A hybrid approach for quantizing complicated motion of a charged particle in time-varying magnetic field

Quantum characteristics of a charged particle subjected to a singular oscillator potential under an external magnetic field is investigated via SU(1,1) Lie algebraic approach together with the invariant operator and the unitary transformation methods. The system we managed is somewhat complicated since we considered not only the time-variation of the effective mass of the system but also the dependence of the external magnetic field on time in an arbitrary fashion. In this case, the system is a kind of time-dependent Hamiltonian systems which require more delicate treatment when we study it. The complete wave functions are obtained without relying on the methods of perturbation and/or approximation, and the global phases of the system are identified. To promote the understanding of our development, we applied it to a particular case, assuming that the effective mass slowly varies with time under a time-dependent magnetic field.     

Surface forces between bottlebrush polymer layers

In this review, I summarize recent experimental investigations of surface and friction forces between bottlebrush structure macromolecules including biolubricants and biomimetic ones by direct force measurements. I also discuss recent experimental investigations of synergy in lubrication in which a question, ‘How do lubricants act together?’, is aimed to be answered. Lastly, challenges and opportunities for developing efficient lubricating systems are outlined.     

Surface forces and friction tuned by thermo-responsive polymer films

Thermo-responsive polymer films have enabled the development of various functional surfaces with switchable interfacial properties. Assessing the surface forces and friction on such films is of paramount importance. On the one hand, it allows us to extract a great deal of information on the interfacial properties of the films, e.g., adhesiveness and lubricity, and how they could be tuned using different stimuli. On the other hand, surface force measurements complement other thin-film analysis methods, e.g., ellipsometry, to better perceive the correlation between the molecular properties of the polymer chains and the interfacial properties of the film. On this basis, we will, herein, provide a concise review of some recent studies on surface forces and friction tuned by thermo-responsive polymer films. This outline comprises a summary of several research works addressing the effects of temperature, solvent composition, and salts on surface forces and friction. In the end, we briefly discuss a few select studies in which the regulation of surface forces by thermo-responsive polymers is examined with an emphasis on the potential applications.     

Comparison of the adhesion forces in single and double-layer coatings on the MEMS surfaces by JKR and DMT models

In many medical and industrial applications, some strategies are needed to control the adhesion forces between the materials, because surface forces can activate or hinder the function of the device. All actual surfaces present some levels of roughness and the contact between two surfaces is transferred by the asperities on the surfaces. The force of the adhesion, which depends on the operating situations, can be influenced by the contact region. The aim of the present study is to predict the adhesion force in MEMS surfaces using the JKR and DMT models. The surfaces of the coating material in this research consisted of the single-layer coating of Gold and Silver, and the double-layer coating of TiO₂/Gold and TiO₂/Silver on the silicon (100) substrates. The depositing was done by the thermal evaporation method. The results showed that the double-layer coating developed by the new deposition method helped the reduction of the adhesion forces between the probe tip and the specimen surface. The predicted adhesion forces between the probe and the specimens with DMT and JKR models were compared with the experimental results. For all specimens, the simulated data by applying the JKR theory were in a good agreement with the adhesion force experimental values.     

Unimodular Fourier multipliers for modulation spaces

We investigate the boundedness of unimodular Fourier multipliers on modulation spaces. Surprisingly, the multipliers with general symbol eiα|ξ|, where α∈[0,2], are bounded on all modulation spaces, but, in general, fail to be bounded on the usual Lp-spaces. As a consequence, the phase-space concentration of the solutions to the free Schrödinger and wave equations are preserved. As a byproduct, we also obtain boundedness results on modulation spaces for singular multipliers |ξ|^−δsin(α|ξ|) for 0?δ?α.     

How far is ‘infinity’?

Our present knowledge of the distribution of matter in the local universe is reviewed. Appropriate boundaries isolating astrophysical systems are sought on the length scales of the solar system, the galaxy and the local group of galaxies. The influence of diffuse matter is compared to that of nearby objects using the geodesic deviation equation. The question of assigning realistic wave zones to some canonical sources of gravitational radiation is briefly reviewed. Taking our local environment as typical, it is found that compact systems of a size similar to that of the solar system can normally be considered isolated. Compact galactic nuclei with low matter flux can probably also be considered isolated.     

Forces controlling protein interactions: theory and experiment

This work reviews both the theory and experimental measurements of the fundamental forces that control protein solution behavior. In addition to the Derjaguin–Landau–Verwey–Overbeek (DLVO) forces, we also discuss the relative importance of hydrodynamic, solvation, and lock-and-key interactions in controlling protein solution behavior. The more common computational methods used to calculate both electrostatic and van der Waals potentials are described. Particular attention is given to the differences between proteins and ideal colloidal particles, and the computational methods used to address those differences. In addition to theoretical investigations of protein interactions, the results of recent direct measurements of the forces governing protein interactions are reviewed. These experimental results provide not only measurements against which the theories can be tested, but also demonstrate directly the relative importance of both DLVO and non-classical DLVO forces in the control of protein behavior.     

Long-range Rydberg-Rydberg interactions and molecular resonances

We present a detailed theoretical treatment to describe the lineshape of molecular resonances in a cold dense gas of rubidium Rydberg atoms. Molecular potentials in Hund's case (c) are calculated by diagonalization of an interaction matrix. We show how the strong ℓ-mixing due to long-range Rydberg-Rydberg interactions can lead to resonances in excitation spectra. Such resonances were first reported in [S.M. Farooqi et al., Phys. Rev. Lett. 91, 183002 (2003)], where single UV photon excitations from the 5s ground state occurred at energies corresponding to normally forbidden transitions or very far detuned from the atomic energies. Here, we focus our attention on resonances at energies corresponding to excited atom pairs (n - 1)p_3/2+(n + 1)p_3/2. Very good agreement between the theoretical and experimental lineshapes is found.     

用Wave CN软件演示声波干涉

利用计算机软件Wave CN直观稳定地演示了声波干涉现象,验证了波的干涉加强和减弱的条件.     

A Crack with Interfacial Bonds in an Isotropic Medium Strengthened with a Regular System of Stringers

An isotropic medium containing a system of foreign transverse rectilinear inclusions is considered. Such a medium can be interpreted as an infinite plate strengthened with a regular system of ribs (stringers) whose cross section is a very narrow rectangle. The medium is weakened by a rectilinear crack. The action of the stringers is replaced with unknown equivalent concentrated forces at the points of their connection with the medium. A model of a crack with areas where its faces interact with each other is investigated. This interaction is modeled by introducing bonds (adhesion forces) between faces in the crack tip zone. The boundary-value problem on equilibrium of the crack under the action of external tensile forces is reduced to a nonlinear singular integral equation, from the solution of which the tractions in the bonds are found. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 773–782, November–December, 2005.