求正交曲线坐标系中速度和加速度的解析方法

引入“广义速度”和“广义加速度”的概念，把正交曲线坐标系或的速度加速度简化为广义坐标及其微商的偏导。     

On the solutions of a dynamic contact problem for a thermoelastic von Kármán plate

We study a dynamic contact problem for a thermoelastic von Kármán plate vibrating against a rigid obstacle. The plate is subjected to a perpendicular force and to a heat source. The dynamics is described by a hyperbolic variational inequality for deflections. The parabolic equation for a thermal strain resultant contains the time derivative of the deflection. We formulate a weak solution of the system and verify its existence using the penalization method. A detailed analysis of the velocity, acceleration, and reaction force of the solution is given. The singular nature of the dynamic contact makes it necessary to treat the acceleration and contact force as time-dependent measures with nonzero singular parts in the zones of contact. Accordingly, the velocity field over the plate suffers (global) jumps at a countable number of times with natural physical interpretations of the signs of the jumps.     

Quantum mechanics in noninertial reference frames: Relativistic accelerations and fictitious forces

One-particle systems in relativistically accelerating reference frames can be associated with a class of unitary representations of the group of arbitrary coordinate transformations, an extension of the Wigner–Bargmann definition of particles as the physical realization of unitary irreducible representations of the Poincaré group. Representations of the group of arbitrary coordinate transformations become necessary to define unitary operators implementing relativistic acceleration transformations in quantum theory because, unlike in the Galilean case, the relativistic acceleration transformations do not themselves form a group. The momentum operators that follow from these representations show how the fictitious forces in noninertial reference frames are generated in quantum theory.     

The O‐Directed Free Radical Hydrostannation of Propargyloxy Dialkyl Acetylenes with Ph3SnH/cat. Et3B. A Refutal of the Stannylvinyl Cation Mechanism

In this Personal Account, we will give an overview of the room temperature O‐directed free radical hydrostannation reaction of propargylically‐oxygenated dialkyl acetylenes with Ph₃SnH and catalytic Et₃B/O₂ in PhMe. We will show how this excellent reaction evolved, and how it has since been used to stereoselectively construct the complex trisubstituted olefin regions of three synthetically challenging natural product targets: (+)‐pumiliotoxin B, (?)‐(3R)‐inthomycin C, and (+)‐acutiphycin. Throughout this Account, we will pay special attention to highlighting important facets of the I?SnPh₃ exchange processes that have so far been used in the various different steric settings that we have addressed, and we will document the range of cross coupling protocols that have critically underpinned the first successful applications of this method in complex natural product total synthesis. Last, but not least, we will comment on various aspects of the O‐directed free radical hydrostannation mechanism that have been published by ourselves, and others, and we will discuss all of the factors that can contribute to the observed stereo‐and regio‐chemical outcomes. We will also challenge and refute the recent non‐directed stannylvinyl cation mechanism put forward by Organ, Oderinde and Froese for our reaction, and we will show how it cannot be operating in these exclusively free radical hydrostannations.     

Sloshing dynamics modulated cryogenic helium fluids driven by gravity gradient or jitter accelerations associated with slew motion in microgravity

The mathematical formulation of the Dewar container sloshing dynamics for a partially filled liquid of cryogenic superfluid helium II driven by the gravity gradient or jitter accelerations associated with slew motion in a microgravity environment are studied. The numerical computation of sloshing dynamics is based on the non-inertia container bounded frame and the solution of time-dependent, three-dimensional partial differential equations subjected to the initial and boundary conditions. This study discloses that the capillary effect of sloshing dynamics governs the liquid-vapor interface fluctuations driven by the gravity gradient or jitter accelerations associated with slew motion in a microgravity environment. The peculiar behavior of superfluid helium in response to sloshing dynamics is also investigated.     

Integrable Hamiltonian N-body problems of goldfish type featuring N arbitrary functions

A simple application of a neat formula relating the time evolution of the N zeros of a (monic) time-dependent polynomial of degree N in the complex variable w to the time evolution of its N coefficients allows to identify integrable Hamiltonian N-body problems in the plane featuring N arbitrary functions, the equations of motions of which are of Newtonian type: accelerations equal forces nonlinearly dependent on the coordinates of the N particle. The motions generally take place in the complex z-plane, or, equivalently, in the Cartesian xy-plane with z = x + iy. It is also easy to identify qualitative features of special subclasses of these models, for instance cases in which all the motions starting from an arbitrary real set of initial data are confined and multiply periodic. It is also indicated how to generate from these models hierarchies of analogous models with analogous properties.     

正交曲线坐标系中加速度的矢量求法

利用矢量法,给出一种求解正交曲线坐标系中加速度的简捷方法。     

Well-posedness results and asymptotic behaviour for a phase transition model taking into account microscopic accelerations

We obtain an existence and uniqueness result to Frémond's phase transition model which take into account microscopic movements and accelerations. Moreover, the irreversible evolution of the phase variable is considered. Next, we perform an asymptotic analysis on the solution to the above problem, as the power of the microscopic acceleration forces goes to zero.