Use Of Momentum Research Articles

Schrödinger's equation as a Hamiltonian system

This article describes the concept of the time-dependent Schrödinger equation (TDSE) as a review to add a detailed understanding of the steps to formulate TDSE which can be seen from the classical mechanic's concept as a mechanical wave function. In this article, a comprehensive approach to the concepts of momentum and energy in particles will be described using operators working on wave functions. The results show that the use of momentum and energy operators can show that TDSE is a Hamiltonian system.

An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics

We propose a new explicit pseudo-energy and momentum conserving scheme for the time integration of Hamiltonian systems. The scheme, which is formally second-order accurate, is based on two key ideas: the integration during the time-steps of forces between free-flight particles and the use of momentum jumps at the discrete time nodes leading to a two-step formulation for the acceleration. The pseudo-energy conservation is established under exact force integration, whereas it is valid to second-order accuracy in the presence of quadrature errors. Moreover, we devise an asynchronous version of the scheme that can be used in the framework of slow–fast time-stepping strategies. The scheme is validated against classical benchmarks and on nonlinear or inhomogeneous wave propagation problems.

Switching of Radiation Force on Optically Trapped Microparticles through Photochromic Reactions of Pyranoquinazoline Derivatives

Photocontrol of mechanical motions of small objects has attracted much attention to develop mesoscopic remote actuators. For this purpose, photoinduced morphological changes of molecules, molecular aggregates, and crystals have been extensively studied in the field of chemistry and materials science. Here, we propose direct use of momenta of light (i.e. radiation force) to control the motion of small objects, through photochromic reactions of pyranoquinazoline (PQ) derivatives. PQ is colorless in visible wavelength region while it is in closed form and undergoes photochemical ring-opening reactions to form colored isomers upon UV light irradiation; the open-ring isomers return to the colorless closed isomers mainly through the thermal back reaction. In the experiment, individual polymer microparticles with diameters of 7 μm incorporating PQ were trapped by optical tweezers. When the trapped microparticle was irradiated with UV light, the microparticle was pushed along the axis of light propagation about a...

Contribution of limb momentum to power transfer in athletic wheelchair pushing

Pushing capacity is a key parameter in athletic racing wheelchair performance. This study estimated the potential contribution of upper limb momentum to pushing. The question is relevant since it may affect the training strategy adopted by an athlete. A muscle-free Lagrangian dynamic model of the upper limb segments was developed and theoretical predictions of power transfer to the wheelchair were computed during the push phase. Results show that limb momentum capacity for pushing can be in the order of 40J per push cycle at 10m/s, but it varies with the specific pushing range chosen by the athlete. Although use of momentum could certainly help an athlete improve performance, quantifying the actual contribution of limb momentum to pushing is not trivial. A preliminary experimental investigation on an ergometer, along with a simplified model of the upper limb, suggests that momentum is not the sole contributor to power transfer to a wheelchair. Muscles substantially contribute to pushing, even at high speeds. Moreover, an optimal pushing range is challenging to find since it most likely differs if an athlete chooses a limb momentum pushing strategy versus a muscular exertion pushing strategy, or both at the same time. The study emphasizes the importance of controlling pushing range, although one should optimize it while also taking the dynamics of the recovery period into account.

Coverage-Dependent Modification of the Surface Electronic Structure of an Organic-Semiconductor-Adsorbate Layer

The electronic structure of a hexa-cata-hexabenzocoronene (HBC)/Cu(111) interface is investigated by two-photon photoemission over a range of coverage from 0 to 2 ML monolayers. It is found that increasing the HBC coverage shifts the vacuum level of the Cu substrate until this shift saturates at a coverage of ∼2 ML. Over this same range of coverage, the Shockley and the bare-surface Cu(111) image-potential states are shown to be quenched, while new unoccupied states appear and grow in strength with coverage. The use of momentum- and polarization-resolved photoemission spectra reveals that the new states are modified image states.

Does cheating pay: the role of externally supplied momentum on muscular force in resistance exercise

Our work investigates the use of "external momentum" in the context of hypertrophy-oriented training. This is momentum supplied to the load (such as a dumbbell) used in an exercise by means of action of muscles not inherently involved in the exercise. We challenge the general consensus that the use of such momentum often described as "cheating" is counterproductive. We focus on the use of external momentum in the shoulder lateral raise and adopt a framework whereby exercise execution is simulated on a computer. This is achieved using a physical model of motion which is combined with anthropomorphic measurements and empirical data of muscular recruitment from previous work. The introduction of moderate momentum (producing initial angular velocities around 57.5° s(-1)) increases the torque of the target muscles even without an increase in the load used. A moderate increase in the load and the use of momentum allows the torque to be increased even further. In contrast, excessive use of momentum results in lower demands on the target muscles, while an excessive increase of the load reduces the total hypertrophy stimulus by virtue of the decreased number of repetitions which can be performed successfully and thus the dramatically shortened time under tension. Our results disprove the conventional belief that the use of external momentum necessarily reduces the overload of the target muscles. A moderate use of external momentum increases both the per-repetition peak torque and the total hypertrophy stimulus in a set.

Editorial: General specialists

Even before moving to Pennsylvania almost three decades ago, I had admired Benjamin Franklin. Not only was he an author, publisher, diplomat, postmaster, political theorist, and one of the founding fathers of USA, but he was also a first-rate technoscientific researcher. Anyone who has seen the numerous fierce storms that sweep the Atlantic seaboard would be glad to learn that Franklin invented the lightning rod. He also invented bifocal glasses, a stove that heats better than an open fireplace yet spews out much less smoke, and a flexible urinary catheter for immobile patients—all devices in common use more than two centuries later. He was the first to map the Gulf Stream to produce navigation charts that trimmed the transatlantic sailing time by two weeks. Spreading snatches of cloth of different colors on snow, he determined the scientific reason for wearing dark clothes in winter to keep warm and light clothes in summer to keep cool. With his most famous experiment that gave him a frightening jolt, he ascertained that lightning is electricity. Franklin was not alone among his technoscientific contemporaries for the diversity of his research activities. Perhaps the most prolific mathematician ever, Leonhard Euler originated graph theory which underlies transmission networks, and also developed the equations of inviscid flow. Simeon Poisson was not only an astronomer and a geometer, but he also conjured up the basic differential equation of potential theory and a distribution of probabilities, along with developing the rational use of momentum in mechanical analysis. And how can the great Carl-Friedrich Gauss be forgotten for his seminal contributions to practically every branch of mathematics and physical sciences? That which today is called multidisciplinarity remained in vogue until perhaps the 1910s. My own hero, James Clerk Maxwell, fathered the fundamental set of electromagnetic equations, a probability density distribution in thermodynamics, color photographs, and even a centrifugal governor for steam engines. Jagadis Chunder Bose carried out pioneering investigations on microwave materials at frequencies as high as 60 GHz; invented artificial chiral composite materials; designed, fabricated, and tested structurally chiral materials; devised semiconductor heterojunctions to detect radio signals; and invented the crescograph to identify the similarities of plant and animal tissue. The rise of the specialist probably occurred in the early 20th century, quite possibly because of the spectacular growth in scientific activity worldwide. Ever more departments and academic majors, each associated with a narrow discipline, were created at universities. Perhaps this trend was led by the Nordic and central European countries, as the names of university departments there would confirm. Perhaps universities in USA were the bellwethers instead. International agencies quickly caught up with the trend, as did also newly independent nations and communist countries. To be sure, there were also those who despised compartmentalization, the medical humorist Richard Gordon among them: “None of [the Yanks] would think of blowing their noses or changing the baby’s nappies without first consulting the appropriate specialist—all American doctors of course being specialists. I tell them I’m a general specialist, and that seems to do the trick.” Necessity being a parent of innovation, narrow compartmentalization is at odds with the broad requirements of need-driven technoscientific research. No wonder, as early as during the 1980s, universities began supplementing the hierarchy of colleges and departments with research centers that cut across disciplinary boundaries. Nowadays, national and international

The Momentum Map Representation of Images

This paper discusses the mathematical framework for designing methods of large deformation matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, a theorem is proved showing that these methods may be designed by using the actions of diffeomorphisms on the image data structure to define their associated momentum representations as (cotangent lift) momentum maps. To illustrate its use, the momentum map theorem is shown to recover the known algorithms for matching landmarks, scalar images and vector fields. After briefly discussing the use of this approach for Diffusion Tensor (DT) images, we explain how to use momentum maps in the design of registration algorithms for more general data structures. For example, we extend our methods to determine the corresponding momentum map for registration using semidirect product groups, for the purpose of matching images at two different length scales. Finally, we discuss the use of momentum maps in the design of image registration algorithms when the image data is defined on manifolds instead of vector spaces.

Biomechanics of aggressive inline skating: Landing and balancing on a grind rail

Currently, only epidemiological injury data have been reported for the new extreme sport of aggressive inline skating, or trick skating. No studies have examined the biomechanics of this sport, which involves repetitive jumping and landing from railings, ramps, and ledges, often over 1 m in height. We present results of a pilot study that examined the effect of skater experience and lower extremity biomechanics on energy absorption ability, and observed balance strategies used during two basic tricks. In these tricks, the skater jumps onto an elevated rail and maintains balance while standing in a single position (stall) or sliding along the rail (grind). Lower extremity joint kinematics, impact force characteristics, and general movement behaviours were examined during landing and balance phases. Ten male skaters performed ten stalls and ten frontside grinds on an instrumented grind rail, capable of measuring vertical force. Vertical impact force was found to decrease with increasing skater experience in stalls (r = −0.84, P = 0.002) and grinds (r = −0.84, P = 0.009). This might imply that less-experienced skaters are (subconsciously) more concerned about maintaining balance than refining technique to minimize impact force. Similar to drop landing experiments, peak impact force decreased with increasing knee flexion during stalls (r = −0.65, P = 0.04). During stalls, skaters demonstrated classic balance maintenance strategies (ankle, hip, or multi-joint) depending on trick length. During grinds, skater centre of mass never passed over the rail base of support, suggesting the use of momentum produced from obliquely approaching the rail.

Continuous momentum management of earth-oriented spacecraft

A controller architecture is developed for momentum management of a control moment gyroscope controlled, Earth-oriented spacecraft that uses gravity gradient and aerodynamic torques generated by spacecraft maneuvering. Parameter selection within the architecture allows suppression of or momentum variations due to constant and periodic disturbances as a function of frequency and axis. The capability provided to center the inertial components of the momentum vector reduces cyclic momentum use. An approximate closed-form solution for the dynamic torque equilibrium attitude (attitude motion requiring no control torque) and conditions for its existence are presented. The general three-axis coupled formulation of the governing equations includes aerodynamic torque derivative effects and permits momentum management of spacecraft with equal principal moments of inertia or orientations with significant pitch-to-roll/yaw coupling.

Experiments on Film in the Elementary Physics Laboratory

The successful use of three films: Momentum of Electrons, The Ultimate Speed, and Time Dilation as “experiments” in the second year Physics Laboratory is described. The regular experiments in the laboratory are used to teach experiment design, measurement, and error calculation; and the film experiments were used to show how real physicists designed and performed their experiments using the same principles. The films also permitted the “use” of equipment not normally available to second-year students. Working in pairs, the students viewed the films, took data from the instruments shown, estimated the error in the measurements, then wrote up the experiment as a normal laboratory report. While the use of Momentum of Electrons as an “experiment” was not as successful as was this use of the other two films, the class was enthusiastic over all three films, and was unanimous in wanting at least one film experiment of this type each year.

Use of momentum and energy equations in two‐phase flow

Use of momentum and energy equations in two‐phase flow