Variation Of Potential Energy Research Articles

Non-linear effects in internal-tide beams, and mixing

A non-linear non-hydrostatic model (MIT-gcm) is used to study the generation and propagation of internal tides. The model domain covers a continental slope and neighbouring parts of the deep ocean and shelf. Uniformity in the along-slope direction is assumed. We focus on the non-linear evolution of the internal tide once generated. In particular, we show that in the main region of generation, over the upper part of the slope, small-scale features occur, indicative of breaking and mixing. Far from the generation region, non-linear processes are important in the reflection of the beam at the bottom, where higher harmonics are generated. This implies an energy transfer toward higher frequencies and the resulting shape of the energy spectra is consistent with observations. Turbulent and mixing processes are analysed by employing an adiabatic sorting method; thus, we calculate the development in time of the available potential energy, the variation in the background potential energy due to irreversible processes, and the distribution of the Cox number (the local turbulent diffusivity normalized by the background diffusivity) over the slope. With rotation, the transfer of energy to higher harmonics is reduced.

Use of Lumbar Point for the Estimation of Potential and Kinetic Mechanical Power in Running

The purpose of this study was to estimate the difference between potential and kinetic mechanical powers in running (Pke, Ppe) calculated from the center of mass and one anatomic point of the body located on the lower part of the runner's back, the “lumbar point.” Six runners undertook a treadmill run at constant velocity and were filmed individually with a video camera (25 Hz). The 3-D motion analysis system, ANIMAN3D, uses a numerical manikin (MAN3D) which compares a voluminal subject (the athlete) directly to the manikin which possesses the same voluminal properties. This analysis system allows the trajectories of the center of mass and the lumbar point to be calculated. Then, from these trajectories, potential and kinetic mechanical powers in running are calculated. The results show that the utilization of the lumbar point rather than the runner's center of mass leads to a significant overestimation of Pkeand a significant underestimation of Ppe(bothp< 0.05). In spite of these differences, however, both methods of calculating Pkeand Ppeare well correlated: respectively,r= 0.92;p≤ 0.01, andr= 0.68;p≤ 0.05. Taking into account that the trajectory of an anatomic point is experimentally easier to access than that of the center of mass, such a point could be used to estimate the evolution of kinetic or potential energy variation in different cases. However, when the lumbar point rather than the center of mass is used to estimate the mechanical energy produced in running, Pkecould appear to be a discriminating parameter, which it is not.

Critical strain for a locally elliptical delamination near the surface of a cylindrical laminated shell under hydrothermal effects

An analytical method is presented to investigate hydrothermal effects on locally buckling for an elliptical delamination near the surface of cylindrical laminated shells. The critical strain of non-linear buckling for a locally elliptic delamination of cylindrical laminated shells is obtained by considering transverse displacements of the elliptically sub-laminated shells. The stacking sequence of sub-laminated shells may be multilayer and asymmetric. The geometrical axis of sub-laminated shells may be arbitrary. The Young's modulus and the thermal and humidity expansion coefficients of the material are considered as functions of temperature change in base-laminated shells. The critical strains of locally buckling for cylindrical laminated shells subjected to hydrothermal effects are extracted for different stacking sequences, and different radii of base-laminated shells, by applying Rayleigh–Ritz method based on second variation of potential energy. From results carried out, it is found that the critical strain from the non-linear buckling for a locally elliptic delamination near the surface of a cylindrical laminated shell presents a lower value than that from linear considerations.

On J-integral and potential energy variation

The divergence theorem has been used in a region containing the crack tip to derive the J-integral from the potential energy variation in most fracture mechanics books. Such a derivation is flawed because of the crack tip stress singularity. The present study describes a rigorous and straightforward derivation of the J-integral from the potential energy variation with crack extension by carefully addressing the effect of the crack tip singularity.

Observed variations of tropical convective available potential energy

Data from selected tropical radiosonde stations (located between 25°S and 25°N) are used to compute multidecadal trends in convective available potential energy (CAPE). Positive trends slightly outnumber negative trends, with the greatest concentration of positive trends occurring in the western Pacific Ocean and the Caribbean Sea. Analysis shows that positive and negative CAPE trends are primarily driven by same‐signed trends in low‐level moisture, while lapse rate trends play a secondary role and may either increase or decrease the magnitude of the CAPE trends. Monthly CAPE anomalies are generally positively correlated with sounding‐derived precipitable water (PW) and lapse rate as well as with Special Sensor Microwave Imager (SSMI)‐derived PW for retrievals located over the sounding location. Sounding‐derived PW estimates for island and coastal locations were averaged and compared to tropical SSMI PW estimates, which are available only over the oceans. The two time series are poorly correlated, suggesting that the limited number of sounding stations considered herein does not adequately capture tropical‐wide variability. The relationship of CAPE changes to PW and lapse rate changes is examined on a variety of timescales for evidence of quasi‐equilibrium (QE) behavior, in which convection acts to maintain an approximately moist adiabatic temperature profile. Strict QE, in which convection maintains an exactly moist adiabatic temperature profile, is assumed in the convective parameterizations of many general circulation models. PW and lapse rate anomalies are negatively correlated on multidecadal timescales and on monthly timescales in heavily raining regions, in support of QE theory. However, no such negative correlation is seen over the course of the seasonal cycle or for monthly timescales in low‐rain areas. CAPE anomalies were compared to nearest‐grid‐point monthly precipitation anomalies derived from surface‐based rain gauges. Correlations are small and centered at about zero. Mean tropical rainfall estimates, based on a combination of satellite and surface gauge data, are uncorrelated with the mean tropical SSMI PW estimates.

The Lagrange problem on an optimal column: old and new results

The paper is devoted to the optimization and post-buckling behavior of columns elastically supported at both ends. The unimodal solutions are analyzed, and it is shown that for nonzero support stiffnesses they are not optimal. The bimodal formulation of the problem is set up. By using analytical expressions for bimodal columns obtained earlier, the bimodal optimal solutions are integrated for different values of the support stiffnesses. With the assumption of geometrical nonlinearity, the post-buckling behavior of the bimodal optimal columns is studied. It is shown that the initial post-buckling behavior is governed by four supercritical solutions emanating from the trivial equilibrium state at the critical load. The stability of the new equilibrium states is investigated by using the second variation of the total potential energy. It is shown that only two post-buckling equilibrium states are stable while the other two are unstable, this conclusion being valid for all considered values of the support stiffnesses. An important limit case of a clamped---simply supported column that has caused debate in many publications is analyzed.

The relationship between the instantaneous velocity field and the rate of moment release in the lithosphere

SUMMARY Instantaneous velocity gradients within the continental lithosphere are often related to the tectonic driving forces. This relationship is direct if the forces are secular, as for the case of loading of a locked section of a subduction interface by the downgoing plate. If the forces are static, as for the case of lateral variations in gravitational potential energy, then velocity gradients can be produced only if the lithosphere has, on average, zero strength. The static force model may be related to the long-term velocity field but not the instantaneous velocity field (typically measured geodetically over a period of several years) because over short time intervals the upper lithosphere behaves elastically. In order to describe both the short- and long-term behaviour of an (elastic) lithosphere‐(viscoelastic) asthenosphere system in a selfconsistent manner, I construct a deformation model termed the expected interseismic velocity (EIV) model. Assuming that the lithosphere is populated with faults that rupture continually, each with a definite mean recurrence time, and that the Earth is well approximated as a linear elastic‐viscoelastic coupled system, I derive a simple relationship between the instantaneous velocity field and the average rate of moment release in the lithosphere. Examples with synthetic fault networks demonstrate that velocity gradients in actively deforming regions may to a large extent be the product of compounded viscoelastic relaxation from past earthquakes on hundreds of faults distributed over large ( >10 6 km 2 ) areas.

Post-Buckling Behavior in Pure Bending of Thin Strips with Arc Cross Section (1st Report, Approximate Deformation Analysis Using Energy Method)

A service cable with flat wires and an woven tube for an sensor of the sliding door was under consideration using the post-buckling behavior in pure bending of thin strips with arc cross section in order to keep quiet and to miniaturize the service system. The post-buckling deformation model was proposed and the post-buckling deformations of the flexible structure were approximately analyzed using the strain energy method for an infinitesimal strain problem of large deformation. The stability of the post-buckling was discussed checking the second variation of the total potential energy. The theoretical predictions were compared with experimental results about the relationship between the radius of curvature under post-buckling and the radius of circular arc and the pure bending moments of the barrel-shape and the saddle-shape deformations, and the correspondence was found to be acceptable.

Dissipative Domain Wall Motion and Macroscopic Response of Ferroelectric Ceramics

We present a model which is based on the notion of a polycrystalline material with grains having a lamellar domain structure. The domain stack is homogenized by analytical methods whereas the interaction of grains is taken into account by the effective medium approximation. Domain wall motion is allowed to take place by considering the total potential energy variation of the polycrystalline material in comparison with microscopic retarding forces. The model is numerically evaluated with data for barium titanate single-crystals. Thus the hysteretic material behavior occurring under large-signal unipolar loading can be correlated with the dissipative domain wall motion. We also get some quantitative information on the fluctuating internal fields.

North Atlantic surface circulation during the 1990's observed with satellite‐tracked drifters

A new compilation of Lagrangian velocity observations describes the state of the North Atlantic surface circulation during the 1990s. Gridded fields of velocity and eddy kinetic energy (EKE) are constructed from trajectories of more than 1500 15‐m drogued satellite‐tracked surface drifters in service between January 1990 and December 1999. This time period overlaps a coordinated field study of circulation and variability in the North Atlantic completed between 1996–2000 as part of the World Ocean Circulation Experiment. We describe the construction of a self‐consistent drifter climatology, present decadal‐mean quasi‐Eulerian velocity and EKE fields computed on a 1° grid, and compare these results with contemporary satellite measurements. Detailed discussion of the inferred surface circulation is focused on three regions: (1) The Gulf Stream and North Atlantic Current, (2) the Labrador Sea and subpolar gyre, and (3) the Caribbean Sea. The swiftest drifter motions were found in the equatorial region and along the tropical, subtropical, and subpolar western boundaries. The maximum instantaneous speed determined from a single (quality‐controlled and filtered) drifter observation was 273 cm s−1 in the Gulf Stream southeast of Cape Cod. The highest EKE value in the North Atlantic (2790 cm2 s−2) was found in the Gulf Stream just downstream of the New England Seamounts. Over most of the Atlantic basin, drifter‐derived EKE values were found to be O(100 cm2 s−2) higher than corresponding values derived from satellite altimetry. In the Labrador Sea a region of sharply elevated EKE appears to be geographically related to the localized ejection of drifters (and by extension, mass and kinetic energy) from the energetic West Greenland Current between 60° and 62°N. When compared to drifter measurements made in the late 1970s our results suggest (but do not statistically confirm) an enhancement and slight northward shift of the zonal Gulf Stream extension. Such a shift is consistent in sign with expectations based on observed interdecadal variations in wind stress and subtropical gyre potential energy associated with the North Atlantic Oscillation.

Nonlinear pure bending of toroidal shells of arbitrary cross-section

The geometrically nonlinear problem of in-plane pure bending of a toroidal shell of arbitrary cross-section (both closed and open) is considered. A finite element algorithm for solution of the problem is proposed. The equilibrium states of the discrete system are determined by an iterative method based on calculation of the coefficients of the first and second variations of the total potential energy. Nonlinear deformation of cylindrical and toroidal shells of closed cross-section is considered. As an example of open cross-sectional contour, a solution for the problem of pure bending of a thin plate is given. The resultant solutions are compared with those of the other authors.

K-0846 圧縮負荷を受ける複合材料積層曲面板の座屈後挙動(G03-15 複合材料)(G03 材料力学部門一般講演)

Postbuckling behaviors of thin laminated plates under uniaxial compression have been discussed by many researchers. However, little research has been performed on the postbuckling behaviors and the secondary buckling phenomenon for thin laminated curved plates which occurs with further increase of load. In this paper, the stability condition of CFRP angle-ply laminated curved plates under uniaxial compression which are simply supported along four edges is determined, using the second variation of total potential energy. The necessity of secondary buckling is proven analytically, and the effects of various factors, such as shape parameter, deflection pattern and average axial shortening, are clarified.

Structure of a model lubricant in a mica slit pore

Grand canonical ensemble Monte Carlo computer simulations are used to study a monolayer octamethylcyclotetrasiloxane (OMCTS) film confined between micalike surfaces to better understand the relationship between fluid properties and the atomic structure of the surfaces. OMCTS packs as a well ordered hexagonally close-packed film for all relative alignments of the surfaces. The orientation of the fluid lattice is guided by the mica surfaces. The angle between the symmetry planes of the fluid and the hexagonal oxygen rings on the mica surfaces is approximately 30°. The coupling between OMCTS and the confining mica surfaces is shown to be intermediate in that (1) the film sustains a shear stress and (2) the hexagonal symmetry of the film becomes distorted when the surfaces are out of registry but the film does not melt. Incrementally shifting one of the surfaces laterally leads to periodic distortions in the fluid lattice that are caused by the fluid being stretched to accommodate variations in the pore space potential energy.

The Numerical Simulation of Nonsupercell Tornadogenesis. Part III: Parameter Tests Investigating the Role of CAPE, Vortex Sheet Strength, and Boundary Layer Vertical Shear

Abstract Nonsupercell tornadogenesis has been investigated in a three-part numerical study. Building on the results of Parts I and II, Part III addresses the sensitivity of nonsupercell tornadogenesis to variations in convective available potential energy (CAPE), outflow boundary vortex sheet strength, and boundary layer vertical shear. A three-dimensional, nonhydrostatic, quasi-compressible convective cloud model has been employed to examine nonsupercell tornado (NST) development in an environment typical of the Colorado high plains. A strong relationship was shown to exist between the magnitude of the environmental CAPE and the structure and intensity of the misocyclones and nonsupercell tornadoes that developed. As CAPE was increased from 0 to 1700 J kg−1, the simulated vortices markedly contracted and intensified. Multiple CAPE thresholds were identified that yielded markedly different vortex intensity. The highest CAPE runs produced NST families with peak ground-relative surface winds of ∼47 m s−1. V...

A MD study of low energy boron bombardment on silicon

Low energy boron bombardment of silicon has been simulated at room temperature by means of molecular dynamics (MD). Tersoff potential T3 was used in the simulation smoothly linked to the universal potential. The boron–silicon interaction was simulated following the ideas of Tersoff for the SiC potential but modified to take into account, in the B–Si interaction, whether or not the neighbours of either of both are entirely or partially boron or silicon atoms. (001) Si–C with (2×1) reconstruction surface was bombarded with boron at energies of 200 and 500 eV, which were initially chosen as good representative values of the low energy range of interest. Reliable results require a reasonable good statistic so that 100 impact points were chosen which were uniformly distributed over a representative area of a (2×1) surface.Special care was taken to determine the kind of damage produced in a Si crystal by the slowing down of boron. It is described in detail the way to determine vacancies and interstitials. The damage produced can be classified in regions were the accumulation of damage does not allow to identify properly the type of defects produced and regions in which defects are isolated and can be beautifully identified in terms of the potential energy variation and the displacements of their neighbours. Clusters of vacancies and interstitials are determined. Mean number of interstitials, vacancies, adatoms, sputtering, etc. are summarised in a table. Range distributions of boron are also determined.

Molecular Dynamics Simulations of the Variation of Structure and Energy in the Solidification of Liquid Au

Bymeans of molecular dynamics simulation technique,the solidification processes of Au under different cooling velocity has been studied.It has been concluded that the cooling velocity is critical to the structure of Au.With pair distribution function and pairsanalysis method,the local symmetry of molecular-cluster has been analyzed.The variations of potential energy with the temperature and the relationship between the energy and the structure of molecular-cluster have also been studied.From the eye of the variation of energy,the conclusion has been discussed.

圧縮負荷を受ける複合材料積層曲面板の座屈強度

Postbuckling behaviors and load-carrying capacity of thin laminated curved plates under uniaxial compression have been discussed by many researchers. However, little research has been performed on the secondary buckling phenomenon for thin laminated curved plate which occurs with further increase of load. In this paper, CFRP laminated curved plates under uniaxial compression which are simply supported along four edges is considered as an example. By a proposed method based on the second variation of total potential energy to judge the stability of postbuckling equilibrium state, the inevitability of secondary buckling is proven analytically, and the effects of various factors, such as dimension of curved plate, assumed virtual displacement pattern, postbukling deflection pattern and average axial shortening, on the secondary buckling values are clarified.

Computer experiments on nano-indentation: A molecular dynamics approach to the elasto-plastic contact of metal copper

Molecular dynamics simulations are used to investigate the micro-mechanisms of nano-indentation for tip to substrate contact. The method combines a many-body interatomic potential derived from the nearest-neighbor EAM and brownian dynamics (BD) approach to simulate a rigid tip indenting Cu (001) surface. Elastic contact and plastic instability of the crystal are investigated through the loading-unloading cycle, the variations of the system potential energy versus the tip approach, the atomic stress distributions and the portraits of atomic trajectories and configurations. For elastic indentation, we find that atomistic stress distributions resembling roughly to those of the continuum Hertzian fields, except for a jump-to-contact phenomenon in the initial contact stage. When the tip approach is beyond some critical value, plastic instability of the substrate occurs, and both the contact load and potential energy decrease dramatically. Detailed calculations reveal that material yield at the atomic level is still governed by the von Mises shear strain-energy criterion, while atomistic trajectories show that the displacements in (010) plane of atoms near the contact region is similar to that in Johnson's cavity model, accompanied by atomic cross-layer movements in [010] direction to release the strain energy. The crystal defects after plastic indentation include subsurface cavities, surface atomic steps and plastic indent.

Direct Observation of One-Dimensional Ga-Atom Migration on a Si(100)-(2×1)-H Surface: A Local Probe of Adsorption Energy Variation

Atomic-scale surface migration of a Ga atom on a hydrogen-terminated Si(100)- $(2\ifmmode\times\else\texttimes\fi{}1)$-H surface is studied using low-temperature scanning tunneling microscopy and first-principles calculations. The Ga atom migrates in a linear potential well confined by adjacent dimer rows and local dihydride defects, and is observed as a continuous linear protrusion (Ga-bar structure) at a narrow range of temperatures near 100 K. We point out that the height of the Ga-bar structure maps out the local variation in potential energy at individual adsorption sites.

Theoretical study of boundary lubrication

We analyzed the dynamics of xenon atoms as lubricant between two Ni(110) slabs in relative motion. Atomic simulations are carried out by using classical molecular dynamics with realistic empirical potentials, where nickel as well as xenon atoms are relaxed. The resistance of the xenon layer against the loading force is examined and critical forces are determined to destroy the lubricant layer at different coverages. The relative motion of slabs in the lateral direction is investigated under constant normal force as a function of coverage ranging from zero to the monolayer xenon. Important lubrication properties of xenon atoms are analyzed by calculating the variation of potential energy, lateral force, and local hydrodynamic pressure. It is predicted that the corrugation of the potential energy associated with the sliding has a minimum value at submonolayer coverage. A phononic energy dissipation mechanism together with the theoretical analysis is proposed.