Variation Of Potential Energy Research Articles

Magnetospheric Energy Principle for Spherically Symmetric Monopolar Magnetospheres

A new magnetospheric energy principle is developed for spherically symmetric monopolar magnetospheres with open straight field lines. The principle is based on the self-adjointness of the force operator, which ensures energy conservation in the unperturbed magnetospheric plasma volume. A Neuman-type boundary condition for the perpendicular displacement at the ionosphere yields a negative contribution to the potential energy variation. This contribution makes high-mode-number incompressible field-line-bending modes unstable owing to the plasma displacement over the spherical ionospheric surface.

Local stress sources in Western Europe lithosphere from geoid anomalies

We propose a method to evaluate the stress generated at the local scale by the spatial variations of the gravitational potential energy (GPE), which is related to inhomogeneous topography and mass distribution in the lithosphere. We show that it is possible to infer these local stress sources from the second spatial derivatives of a geoid height grid, used as a proxy of the GPE. The coherence of the method is validated on a passive margin, the Bay of Biscay. The result is that expected in such a geological configuration, with extensional local stress sources with the maximum horizontal principal stress parallel to the margin and compressive sources with the maximum horizontal principal stress perpendicular to the margin in the continental and oceanic lithosphere, respectively. We apply the method to Western Europe in order to provide a better understanding of the complex spatial variation of the present-day tectonic activity. Our results indicate a stress pattern from the local sources dominated by short-space-wavelength (of the order of a few tens of kilometers) variations in the tectonic style and in the direction of the maximal horizontal principal stress σ H . A comparison of the σ H orientations and tectonic style from the local sources with the ones of the World Stress Map (WSM) data set indicates that the local stress sources can be representative of the deviatoric stress state in some regions. Our results explain 71% of the faulting styles for the earthquake fault-plane solutions in the WSM, which is better than the classical compressive NW-SE stress field model. In the central part of the Pyrenees, the agreement between earthquake fault-slip directions and the direction of shear stress from the local sources acting on the associated fault planes is compatible with the extensional stress field evidenced by recent investigations.

Post-Buckling Stability Analysis of Composite Laminated Flat Plates with Initial Deflection under Biaxial Compression

Advanced fiber-reinforced laminated plates have been used as structural members in various applications by virtue of their high specific strength and stiffness. This paper considers, by use of the second variation of the total potential energy, secondary buckling of cross-ply laminated plates with an initial deflection under biaxial compression that is simply supported along four edges. The occurrence of secondary buckling is proven analytically and the effects of the initial deflection, outer lamination angle, number of layers, biaxial compressive load ratio and post-buckling deflection pattern are discussed. [doi:10.2320/matertrans.M2013111]

A global morphology of gravity wave activity in the stratosphere revealed by the 8‐year SABER/TIMED data

From 8 years' SABER/TIMED temperature profiles between January 2002 and December 2009, we studied the activity of gravity waves in the stratosphere globally. Global distribution of stratospheric gravity wave potential energy was calculated from the temperature perturbations. Seasonal comparison of gravity wave potential energy Ep shows an annual variation in middle and high latitudes and a semiannual variation in the tropics. Around the equator, gravity wave interannual enhancements are identified just below the zonal wind zero (u = 0) contours corresponding to descending eastward shear phase of the QBO. Furthermore, we provide observation evidence to support the conclusion that the deep convection is a major source for the observed tropical gravity wave activity. The considerable longitude variations of largest potential energy around the equator are related not only to the specific topography and tropical convections but also to many other factors. We can infer that topography and tropical deep convection are the important sources of the gravity waves in the stratosphere, but the observed gravity waves in the tropical/subtropical stratosphere are strongly affected by winds with different QBO phases.

Diffusion of Si and C atoms on and between graphene layers

The growth of epitaxial graphene on SiC surfaces is accompanied by the evaporation of Si atoms during the growth process. The continuous loss of Si atoms takes place even after the surface graphene layers are formed. Understanding the atomic transport process involved is critical in establishing a growth mechanism to model and control the process. Using density functional theory, we have calculated the potential energy variation and studied the diffusion of Si and C atoms on a single layer of graphene and between graphene sheets. Our results show that Si atoms can move almost freely on graphene and between graphene layers, while C atoms have much larger diffusion barriers. This work provides a detailed description of the energetics of relevant processes in the growth of epitaxial graphene on SiC surfaces.

Uplift prior to continental breakup: Indication for removal of mantle lithosphere?

Uplift or reduced subsidence prior to continental breakup is a key component of the rift-drift transition. This uplift causes lateral variations in the lithospheric potential energy, which can increase intraplate deviatoric tension, thereby facilitating continental rupture. There is a growing body of evidence that pre-breakup uplift is a global phenomenon characteristic of magmatic and magma-poor rifted margins. Evidence is provided by the subaerial extrusion of lava interpreted from drill logs, stratigraphic records, the presence of breakup unconformities, and the spatial extent of uplift associated with Afar (the Ethiopian-Somali plateau), which may be at the stage of rupture. Previously discussed mechanisms contributing to this uplift include phase transitions, dynamic uplift from mantle plumes, and magmatic underplated bodies. We show in this study that dynamic uplift resulting from passive upwelling asthenosphere below the rift is limited (∼200 m). Isostatic arguments suggest that removal of mantle lithosphere is a necessary and effective mechanism for uplift coincident with rupture. The combination of mantle phase transitions and a very thin mantle lid produces an excess potential energy state (as evidenced by a positive geoid anomaly) and leads to tensional forces favorable for rupture. These results underpin our proposed model for continental breakup where removal of mantle lithosphere by either detachment or formation of gravitational instabilities is a characteristic process. Observations of depth-dependent thinning and geochemical data support this model.

Shape and topology sensitivity analysis and its application to structural design

Theincrementalsensitivityanalysisassociatedwithvariationofstructurematerialparameters,shape or topology variation is generally discussed by analyzing the evolution of potential and complementary ener- gies, or arbitrary functionals of state fields. The concept of configuration and sensitivity generalized forces is used in presenting the sensitivity derivatives. The general reciprocity relations are derived for the case of potential or complementary energy variations. The topology variations in bar structures related to introduction of elements and introduction of inclusions and voids in plates are discussed, and the sensitivity forces are derived. the variations of state fields and of structure response functionals are required in redesign or optimal design problems. The sensitivity analysis provides a general methodology of derivation of sensitivity derivatives or variations with respect to structural parameters. In optimal design problems the sensitivity derivatives provide the gradients of the objective function and of design constraints that can be used in the incremental procedure tending to an optimal solution, cf. Haug et al. (1), Haftka et al. (2). In the present paper first the incremental structure evolution will be discussed with introduced configuration and sensitivity forces associated with the variation of structural parameters. The reciprocity relations for the increments of configuration forces and structural parameters are derived in Sect. 2. In Sect. 3 the topological variation in truss or frame structures is considered with the sensitivity derivatives presented analytically. In Sect. 4 the sensitivity of an arbitrary displacement functional is provided for the case of an inclusion or void introduced in a homogeneous plate. In Sect. 5 some applications of sensitivity analysis to structural design are discussed. 2 Configurational and sensitivity forces, reciprocity relations Consider an elastic structure for which the stress, strain and displacement fields are σ , e, u and the structure parameter(ordesign)vectorisdenotedby s.Thestructureisassumedtobeloadedbythetraction T 0 = λ s T 0 (x)

Heavy rainfall occurrences in northeast India

AbstractIn operational meteorology, forecasting heavy rainfall (HRF) events has been a long‐standing challenge in India. This is especially true in certain regions where the physical geography lends itself to the creation of such HRF events. Northeast India (NEI) is one such region within the Asian monsoon zone, which receive very HRF during the pre‐monsoon and summer monsoon season and the summer–autumn transition month of October. These events cause flooding, damage crops and bring life to standstill. In the present work, the characteristics of HRF events in NEI are studied. The seasonal and spatial variations of HRF occurrences are analysed using 31 year (1971–2001) of daily rainfall data from 15 rainfall stations. Using the daily data obtained from the Indian Meteorological Department, the most favorable locations were found for the stations between 27.5°N and 28.1°N. The most favorable time of occurrence of these events are between 10 June and 5 August. July records the largest number of HRF events followed by June and August. The aggregate of extreme rain events over the region has a significant decreasing trend over the region. Before the monsoon sets in, there is considerable thunderstorm (TS) activity in this region in the month of April and May that are also the cause of HRF events. While many of these HRF events occur associated with the pre‐monsoon Nor'westers (tornadoes), some severe TSs may occur during the monsoon season. So, we present a climatology of severe TS days. Also we present the annual and seasonal variation of convective available potential energy (CAPE) and convective inhibition energy (CINE) at Guwahati as the index of the thermal instability. Between 1973 and 2001, CAPE shows a decreasing trend whereas CINE shows an increasing trend which seems reasonable due to the HRF events' decreasing trend. Copyright © 2012 Royal Meteorological Society

Analysis of partially embedded beams in two-parameter foundation

In this study, Pasternak foundation model, which is a two parameter foundation model, is used to analyze the behavior of laterally loaded beams embedded in semi-infinite media. Total potential energy variation of the system is written to formulate the problem that yielded the required field equations and the boundary conditions. Shear force discontinuities are exposed within the boundary conditions by variational method and are validated by photo elastic experiments. Exact solution of the deflection of the beam is obtained. Both foundation parameters are obtained by self calibration for this particular problem and loading type in this study. It is shown that, like the first parameter k, the second foundation parameter G also depends not only on the material type but also on the geometry and the loading type of the system. On the other hand, surface deflection of the semi infinite media under singular loading is obtained and another method is proposed to determine the foundation parameters using the solution of this problem.

初期たわみを考慮した複合材料積層平板の二軸圧縮座屈後の安定解析

Advanced fiber-reinforced laminated plates have been used for structural members in various fields, by virtue of their high specific strength and stiffness. This paper considers, by use of the second variation of the total potential energy, secondary buckling of cross-ply laminated plates with initial deflection under biaxial compression that is simply supported along four edges. The occurrence of secondary buckling is proven analytically, and the effects of various factors, such as initial imperfection, outer lamination angle, number of layers, biaxial compressive load ratio, and postbuckling deflection pattern, are discussed.

A Study on Nanocutting of Monocrystalline Silicon by Molecular Dynamics Simulation

Three dimensional molecular dynamics simulation on the nanocutting of monocrystalline silicon is carried out to investigate the material deformation behaviors and atomic motion characteristics of the machined workpiece. A deformation criterion is developed to determine the material deformation and phase transformation behavior in the subsurface layer based on the single-atom potential energy variations. The results show that the machined chips suffer a complex phase transformation and eventually present an amorphous structure caused by the plastic deformation behavior. A polycrystalline structure is obtained on the machined surface. Both plastic and elastic deformation simultaneously takes place on the machined surface, and elastic deformation takes place under the machined surface. In order to further unveil the mechanism of nanocutting process, the displacements of all atoms are also simulated. The simulation results shows that different atomic motions occur in different regions in the workpiece, and the chips formations occur via extrusion.

Comparison of Tetrahedral Order, Liquid State Anomalies, and Hydration Behavior of mTIP3P and TIP4P Water Models.

The relationship between local tetrahedral order, tagged particle potential energy, and coordination number is studied for mTIP3P and TIP4P models of water in the bulk as well as in the neighborhood of a small peptide. The tendency of water molecules with different binding or tagged particle potential energies to occupy environments with different degrees of disorder can be effectively illustrated by constructing tetrahedral order distributions and corresponding entropy metrics conditional on restricted ranges of local binding energy. At the state point corresponding to the onset of the density anomaly, the correlation between tetrahedral entropy versus tagged potential energy is strong and virtually identical for mTIP3P and TIP4P. In TIP4P, this correlation is retained up to temperatures as high as 300 K, while it is lost by 250 K in mTIP3P. In the 250-300 K regime that is important for biomolecular simulations, mTIP3P behaves essentially as a simple liquid while TIP4P shows the density and related anomalies characteristic of water. We also study the number of water molecules, the tetrahedral order, and the tagged molecule potential energies for water molecules as a function of the distance from the peptide for the 16-residue β-hairpin fragment of 2GB1 in mTIP3P and TIP4P solvents. The hydration shell coordination profiles (n(r)) of the number of water molecules are almost identical in the two solvents, but the radial variation in the local energies and local order show significant differences. The residue-wise variation in the tagged potential energy of water molecules within the first hydration shell is qualitatively similar in the two models. A comparison of the tetrahedral order distributions of water molecules lying at different distances from the biomolecular solute shows that the perturbation in the local tetrahedral order distributions of the bulk solvent due to the presence of the solute is marginal. Thus, in the 250-300 K regime, the mTIP3P and TIP4P water models show qualitatively different behavior in terms of the relationship between tetrahedral order and local energy, but as solvents in the neighborhood of a biomolecular solute, the differences between the two models are only quantitative and not qualitative.

Cosolvent Effects on the Spontaneous Formation of Nanorod Vesicles in Catanionic Mixtures in the Rich Cationic Region

The aggregation behavior of cation-rich catanionic mixtures of cetyltrimethyl ammonium bromide (CTAB) and sodium dodecyl sulfate (SDS) was investigated in water-ethylene glycol (EG) solutions by performing surface tension, electrical conductivity, pulsed field gradient nuclear magnetic resonance, transmission electron microscopy, and cyclic voltammetry measurements. Different physicochemical properties such as the critical micelle concentration, degree of counterion dissociation (α), interfacial properties, aggregation numbers, morphology of aggregates, and interparticle interaction parameters were determined. Cosolvent effects on the interactions between the two surfactants CTAB and SDS were analyzed on the basis of regular solution theory, both for mixed monolayers at the air/liquid interface (β(δ)) and for mixed micelles. It was shown that an excess of cationic surfactant resulted in the formation of nonspherical vesicles. These were predominantly nanorod vesicles in water-EG mixed solvents. The interparticle interactions were assessed in terms of cosolvent effects on the micellar surface charge density, the sphere-to-rod morphology change, and the phase transition from vesicles to mixed micelles. Moreover, the variation of the repulsive electrostatic potential energy between two pairs of aggregates was investigated for two modes of nanostructural transition, namely the transition between spherical and rod-like micelles and the transition between rod-like micelles and nanorod vesicles.

Characterization of an Oxide Trap Leading to Random Telegraph Noise in Gate-Induced Drain Leakage Current of DRAM Cell Transistors

An accurate method for extracting the depth and the energy level of an oxide trap from random telegraph noise (RTN) in the gate-induced drain leakage (GIDL) current of a metal-oxide-semiconductor field-effect transistor (MOSFET) is developed, which correctly accounts for variation in surface potential and Coulomb energy. The technique employs trap capture and emission times defined from the characteristics of GIDL. Ignoring this variation in surface potential leads to an error of up to 116% in trap depth for 80-nm technology generation MOSFETs. RTN amplitude as a function of MOSFET drain-gate voltage is also investigated.

A quantum chemical study of the structure and energy of β-diketonates. XVII. Internal rotation of radical substituents in β-diketonate molecules

A quantum chemical study of the internal rotation of CX3 (X = H, F, CH3) radical substituents in scandium and calcium β-diketonate complexes is performed. Calculations are carried out using the GAUSSIAN-03 program at the HF and DFT/B3LYP levels with relativistic effective core pseudo-potentials and valence double zeta basis sets. Analytical expressions V(φ) are obtained that describe the potential energy variation during the rotation of CX3 groups. The rotation of CH3 and CF3 groups is shown to be described by a simple potential of the form V = V0/2 + V3cos(3φ), while for the description of the rotation of tert-butyl groups it is required to use a more complex function V = V0/2 + V3cos(3φ) + V6cos(6φ). Based on the obtained expressions for V(φ), the effective torsion angles φef of the rotation of CX3 groups are calculated for different temperatures. It is shown that φef obtained based on the quantum chemical calculations are close to the values obtained in electron diffraction experiments.

Simulation of low frequency Buneman instability of a current-driven plasma by particle in cell method

The nonlinear dynamics of low frequency Buneman instability in a current-driven cold unmagnetized plasma are studied using particle in cell simulation. Simulations of the Buneman instability show that the electron density profile has sharp peaks and the amplitude of the peaks changes with time. Also, the nonlinear evolution of this instability and saturation time is investigated by the time variation of the electric potential energy in the plasma. Moreover, the electron trapping phenomena and the formation of phase space electron holes are presented by considering the phase space diagram and electron distribution function. Finally, the ion mass effect on saturation time is investigated and it is found that the saturation time increases by increasing the ion mass and the saturation level is not very sensitive to the ion mass.

Level Set-Based Robust Topology Optimization for Coupled Thermal and Structural Problems Considering Uncertainty

In this paper, a robust design method is applied to the topology optimization for coupled thermal and structural problem. For the robust topology optimization, the objective function is defined as a combination of maximizing total potential energy for the thermal and structural stiffness and minimizing variation in the total potential energy under uncertainties on design parameters such as conduction of heat, heat transfer coefficient, Young's modulus and applied load. The variation in the total potential energy is evaluated using the first-order derivation under assumption that uncertainties are relatively small. As the topology optimization method, the formulation of a level set boundary expressions based on the concept of the phase field method is applied. This method allows topological changes with clearly boundary expressions during the optimization procedure. Furthermore, the geometrical complexity of the obtained optimal configurations can be controlled by adjusting a regularization factor, and the obtained optimal configurations are free of checkerboards and grayscales. Through numerical examples, the effect that uncertain conduction of heat, heat transfer, Young's modulus and applied load have upon the obtained configurations is investigated by comparing with deterministic optimum topology design results.

Unconstrained and Cauchy-Born-constrained atomistic systems: deformational and configurational mechanics

In this contribution, the deformational and configurational mechanics of (elastic) discrete atomistic systems in relation to their continuum counterparts are considered for the quasi-static case. Thereby, we firstly investigate the basic unconstrained case in the sense of lattice statics as a reference. Based on these results, we consider two Cauchy-Born-type constraints that (locally) describe the change of the position of atoms (between the material and the spatial configuration) in terms of either a linear or a quadratic map, respectively. Insertion of these kinematic constraints into the variation of the total potential energy of the unconstrained case renders eventually Cauchy-Born-type definitions for atomistic stresses and hyperstresses, for both deformational and configurational cases. In the continuum limit, these are the relevant continuum stresses and hyperstresses contributing to the local force balances of first- (classical) and second-order (non-classical) gradient continua (here first- and second-order gradient refers to the highest gradient of the deformation map characterizing the kinematics). It is emphasized that the atomistic and the Cauchy-Born-type configurational quantities represent novel and unexpected contributions. Among other things, they may be useful in assessing the singular or non-singular character of deformation fields at crack tips and comparing numerical estimates resulting from atomistic simulations with analytical predictions resulting from solutions of related boundary value problems for gradient continua.

Extension on the Tibetan plateau: recent normal faulting measured by InSAR and body wave seismology

We use InSAR and body wave modelling to determine the faulting parameters for a series of five Mw 5.9–7.1 normal faulting earthquakes that occurred during 2008, including the March 20 Yutian earthquake (Mw 7.1), one of the largest normal faulting events to have occurred recently on the continents. We also study three earlier normal faulting earthquakes that occurred in southern Tibet between 1992 and 2005. Coseismic deformation for each of these eight events is measured with ascending and descending interferograms from ENVISAT, ERS and ALOS SAR data. Elastic dislocation modelling of the line-of-sight InSAR displacements and body wave seismological modelling of P and SH waves are used to estimate fault parameters and are found to be in good agreement for all the events studied. The use of InSAR to measure deformation allows a relatively precise determination of the fault location in addition to resolving the focal plane ambiguity. Only five of the eight events are associated with a clear surface topographic feature, suggesting that an underestimation of the amount of extension would result from using the surface expressions of normal faulting alone. The observations, in all cases, are consistent with slip on planar surfaces, with dips in the range 40–50°, that penetrates the uppermost crust to a depth of 10–15 km. We find no evidence for active low-angle (dip less than 30°) normal faulting. The contribution of the normal faulting to overall extension estimated by summing seismic moments over earthquakes for the past 43 yr is 3–4 mm yr−1, or 15–20 per cent of the rates of extension measured across the plateau using GPS. 85 per cent of the moment release in normal faulting over the past 43 yr has occurred in regions whose surface height exceeds 5 km. This observation adds weight to the suggestions that the widespread normal faulting on the plateau is the result of variations in the gravitational potential energy of the lithosphere.

Land–Atmosphere Interactions during a Northwestern Argentina Low Event

Abstract The impact of changes in soil moisture in subtropical Argentina in rainfall distribution and low-level circulation is studied with a state-of-the-art regional model in a downscaling mode, with different scenarios of soil moisture for a 10-day period. The selected case (starting 29 January 2003) was characterized by a northwestern Argentina low event associated with well-defined low-level northerly flow that extended east of the Andes over subtropical latitudes. Four tests were conducted at 40-km horizontal resolution with 31 sigma levels, decreasing and increasing the soil moisture initial condition by 50% over the entire domain, and imposing a 50% reduction over northwest Argentina and 50% increase over southeast South America. A control run with NCEP/Global Data Assimilation System (GDAS) initial conditions was used to assess the impact of the different soil moisture configurations. It was found that land surface interactions are stronger when soil moisture is decreased, with a coherent reduction of precipitation over southern South America. Enhanced northerly winds result from an increase in the zonal gradient of pressure at low levels. In contrast, when soil moisture is increased, smaller circulation changes are found, although there appears to be a local feedback effect between the land and precipitation. The combined effects of changes in the circulation and in local stratification induced by soil wetness modifications, through variations in evaporation and Convective Available Potential Energy (CAPE), are in agreement with what has been found by other studies, resulting in coherent modifications of precipitation when variations of CAPE and moisture flux convergence mutually reinforce.