular Media

Aristotle's statement that the whole is more than the sum of its parts aptly describes the essence of a granular material's rich and complex behaviour, which ultimately arises from internal mechanisms developed on many length scales. Recently, non-invasive experimental studies have given remarkable insight into the evolution of these mechanisms, thereby providing benchmarks and a unique opportunity for the theoretical modelling of these systems. This paper focuses on the challenges of capturing these multiscale mechanisms within the framework of continuum theory. In particular, a new approach toward developing a non-local micropolar constitutive model of granular media using micromechanics and internal variable theory is discussed. To demonstrate the predictive potential of these models, we present their application in the analysis of two fundamental problems to the mechanics of granular media: (i) formation and evolution of shear bands (the precursors of material failure), (ii) the classical Flamant problem. Finally, we briefly discuss the computational challenges in bridging the gap between micromechanical studies of granular media and the applications of continuum theory on the macro-scale via a finite element analysis of the flat punch problem. In practice, this problem is used to assess the load bearing capacity of a material and is fundamental to civil and structural engineering.