Quantum Brownian motion and the second law of thermodynamics

We consider a single harmonic oscillator coupled to a bath at zero temperature. As is well-known, the oscillator then has a higher average energy than that given by its ground state. Here we show analytically that for a damping model with arbitrarily discrete distribution of bath modes and damping models with continuous distributions of bath modes with cut-off frequencies, this excess energy is less than the work needed to couple the system to the bath, therefore, the quantum second law is not violated. On the other hand, the second law may be violated for bath modes without cut-off frequencies, which are, however, physically unrealistic models. An erratum to this article is available at .     

Robert Hooke’s Seminal Contribution to Orbital Dynamics

During the second half of the seventeenth century, the outstanding problem in astronomy was to understand the physical basis for Keplers laws describing the observed orbital motion of a planet around the Sun. In the middle 1660s,Robert Hooke (1635–1703) proposed that a planets motion is determined by compounding its tangential velocity with the change in radial velocity impressed by the gravitational attraction of the Sun, and he described his physical concept to Isaac Newton (1642–1726) in correspondence in 1679. Newton denied having heard of Hookes novel concept of orbital motion, but shortly after their correspondence he implemented it by a geometric construction from which he deduced the physical origin of Keplers area law,which later became Proposition I, Book I, of his Principia in 1687.Three years earlier, Newton had deposited a preliminary draft of it, his De Motu Corporum in Gyrum (On the Motion of Bodies), at the Royal Society of London, which Hooke apparently was able to examine a few months later, because shortly there-after he applied Newtons construction in a novel way to obtain the path of a body under the action of an attractive central force that varies linearly with the distance from its center of motion (Hookes law). I show that Hookes construction corresponds to Newtons for his proof of Keplers area law in his De Motu. Hookes understanding of planetary motion was based on his observations with mechanical analogs. I repeated two of his experiments and demonstrated the accuracy of his observations.My results thus cast new light on the significance of Hookes contributions to the development of orbital dynamics, which in the past have either been neglected or misunderstood.Michael Nauenberg is Professor Emeritus of Physics at the University of California, Santa Cruz. His primary research has been in theoretical physics, but he also has written several articles and coedited a book on the historical development of dynamics by Huygens, Newton, and Hooke.     

气管支气管树内气流和颗粒运动的大涡模拟

为更精确地描述真实人体呼吸道内的空气流动,明晰颗粒的运动沉积规律,本文从直接医学CT扫描得到的原始数据出发,利用图像辨识技术,重构了一个男性真人气管支气管树前三级的三维几何模型.采用大涡模拟的方法计算了非规则几何曲面结构内的气体流动现象,并在拉格朗日框架下跟踪颗粒的运动规律.数值计算得到了气流场的三维分布,以及颗粒的运动轨迹情况,结果表明现有基于Weibel的对称模型与真实人体的几何结构有较大的差异,而几何结构对流动影响较大;受非对称复杂结构影响,在不同截面的二次气流速度的分布规律不同;分叉后颗粒进入左右支气管的数量有明显的不同.     

Fluctuating semiflexible polymer ribbon constrained to a ring

Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer bundle is captured by the elastic ribbon model. We investigate the effects a ring geometry induces to a thermally fluctuating ribbon, finding bend-bend coupling in addition to twist-bend coupling. Furthermore, due to the geometric constraint the polymer's effective bending stiffness increases. A new parameter for experimental investigations of polymer bundles is proposed: the mean square diameter of a ribbonlike ring, which is determined analytically in the semiflexible limit. Monte Carlo simulations are performed which affirm the model's prediction up to high flexibility.     

开边界条件下一类新Hubbard模型的精确解

用坐标Bethe ansatz方法详细研究了开边界条件下一类新Hubbard模型的可积性问题. 得到了系统的能谱、可积边界条件和Bethe ansatz方程.     

An occlusion-adaptive tracker based on sparse representation using alternating direction method of multipliers

Recently, sparse representation has been applied to visual tracking with satisfactory performance. However, partial occlusion and computational complexity are two main obstructions in developing sparse-based tracking. In this paper, a simple yet robust tracker based on patch-based sparse representation is proposed. An adaptive motion model, including adaptive sampling regions and adaptive particle numbers, is proposed to improve the sampling efficiency. A self-adjustable segmentation approach is proposed to segment the target into local patches. A patch-based observation model, which is occlusion-adaptive, is constructed by solving a set of L1-regularized least squares problems. The L1-regularized least squares problem is solved using the alternating direction method of multipliers (ADMM). Both quantitative and qualitative experiments are conducted on several challenging image sequences and the comparisons with several state-of-the-art trackers demonstrate the effectiveness and efficiency of our tracker.     

Compare study between smoothing efficiencies of epicyclic motion and orbital motion

The smoothing efficiencies of epicyclic motion and orbital motion in CCOS (computer controlled optical surfacing) were compared. CCOS polishing can smooth out mid-to-high spatial frequency errors which are smaller than tool size on optical mirrors due to the rigidity of polishing tools. The smoothing efficiencies of epicyclic motion and orbital motion with pitch lap and RC lap were compared and the result proved pitch lap with epicyclic motion smoothed ∼1.6 times faster than pitch lap with orbital motion while RC lap with epicyclic motion smoothed ∼1.85 times faster than RC lap with orbital motion.     

Solid-State 17O NMR studies of organic and biological molecules: Recent advances and future directions

This Trends article highlights the recent advances published between 2012 and 2015 in solid-state ¹⁷O NMR for organic and biological molecules. New developments in the following areas are described: (1) new oxygen-containing functional groups, (2) metal organic frameworks, (3) pharmaceuticals, (4) probing molecular motion in organic solids, (5) dynamic nuclear polarization, and (6) paramagnetic coordination compounds. For each of these areas, the author offers his personal views on important problems to be solved and possible future directions.     

Influence of angular momentum in axially symmetric potentials with octupole deformation

The chaotic classical single-particle motion in an oblate octupole deformed potential with a non-zero z-component of angular momentum Lz is investigated. The stability analysis of the trajectories shows that with increasing rotation of the system, the unstable negative curvature regions of the effective potential surface decrease, which converts the chaotic motion of the system into a regular one.     

Kinematics in matrix gravity

We develop the kinematics in Matrix Gravity, which is a modified theory of gravity obtained by a non-commutative deformation of General Relativity. In this model the usual interpretation of gravity as Riemannian geometry is replaced by a new kind of geometry, which is equivalent to a collection of Finsler geometries with several Finsler metrics depending both on the position and on the velocity. As a result the Riemannian geodesic flow is replaced by a collection of Finsler flows. This naturally leads to a model in which a particle is described by several mass parameters. If these mass parameters are different then the equivalence principle is violated. In the non-relativistic limit this also leads to corrections to the Newton’s gravitational potential. We find the first and second order corrections to the usual Riemannian geodesic flow and evaluate the anomalous nongeodesic acceleration in a particular case of static spherically symmetric background.