Total Internal Energy Research Articles

A Steady-State Approximation to the Two-Dimensional Master Equation for Chemical Kinetics Calculations.

In the field of chemical kinetics, the solution of a two-dimensional master equation that depends explicitly on both total internal energy (E) and total angular momentum (J) is a challenging problem. In this work, a weak-E/fixed-J collisional model (i.e., weak-collisional internal energy relaxation/free-collisional angular momentum relaxation) is used along with the steady-state approach to solve the resulting (simplified) two-dimensional (E,J)-grained master equation. The corresponding solutions give thermal rate constants and product branching ratios as functions of both temperature and pressure. We also have developed a program that can be used to predict and analyze experimental chemical kinetics results. This expedient technique, when combined with highly accurate potential energy surfaces, is cable of providing results that may be meaningfully compared to experiments. The reaction of singlet oxygen with methane proceeding through vibrationally excited methanol is used as an illustrative example.

General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures.

This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model's accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy relaxation model, which can only be applied to molecules, the new model is applicable to atoms, molecules, ions, and their mixtures. Numerical examples and model validations are carried out with two gas mixtures using the maximum entropy linear model: one mixture consists of nitrogen molecules undergoing internal excitation and dissociation and the other consists of nitrogen atoms undergoing internal excitation and ionization. Results show that the original hundreds to thousands of microscopic equations can be reduced to two macroscopic equations with almost perfect agreement for the total number density and total internal energy using only one or two groups. We also obtain good prediction of the microscopic state populations using 5-10 groups in the macroscopic equations.

Two-temperature equation of state for aluminum and gold with electrons excited by an ultrashort laser pulse

A short laser pulse converts metal into a two- temperature state with the electron temperature higher than the ion temperature. To describe the electron contributions to the total internal energy and pressure arising as a result of electron heating, we develop the new analytic approxi- mation formulae for two-temperature thermodynamics of metal. Those approximations are based on quantum cal- culations performed with density functional theory (DFT) packages. DFT calculations provide the internal energies and pressures for densities of the order of solid-state den- sity and for electron temperatures up to 55 kK. The new analytic approximations give a better accuracy in hydrody- namic simulation of laser-matter interaction and should be used instead of the less accurate expressions based on the Fermi model of ideal electron gas, which is widely used for two-temperature states of metal.

Friedmann equations from nonequilibrium thermodynamics of the Universe: A unified formulation for modified gravity

Inspired by the Wald-Kodama entropy $S=A/(4G_{\text{eff}})$ where $A$ is the horizon area and $G_{\text{eff}}$ is the effective gravitational coupling strength in modified gravity with field equation $R_{\mu\nu}-Rg_{\mu\nu}/2=$ $8\pi G_{\text{eff}} T_{\mu\nu}^{\text{(eff)}}$, we develop a unified and compact formulation in which the Friedmann equations can be derived from thermodynamics of the Universe. The Hawking and Misner-Sharp masses are generalized by replacing Newton's constant $G$ with $G_{\text{eff}}$, and the unified first law of equilibrium thermodynamics is supplemented by a nonequilibrium energy dissipation term $\mathcal{E}$ which arises from the revised continuity equation of the perfect-fluid effective matter content and is related to the evolution of $G_{\text{eff}}$. By identifying the mass as the total internal energy, the unified first law for the interior and its smooth transit to the apparent horizon yield both Friedmann equations, while the nonequilibrium Clausius relation with entropy production for an isochoric process provides an alternative derivation on the horizon. We also analyze the equilibrium situation $G_{\text{eff}}=G=\text{constant}$, provide a viability test of the generalized geometric masses, and discuss the continuity/conservation equation. Finally, the general formulation is applied to the FRW cosmology of minimally coupled $f(R)$, generalized Brans-Dicke, scalar-tensor-chameleon, quadratic, $f(R,\mathcal{G})$ generalized Gauss-Bonnet and dynamical Chern-Simons gravity. In these theories we also analyze the $f(R)$-Brans-Dicke equivalence, find that the chameleon effect causes extra energy dissipation and entropy production, geometrically reconstruct the mass $\rho_m V$ for the physical matter content, and show the self-inconsistency of $f(R,\mathcal{G})$ gravity in problems involving $G_{\text{eff}}$.

RADIO OBSERVATIONS REVEAL A SMOOTH CIRCUMSTELLAR ENVIRONMENT AROUND THE EXTRAORDINARY TYPE Ib SUPERNOVA 2012au

We present extensive radio and X-ray observations of SN 2012au, an energetic, radio-luminous supernova of Type Ib that exhibits multi-wavelength properties bridging subsets of hydrogen-poor superluminous supernovae, hypernovae, and normal core-collapse supernovae. The observations closely follow models of synchrotron emission from a shock-heated circumburst medium that has a wind density profile (rho alpha r(-2)). We infer a sub-relativistic velocity for the shock wave v approximate to 0.2 c and a radius of r approximate to 1.4 x 10(16) cm at 25 days after the estimated date of explosion. For a wind velocity of 1000 km s(-1), we determine the mass-loss rate of the progenitor to be M = 3.6 x 10(-6) M-circle dot yr(-1), consistent with the estimates from X-ray observations. We estimate the total internal energy of the radio-emitting material to be E approximate to 10(47) crg, which is intermediate to SN 1998bw and SN 2002ap. The evolution of the radio light curve of SN 2012au is in agreement with its interaction with a smoothly distributed circumburst medium and the absence of stellar shells ejected from previous outbursts out to r approximate to 10(17) cm from the supernova site. We conclude that the bright radio emission from SN 2012au was not dissimilar from other core-collapse supernovae despite its extraordinary optical properties, and that the evolution of the SN 2012au progenitor star was relatively quiet, marked with a steady mass loss, during the final years preceding explosion.

Measuring the heat capacity in a Bose-Einstein condensation using global variables

Phase transitions are well understood and generally followed by the behavior of the associated thermodynamic quantities, such as in the case of the $\lambda$ point superfluid transition of liquid helium, which is observed in its heat capacity. In the case of a trapped Bose-Einstein condensate (BEC), the heat capacity cannot be directly measured. In this work, we present a technique able to determine the global heat capacity from the density distribution of a weakly interacting gas trapped in an inhomogeneous potential. This approach represents an alternative to models based on local density approximation. By defining a pair of global conjugate variables, we determine the total internal energy and its temperature derivative, the heat capacity. We then apply the technique to a trapped $^{87}$Rb BEC a $\lambda$-type transition dependent on the atom number is observed, and the deviations from the non-interacting, ideal gas case are discussed. Finally we discuss the chances of using this method to study the heat capacity at $T \rightarrow 0$.

A Simple and Rapid Evaluation of Explosive Performance – The Disc Acceleration Experiment

AbstractIt is crucial in the development of a new explosive to obtain an evaluation of performance early in the process when the availability of material is limited. Evaluation requires dynamic measurements of detonation velocity, pressure, and expansion energy – typically in separate experiments that require large amounts of material, time, and expense. There is also a need for evaluation of the total available thermodynamic energy. The dynamic evaluations, in particular, have been a major hindrance to development of new explosives. The new experimental testing method to be described here requires small charges and obtains accurate measurement of all three of the detonation performance characteristics in a single test. The design, a Disc Acceleration eXperiment (DAX), provides an initial condition of steady detonation and a charge‐geometry amenable to 2D hydrodynamic simulations. The velocity history of a metal disk attached to the end of the explosive charge is measured with Photonic Doppler Velocimetry (PDV). This disc velocity data is analyzed to give both CJ pressure and expansion energy. The detonation velocity is obtained with probes along the charge length. The experiments and subsequent analyses are concentrated on LX‐16, a known PETN based explosive, for the purpose of establishing the accuracy of the method and to provide a standard for comparison with other explosives. We present details of the experimental design and also detonation velocity and PDV results from a number of experiments. The total available internal energy for the explosive was obtained from published detonation calorimetry measurements by Ornellas [1], and from thermodynamic equilibrium calculations. An equation‐of‐state (EOS) for LX‐16 was derived from hydrodynamic simulations of thin plate‐push velocity‐time data. We will show a successful comparison with a previously published Jones‐Wilkins‐Lee (JWL) EOS for PETN by Green and Lee [2–4].

Fluctuations in the uniform shear flow state of a granular gas

Using kinetic theory we analyse the fluctuations of the total internal energy of a granular gas under stationary uniform shear flow, and find that they are coupled to fluctuations in the different components of the total pressure tensor. Explicit expressions for all the possible one- and two-time cross and auto correlations of the fluctuations are obtained for the two dimensional case. For the range of inelasticity considered, good agreement is found between the theoretical predictions and Molecular Dynamics simulations.

Design of RC frames for pre-selected collapse mechanism and target displacement using energy–balance

In earthquake-prone countries, structures may be exposed to several seismic loads in any stage of building’s life. It is expected that the structures designed by engineers will show ductile behaviour under the effect of vertical and lateral loads and remain stable without making a sudden collapse. In consequence of nonlinear behaviour, plastic hinges are expected to form in structural members which are under the effect of external loads. Earthquake input energy is dissipated in plastic hinges, so, structures behave ductile. In this study, total energy of RC frames is calculated and the energy-based base shear force is determined by equating the total internal energy to the work done by external lateral design forces for pre-selected target displacement and collapse mechanism. Sections of RC frames are controlled if they can resist the calculated design lateral loads or not. If the capacity of the sections cannot withstand the external design loads, the design is rearranged and new sections are chosen. Beam and column sections that can resist the design loads securely are accepted as final sections of the energy-based design methodology. Pre-selected target displacement for desired performance level is checked using the results of nonlinear analyses. The results of the presented design methodology in this study are compatible with the results of nonlinear analyses.

Radical intermediates in the addition of OH to propene: photolytic precursors and angular momentum effects.

We investigate the photolytic production of two radical intermediates in the reaction of OH with propene, one from addition of the hydroxyl radical to the terminal carbon and the other from addition to the center carbon. In a collision-free environment, we photodissociate a mixture of 1-bromo-2-propanol and 2-bromo-1-propanol at 193 nm to produce these radical intermediates. The data show two primary photolytic processes occur: C-Br photofission and HBr photoelimination. Using a velocity map imaging apparatus, we measured the speed distribution of the recoiling bromine atoms, yielding the distribution of kinetic energies of the nascent C3H6OH radicals + Br. Resolving the velocity distributions of Br((2)P(1/2)) and Br((2)P(3/2)) separately with 2 + 1 REMPI allows us to determine the total (vibrational + rotational) internal energy distribution in the nascent radicals. Using an impulsive model to estimate the rotational energy imparted to the nascent C3H6OH radicals, we predict the percentage of radicals having vibrational energy above and below the lowest dissociation barrier, that to OH + propene; it accurately predicts the measured velocity distribution of the stable C3H6OH radicals. In addition, we use photofragment translational spectroscopy to detect several dissociation products of the unstable C3H6OH radicals: OH + propene, methyl + acetaldehyde, and ethyl + formaldehyde. We also use the angular momenta of the unstable radicals and the tensor of inertia of each to predict the recoil kinetic energy and angular distributions when they dissociate to OH + propene; the prediction gives an excellent fit to the data.

English

In this work, 3D model of D2 dopamine receptor was determined by comparative homology modeling program MODELLER. The computed model's energy was minimized and validated using PROCHECK and Errat tool to obtain a stable model structure and was submitted in Protein Model Database (PMDB-ID: PM0079251). Stable model was used for molecular docking against Risperidone and their 15 derivatives using AutoDock 4.2, which resulted in energy-based descriptors such as Binding Energy, Ligand Efficiency, Inhib Constant, Intermol energy, vdW + Hbond + desolv Energy, Electrostatic Energy, Total Internal Energy and Torsional Energy. After that, we have built quantitative structure activity relationship (QSAR) model, which was trained and tested on Risperidone and their 15 derivatives having activity value pKi in µM. For QSAR modeling, Multiple Linear Regression model was engendered using energy-based descriptors yielding correlation coefficient r2 of 0.513. To assess the predictive performance of QSAR models, different cross-validation procedures were adopted. Our results suggests that ligand-receptor binding interactions for D2 employing QSAR modeling seems to be a promising approach for prediction of pKi value of novel antagonists against D2 receptor.

The particle content of low-power radio galaxies in groups and clusters

The synchrotron-radiating particles and magnetic fields in low-power radio galaxies (including most nearby cluster-centre sources), if at equipartition, can provide only a small fraction of the total internal energy density of the radio lobes or plumes, which is now well constrained via X-ray observations of their external environments. We consider the constraints on models for the dominant energy contribution in low-power radio-galaxy lobes obtained from a detailed comparison of how the internal equipartition pressure and external pressure measured from X-ray observations evolve with distance for two radio galaxies, 3C 31 and Hydra A. We rule out relativistic-lepton dominance of the radio lobes, and conclude that models in which magnetic field or relativistic protons/ions carried up the jet dominate lobe energetics are unlikely. Finally, we argue that entrainment of material from the jet surroundings can provide the necessary pressure, and construct a simple self-consistent model of the evolution of the entrainment rate required for pressure balance along the 100-kpc scale plumes of 3C 31. Such a model requires that the entrained material is heated to temperatures substantially above that of the surrounding intra-group or cluster medium, and that the temperature of the thermal component of the jet increases with distance, though remaining sub-relativistic.

A Crashworthy Problem on Composite Structures Using a Mathematical Approach

Abstract During the last decades the attention given to vehicle crash energy management has been centred on composite structures. The use of fibre-reinforced plastic composite materials in automotive structures, in fact, may result in many potential economic and functional benefits due to their improved properties respect to metal ones, ranging from weight reduction to increased strength and durability features. Although significant experimental work on the collapse of fibre-reinforced composite shells has been carried out, studies on the theoretical modelling of the crushing process are quite limited since the complex and brittle fracture mechanisms of composite materials. Moreover most of the studies have been directed towards the axial crush analysis, because it represents more or less the most efficient design. A mathematical approach on the failure mechanisms, pertaining to the stable mode of collapse of thin-walled composite structures subjected to axial loading, is investigated. The analysis is conducted from an energetic point of view. The main energy contributions to the absorption (bending, petal formation, circumferential delamination, friction) are identifies and then the total internal energy is equated to the work done by the external load. The total crushing process can be seen as a succession of deformation states, each responsible for a partial absorption. The minimum configuration for each impact force in the specific state of deformation, function of several variables and dependent on geometric and material parameters is obtained. A comparison between theory and experiments concerning crushing loads and total displacements is presented, showing how the proposed analytical model is effective in predicting the energy absorption capability of axially collapsing composite shells.

The dynamic triple peak impact factor in traumatic brain injury influences native protein structures in gray and white matter as measured with computational simulation

Background: Traumatic brain injuries (TBIs) cause a substantial burden to the patient, relatives, and the society as a whole. Much experience and knowledge during the last two decades have improved the neurosurgical treatment as well as the outcome. However, there is still much debate on what actually happens when external kinetic energy is transferred to the head immediately after a TBI. Better knowledge about the cascades of mechanical events at the time of accident is a prerequisite to further reduce the burden in all categories and improve the neurosurgical care of TBI patients.Methods: In the present study, we use the finite element modeling of the human brain to numerically simulate impact velocities of 10, 6, and 2 m/s to clarify some of the immediate consequences of the external kinetic energy transfer focusing on the gray (GM) and white matters (WM).Results: The numerical simulation was focused on the external kinetic energy transfer with a level of 227·3 J reaching the head, intracranial pressure (ICP), strain energy density, 1st principal strain level, and their respective impacts on the brain tissue. The results show that, for a 10 m/s impact, a total internal potential energy of 208·6 J was absorbed, of which 14·3% (29·81 J) was absorbed by the scalp, 22·05% (46·0 J) by the outer compact bone, 17·12% (35·72 J) by the porous bone, 27·44% (57·23 J) by the inner compact bone, and 7·31% (15·24 J) by the facial bone. The rest of the internal potential energy was defined to reach the GM (3·6%, 7·51 J) and the WM 1·59% (3·31 J). Also, the ICP, strain energy density, and 1st principal strain levels, defined as the dynamic triple peak impact factor, influenced the GM and WM with their own impact peaks during the first 10 ms after the accident and were the highest for the 10 and 6 m/s impacts, while the 2 m/s impact had only a slight influence on the GM and WM structures.Conclusions: The present study shows for the first time that following an impact of 10 m/s, 88·31% of the calculated external kinetic energy was absorbed by the external parts of the head before the remaining energy of 5·19% reached the GM and WM. GM absorbed about twice as much of the energy compared to the WM. It is suggested that the dynamic triple peak impact factor may have a profound effect on native protein structures in the cerebral metabolism after a TBI.

Rapid structural change in synaptosomal-associated protein 25 (SNAP25) precedes the fusion of single vesicles with the plasma membrane in live chromaffin cells

The SNARE complex consists of the three proteins synaptobrevin-2, syntaxin, and synaptosomal-associated protein 25 (SNAP25) and is thought to execute a large conformational change as it drives membrane fusion and exocytosis. The relation between changes in the SNARE complex and fusion pore opening is, however, still unknown. We report here a direct measurement relating a change in the SNARE complex to vesicle fusion on the millisecond time scale. In individual chromaffin cells, we tracked conformational changes in SNAP25 by total internal reflection fluorescence resonance energy transfer (FRET) microscopy while exocytotic catecholamine release from single vesicles was simultaneously recorded using a microfabricated electrochemical detector array. A local rapid and transient FRET change occurred precisely where individual vesicles released catecholamine. To overcome the low time resolution of the imaging frames needed to collect sufficient signal intensity, a method named event correlation microscopy was developed, which revealed that the FRET change was abrupt and preceded the opening of an exocytotic fusion pore by ∼90 ms. The FRET change correlated temporally with the opening of the fusion pore and not with its dilation.

On damping effects in Timoshenko beams

In this paper, the dynamic response of a Timoshenko beam with distributed internal viscous damping (DIVD) is analyzed with the aim to ascertain their relative effects on the whole range of beam slenderness. With respect to some previous and quite recent works, some further and fundamental generalizations are therefore introduced. First, the decoupling of shear and bending damping mechanisms, with or without the presence of the external classical viscous contribution. This splitting allows the outlining of the relevant influences on the dynamic response associated to any singular damping mechanism and the evaluation of the modal critical damping. As a second contemporary step, an explicit dependency is set upon the shear slenderness of the beam model, allowing to study the dependence of each single damping mechanism upon the relevant kinematic model, spanning from truly Bernoulli's behavior to mainly Shear controlled responses. According to the selected damping model, the dynamic behavior automatically selects the characteristics of kinematical response (relative levels of shear and bending contributions) depending of the minimization of the total internal energy (i.e. elastic energy and dissipation). In the folds of this study, the problem of optimal piece-wise constant distribution of DIVD is finally also addressed, firstly showing that is possible to find non-trivial and interesting solutions.

73 Molecular dynamics approach for DNA duplex thermal stability prediction

Development of new derivatives and analogs of nucleic acids (NA) with precalculated physico-chemical properties is important, both in practice and basic research. Unfortunately, these studies remain laborious, costly, and time-consuming. I silico research probably could resolve this problem due to the significant progress in development of computer software and hardware. The aim of this work is to study a molecular dynamics approach for nucleic acid hybridization enthalpy calculation. The enthalpies of DNA duplex formation were calculated as a difference of the total internal energy of double- and single-stranded states which were averaged from a 10 ns MD trajectory computed with Amber 11 software (UCSF, USA). Computations were performed on NVIDIA GTX580/Intel i7-2600 hardware and resources of Siberian the Supercomputer Center (ICMMG SB RAS). The use of a GPU has speeded up the modeling in implicit solvent up to 60 times and up to 30 times in explicit solvent in comparison with the one node of a CPU. To determine the optimal parameter set of modeling, we have used Dickerson–Drew dodecamer (DDD) 5'-CGCGAATTCGCG-3' with well characterized secondary structure and thermal stability. We have varied force field, temperature, heating protocol, and ion concentration in implicit and explicit solvent, solvent shell radius and compared averaged structures with those experimentally obtained. Using optimal parameters of modeling, we have shown that hybridization enthalpy of DDD correlates well with experimental and calculated ones of the nearest neighbor models’ enthalpies (Lomzov et.al., 2006). The differences were <15% whereas the experimental accuracy is about 10%. To verify the MD predictive ability, we have collected a database of experimentally determined thermodynamic parameters (enthalpy and entropy) of hybridization of 272 oligodeoxyribonucleotides. The length of oligonucleotides varies from 4 up to 16 base pairs (aver. 9 bp), GC-content 0-100% (aver. 57%). The total energy of oligonucleotide or duplex was averaged over 10 000 snapshots of 10 ns trajectories simulated with the optimal parameter set. The correlation between the values of hybridization enthalpies obtained experimentally and calculated using MD are shown in the figure. The RMSD and average error values of calculated and experimental enthalpies were less than 12 and 15%, respectively. The results obtained show that MD modeling allows one to calculate enthalpy of matched DNA duplexes with surprisingly good accuracy.

Direct molecular interaction of caveolin-3 with KCa1.1 channel in living HEK293 cell expression system

Caveolin family is supposed to be essential molecules for the formation of not only caveola structure on cell membrane but also functional molecular complexes in them with direct and/or indirect interaction with other membrane and/or submembrane associated proteins. The direct coupling of caveolin-1 (cav1) with large conductance Ca2+-activated K+ channel, KCa1.1 has been established in several types of cells and in expression system as well. The possible interaction of caveolin-3 (cav3), which shows expression in some differential tissues from cav1, with KCa1.1 remains to be determined. In the present study, the density of KCa1.1 current expressed in HEK293 cells was significantly reduced by the co-expression of cav3, as well as cav1. The co-localization and direct interaction of GFP- or CFP-labeled cav3 (GFP/CFP-cav3) with YFP- or mCherry-labeled KCa1.1 (KCa1.1-YFP/mCherry) were clearly demonstrated by single molecular image analyses using total internal reflection fluorescence (TIRF) microscopy and fluorescence resonance energy transfer (FRET) analyses with acceptor photobleaching method. The deletion of suggested cav1-binding motif in C terminus region of KCa1.1 (KCa1.1ΔCB-YFP) resulted in the marked decrease in cell surface expression, co-localization and FRET efficiency with CFP-cav3 and CFP-cav1. The FLAG-KCa1.1 co-immunoprecipitation with GFP-cav3 or GFP-cav1 also supported their direct molecular interaction. These results strongly suggest that cav3 possesses direct interaction with KCa1.1, presumably at the same domain for cav1 binding. This interaction regulates KCa1.1 expression to cell surface and the formation of functional molecular complex in caveolae in living cells.

Dynamic lateral crushing of empty and sandwich tubes

The dynamic lateral crushing behaviour of short empty and sandwich circular tubes is examined in this paper. Unlike the conventional impact method, the specimens were placed on the bottom platen of an Instron machine with a constant upwards velocity and then the tube collided with the fixed upper rigid platen. Load-deflection curves of empty tubes were first obtained and analysed. From the viewpoint of deformation modes and plastic strain energy absorbed by the tube quadrants around the proximal surface and distal surface, a critical velocity of impact is determined which corresponds to a mode change. A relationship is found to exist between the critical velocity and thickness-to-diameter ratio as well as the yield stress and density of the material. To understand the dynamic crushing behaviour of short aluminium foam-filled sandwich tubes by two rigid platens, further tests and corresponding finite element analysis were performed, respectively. Similar to the observations in the quasi-static tests, the mode of dynamic collapse is bending, with the formation of plastic bending zones accompanied with core crushing. Corresponding FE models for ABAQUS/Explicit were developed and validated against the experimental observations. Detailed deformation features and energy absorption characteristics during the crushing process were identified. It was found that increasing the compression velocity leads to an increase in the total internal plastic energy dissipation for both empty and sandwich tube. The propagation of plastic bending in the form of double-moving-hinges is the main mechanism of energy dissipation, as opposed to the low velocity impact which involves stationary plastic deformation zones.

Internal energy fluctuations of a granular gas under steady uniform shear flow

The stochastic properties of the total internal energy of a dilute granular gas in the steady uniform shear flow state are investigated. A recent theory formulated for fluctuations about the homogeneous cooling state is extended by analogy with molecular systems. The theoretical predictions are compared with molecular dynamics simulation results. Good agreement is found in the limit of weak inelasticity, while systematic and relevant discrepancies are observed when the inelasticity increases. The origin of this behavior is discussed.