Time dependence of breakdown in a global fiber-bundle model with continuous damage.

PubMed

Moral, L; Moreno, Y; Gómez, J B; Pacheco, A F

2001-06-01

A time-dependent global fiber-bundle model of fracture with continuous damage is formulated in terms of a set of coupled nonlinear differential equations. A first integral of this set is analytically obtained. The time evolution of the system is studied by applying a discrete probabilistic method. Several results are discussed emphasizing their differences with the standard time-dependent model. The results obtained show that with this simple model a variety of experimental observations can be qualitatively reproduced.

Numerical Predictions of Damage and Failure in Carbon Fiber Reinforced Laminates Using a Thermodynamically-Based Work Potential Theory

NASA Technical Reports Server (NTRS)

Pineda, Evan Jorge; Waas, Anthony M.

2013-01-01

A thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, referred to as enhanced Schapery theory (EST), utilizes separate ISVs for modeling the effects of damage and failure. Consistent characteristic lengths are introduced into the formulation to govern the evolution of the failure ISVs. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs are derived. The theory is implemented into a commercial finite element code. The model is verified against experimental results from two laminated, T800/3900-2 panels containing a central notch and different fiber-orientation stacking sequences. Global load versus displacement, global load versus local strain gage data, and macroscopic failure paths obtained from the models are compared against the experimental results.

Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range. Part 1: constitutive equations

NASA Astrophysics Data System (ADS)

Kari, Leif

2017-09-01

The constitutive equations of chemically and physically ageing rubber in the audible frequency range are modelled as a function of ageing temperature, ageing time, actual temperature, time and frequency. The constitutive equations are derived by assuming nearly incompressible material with elastic spherical response and viscoelastic deviatoric response, using Mittag-Leffler relaxation function of fractional derivative type, the main advantage being the minimum material parameters needed to successfully fit experimental data over a broad frequency range. The material is furthermore assumed essentially entropic and thermo-mechanically simple while using a modified William-Landel-Ferry shift function to take into account temperature dependence and physical ageing, with fractional free volume evolution modelled by a nonlinear, fractional differential equation with relaxation time identical to that of the stress response and related to the fractional free volume by Doolittle equation. Physical ageing is a reversible ageing process, including trapping and freeing of polymer chain ends, polymer chain reorganizations and free volume changes. In contrast, chemical ageing is an irreversible process, mainly attributed to oxygen reaction with polymer network either damaging the network by scission or reformation of new polymer links. The chemical ageing is modelled by inner variables that are determined by inner fractional evolution equations. Finally, the model parameters are fitted to measurements results of natural rubber over a broad audible frequency range, and various parameter studies are performed including comparison with results obtained by ordinary, non-fractional ageing evolution differential equations.

The fast debris evolution model

NASA Astrophysics Data System (ADS)

Lewis, H. G.; Swinerd, G. G.; Newland, R. J.; Saunders, A.

2009-09-01

The 'particles-in-a-box' (PIB) model introduced by Talent [Talent, D.L. Analytic model for orbital debris environmental management. J. Spacecraft Rocket, 29 (4), 508-513, 1992.] removed the need for computer-intensive Monte Carlo simulation to predict the gross characteristics of an evolving debris environment. The PIB model was described using a differential equation that allows the stability of the low Earth orbit (LEO) environment to be tested by a straightforward analysis of the equation's coefficients. As part of an ongoing research effort to investigate more efficient approaches to evolutionary modelling and to develop a suite of educational tools, a new PIB model has been developed. The model, entitled Fast Debris Evolution (FADE), employs a first-order differential equation to describe the rate at which new objects ⩾10 cm are added and removed from the environment. Whilst Talent [Talent, D.L. Analytic model for orbital debris environmental management. J. Spacecraft Rocket, 29 (4), 508-513, 1992.] based the collision theory for the PIB approach on collisions between gas particles and adopted specific values for the parameters of the model from a number of references, the form and coefficients of the FADE model equations can be inferred from the outputs of future projections produced by high-fidelity models, such as the DAMAGE model. The FADE model has been implemented as a client-side, web-based service using JavaScript embedded within a HTML document. Due to the simple nature of the algorithm, FADE can deliver the results of future projections immediately in a graphical format, with complete user-control over key simulation parameters. Historical and future projections for the ⩾10 cm LEO debris environment under a variety of different scenarios are possible, including business as usual, no future launches, post-mission disposal and remediation. A selection of results is presented with comparisons with predictions made using the DAMAGE environment model. The results demonstrate that the FADE model is able to capture comparable time-series of collisions and number of objects as predicted by DAMAGE in several scenarios. Further, and perhaps more importantly, its speed and flexibility allows the user to explore and understand the evolution of the space debris environment.

Numerical Implementation of a Multiple-ISV Thermodynamically-Based Work Potential Theory for Modeling Progressive Damage and Failure in Fiber-Reinforced Laminates

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Waas, Anthony M.

2011-01-01

A thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, enhanced Schapery theory (EST), utilizes separate ISVs for modeling the effects of damage and failure. Damage is considered to be the effect of any structural changes in a material that manifest as pre-peak non-linearity in the stress versus strain response. Conversely, failure is taken to be the effect of the evolution of any mechanisms that results in post-peak strain softening. It is assumed that matrix microdamage is the dominant damage mechanism in continuous fiber-reinforced polymer matrix laminates, and its evolution is controlled with a single ISV. Three additional ISVs are introduced to account for failure due to mode I transverse cracking, mode II transverse cracking, and mode I axial failure. Typically, failure evolution (i.e., post-peak strain softening) results in pathologically mesh dependent solutions within a finite element method (FEM) setting. Therefore, consistent character element lengths are introduced into the formulation of the evolution of the three failure ISVs. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs is derived. The theory is implemented into commercial FEM software. Objectivity of total energy dissipated during the failure process, with regards to refinements in the FEM mesh, is demonstrated. The model is also verified against experimental results from two laminated, T800/3900-2 panels containing a central notch and different fiber-orientation stacking sequences. Global load versus displacement, global load versus local strain gage data, and macroscopic failure paths obtained from the models are compared to the experiments.

A Thermodynamically-Based Mesh Objective Work Potential Theory for Predicting Intralaminar Progressive Damage and Failure in Fiber-Reinforced Laminates

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Waas, Anthony M.

2012-01-01

A thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, enhanced Schapery theory (EST), utilizes separate ISVs for modeling the effects of damage and failure. Damage is considered to be the effect of any structural changes in a material that manifest as pre-peak non-linearity in the stress versus strain response. Conversely, failure is taken to be the effect of the evolution of any mechanisms that results in post-peak strain softening. It is assumed that matrix microdamage is the dominant damage mechanism in continuous fiber-reinforced polymer matrix laminates, and its evolution is controlled with a single ISV. Three additional ISVs are introduced to account for failure due to mode I transverse cracking, mode II transverse cracking, and mode I axial failure. Typically, failure evolution (i.e., post-peak strain softening) results in pathologically mesh dependent solutions within a finite element method (FEM) setting. Therefore, consistent character element lengths are introduced into the formulation of the evolution of the three failure ISVs. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs is derived. The theory is implemented into commercial FEM software. Objectivity of total energy dissipated during the failure process, with regards to refinements in the FEM mesh, is demonstrated. The model is also verified against experimental results from two laminated, T800/3900-2 panels containing a central notch and different fiber-orientation stacking sequences. Global load versus displacement, global load versus local strain gage data, and macroscopic failure paths obtained from the models are compared to the experiments.

Combined meso-scale modeling and experimental investigation of the effect of mechanical damage on the transport properties of cementitious composites

NASA Astrophysics Data System (ADS)

Raghavan, Balaji; Niknezhad, Davood; Bernard, Fabrice; Kamali-Bernard, Siham

2016-09-01

The transport properties of cementitious composites such as concrete are important indicators of their durability, and are known to be heavily influenced by mechanical loading. In the current work, we use meso-scale hygro-mechanical modeling with a morphological 3D two phase mortar-aggregate model, in conjunction with experimentally obtained properties, to investigate the coupling between mechanical loading and damage and the permeability of the composite. The increase in permeability of a cylindrical test specimen at 28% aggregate fraction during a uniaxial displacement-controlled compression test at 85% of the peak load was measured using a gas permeameter. The mortar's mechanical behavior is assumed to follow the well-known compression damaged plasticity (CDP) model with isotropic damage, at varying thresholds, and obtained from different envelope curves. The damaged intrinsic permeability of the mortar evolves according to a logarithmic matching law with progressive loading. We fit the matching law parameters to the experimental result for the test specimen by inverse identification using our meso-scale model. We then subject a series of virtual composite specimens to quasi-static uniaxial compressive loading with varying boundary conditions to obtain the simulated damage and strain evolutions, and use the damage data and the previously identified parameters to determine the evolution of the macroscopic permeability tensor for the specimens, using a network model. We conduct a full parameter study by varying aggregate volume fraction, granulometric distribution, loading/boundary conditions and "matching law" parameters, as well as for different strain-damage thresholds and uniaxial loading envelope curves. Based on this study, we propose Avrami equation-based upper and lower bounds for the evolution of the damaged permeability of the composite.

Prediction Of Formability In Sheet Metal Forming Processes Using A Local Damage Model

NASA Astrophysics Data System (ADS)

Teixeira, P.; Santos, Abel; César Sá, J.; Andrade Pires, F.; Barata da Rocha, A.

2007-05-01

The formability in sheet metal forming processes is mainly conditioned by ductile fracture resulting from geometric instabilities due to necking and strain localization. The macroscopic collapse associated with ductile failure is a result of internal degradation described throughout metallographic observations by the nucleation, growth and coalescence of voids and micro-cracks. Damage influences and is influenced by plastic deformation and therefore these two dissipative phenomena should be coupled at the constitutive level. In this contribution, Lemaitre's ductile damage model is coupled with Hill's orthotropic plasticity criterion. The coupling between damaging and material behavior is accounted for within the framework of Continuum Damage Mechanics (CDM). The resulting constitutive equations are implemented in the Abaqus/Explicit code, for the prediction of fracture onset in sheet metal forming processes. The damage evolution law takes into account the important effect of micro-crack closure, which dramatically decreases the rate of damage growth under compressive paths.

Micromechanics Modeling of Composites Subjected to Multiaxial Progressive Damage in the Constituents

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Aboudi, Jacob; Amold, Steven M.

2010-01-01

The high-fidelity generalized method of cells composite micromechanics model is extended to include constituent-scale progressive damage via a proposed damage model. The damage model assumes that all material nonlinearity is due to damage in the form of reduced stiffness, and it uses six scalar damage variables (three for tension and three for compression) to track the damage. Damage strains are introduced that account for interaction among the strain components and that also allow the development of the damage evolution equations based on the constituent material uniaxial stress strain response. Local final-failure criteria are also proposed based on mode-specific strain energy release rates and total dissipated strain energy. The coupled micromechanics-damage model described herein is applied to a unidirectional E-glass/epoxy composite and a proprietary polymer matrix composite. Results illustrate the capability of the coupled model to capture the vastly different character of the monolithic (neat) resin matrix and the composite in response to far-field tension, compression, and shear loading.

A procedure for utilization of a damage-dependent constitutive model for laminated composites

NASA Technical Reports Server (NTRS)

Lo, David C.; Allen, David H.; Harris, Charles E.

1992-01-01

Described here is the procedure for utilizing a damage constitutive model to predict progressive damage growth in laminated composites. In this model, the effects of the internal damage are represented by strain-like second order tensorial damage variables and enter the analysis through damage dependent ply level and laminate level constitutive equations. The growth of matrix cracks due to fatigue loading is predicted by an experimentally based damage evolutionary relationship. This model is incorporated into a computer code called FLAMSTR. This code is capable of predicting the constitutive response and matrix crack damage accumulation in fatigue loaded laminated composites. The structure and usage of FLAMSTR are presented along with sample input and output files to assist the code user. As an example problem, an analysis of crossply laminates subjected to two stage fatigue loading was conducted and the resulting damage accumulation and stress redistribution were examined to determine the effect of variations in fatigue load amplitude applied during the first stage of the load history. It was found that the model predicts a significant loading history effect on damage evolution.

Herbivore pressure increases toward the equator

PubMed Central

Salazar, Diego; Marquis, Robert J.

2012-01-01

Increases in species diversity and density from higher to lower latitudes are well documented. Nevertheless, the consequences of these changes in diversity for structuring ecological communities and influencing biotic evolution are largely unknown. It is widely believed that this increase in species diversity is associated with increased intensity of ecological interactions closer to the equator. For plant–herbivore interactions in particular, the predictions are that, at lower latitudes, plants will be attacked by more individual herbivores, more herbivore species, and more specialized herbivores and, therefore, will suffer greater damage. We used a large-scale latitudinal transect from Mexico to Bolivia to quantify changes in leaf damage, diversity, and abundance of lepidopteran larvae on two widely distributed host species of the genus Piper (Piperaceae). We show that both density and species richness of herbivores were highest at the equator and decreased with increasing latitude, both northward and southward. Contrary to expectation, however, this increase in herbivore diversity was attributable to the addition of generalist not specialist species. Finally, and again contrary to expectation, the increase in herbivore density with decreasing latitude did not produce a corresponding damage gradient. We propose that the lack of a latitudinal concordance between increases in herbivore density and diversity with decreasing latitude, and the resulting herbivore damage, supports the hypothesis of better plant antiherbivore defenses at lower latitudes. Furthermore, the changes in the relative abundance of generalist vs. specialist species suggest that the nature of the selective pressure is intrinsically different between higher and lower latitudes. PMID:22802664

Effects of processing history on the evolution of surface damage layer and dislocation substructure in large grain niobium cavities

DOE PAGES

Kang, D.; Bieler, T. R.; Compton, C.

2015-12-16

Large grain niobium (Nb) is being investigated for fabricating superconducting radiofrequency cavities as an alternative to the traditional approach using fine grain polycrystalline Nb sheets. Past studies have identified a surface damage layer on fine grain cavities due to deep drawing and demonstrated the necessity for chemical etching on the surface. However, the origin of and depth of the damage layer are not well understood, and similar exploration on large grain cavities is lacking. In this work, electron backscatter diffraction (EBSD) was used to examine the cross sections at the equator and iris of a half cell deep drawn frommore » a large grain Nb ingot slice. The results indicate that the damage (identified by a high density of geometrically necessary dislocations) depends on crystal orientations, is different at the equator and iris, and is present through the full thickness of a half cell in some places. After electron backscatter diffraction, the specimens were heat treated at 800 °C or 1000 °C for two hours, and the same areas were reexamined. A more dramatic decrease in dislocation content was observed at the iris than the equator, where some regions exhibited no change. The specimens were then etched and examined again, to determine if the subsurface region behaved differently than the surface. As a result, little change in the dislocation substructure was observed, suggesting that the large grain microstructure is retained with a normal furnace anneal.« less

Non-local damage rheology and size effect

NASA Astrophysics Data System (ADS)

Lyakhovsky, V.

2011-12-01

We study scaling relations controlling the onset of transiently-accelerating fracturing and transition to dynamic rupture propagation in a non-local damage rheology model. The size effect is caused principally by growth of a fracture process zone, involving stress redistribution and energy release associated with a large fracture. This implies that rupture nucleation and transition to dynamic propagation are inherently scale-dependent processes. Linear elastic fracture mechanics (LEFM) and local damage mechanics are formulated in terms of dimensionless strain components and thus do not allow introducing any space scaling, except linear relations between fracture length and displacements. Generalization of Weibull theory provides scaling relations between stress and crack length at the onset of failure. A powerful extension of the LEFM formulation is the displacement-weakening model which postulates that yielding is complete when the crack wall displacement exceeds some critical value or slip-weakening distance Dc at which a transition to kinetic friction is complete. Scaling relations controlling the transition to dynamic rupture propagation in slip-weakening formulation are widely accepted in earthquake physics. Strong micro-crack interaction in a process zone may be accounted for by adopting either integral or gradient type non-local damage models. We formulate a gradient-type model with free energy depending on the scalar damage parameter and its spatial derivative. The damage-gradient term leads to structural stresses in the constitutive stress-strain relations and a damage diffusion term in the kinetic equation for damage evolution. The damage diffusion eliminates the singular localization predicted by local models. The finite width of the localization zone provides a fundamental length scale that allows numerical simulations with the model to achieve the continuum limit. A diffusive term in the damage evolution gives rise to additional damage diffusive time scale associated with the structural length scale. The ratio between two time scales associated with damage accumulation and diffusion, the damage diffusivity ratio, reflects the role of the diffusion-controlled delocalization. We demonstrate that localized fracturing occurs at the damage diffusivity ratio below certain critical value leading to a linear scaling between stress and crack length compatible with size effect for failures at crack initiation. A subseuqent quasi-static fracture growth is self-similar with increasing size of the process zone proportional to the fracture length. At a certain stage, controlled by dynamic weakening, the self-similarity breaks down and crack velocity significantly deviates from that predicted by the quasi-static regime, the size of the process zone decreases, and the rate of crack growth ceases to be controlled by the rate of damage increase. Furthermore, the crack speed approaches that predicted by the elasto-dynamic equation. The non-local damage rheology model predicts that the nucleation size of the dynamic fracture scales with fault zone thickness distance of the stress interraction.

Effect of deformation induced nucleation and phase mixing, a two phase model for the ductile deformation of rocks.

NASA Astrophysics Data System (ADS)

Bevillard, Benoit; Richard, Guillaume; Raimbourg, Hugues

2017-04-01

Rocks are complex materials and particularly their rheological behavior under geological stresses remains a long-standing question in geodynamics. To test large scale lithosphere dynamics numerical modeling is the main tool but encounter substantial difficulties to account for this complexity. One major unknown is the origin and development of the localization of deformation. This localization is observed within a large range of scales and is commonly characterized by sharp grain size reduction. These considerations argues for a control of the microscopical scale over the largest ones through one predominant variable: the mean grain-size. However, the presence of second phase and broad grain-size distribution may also have a important impact on this phenomenon. To address this question, we built a model for ductile rocks deformation based on the two-phase damage theory of Bercovici & Ricard 2012. We aim to investigate the role of grain-size reduction but also phase mixing on strain localization. Instead of considering a Zener-pining effect on damage evolution, we propose to take into account the effect of the grain-boundary sliding (GBS)-induced nucleation mechanism which is better supported by experimental or natural observations (Precigout et al 2016). This continuum theory allows to represent a two mineral phases aggregate with explicit log-normal grain-size distribution as a reasonable approximation for polymineralic rocks. Quantifying microscopical variables using a statistical approach may allow for calibration at small (experimental) scale. The general set of evolutions equations remains up-scalable provided some conditions on the homogenization scale. Using the interface density as a measure of mixture quality, we assume unlike Bercovici & Ricard 2012 that it may depend for some part on grain-size . The grain-size independent part of it is being represented by a "contact fraction" variable, whose evolution may be constrained by the dominant deformation mechanism. To derive the related evolution equations and account for the interdependence of thermodynamic state variables, we use Onsager's thermodynamic extremum principle. Eventually, we solve for our set of equations using an Anorthite/Pyroxene gabbroic composition. The results are used to discuss the interaction between grain-size reduction and phase mixing on strain localization on several simple cases. Bercovici D, Ricard Y (2012) Mechanisms for the generation of plate tectonics by two phase grain damage and pinning. Physics of the Earth and Planetary Interiors 202-203:27-55 Precigout J, Stunitz H (2016) Evidence of phase nucleation during olivine diffusion creep: A new perspective for mantle strain localisation. Earth and Planetary Science Letters 405:94-105

Hypervelocity impact and dynamic fragmentation of brittle materials

NASA Astrophysics Data System (ADS)

Agrawal, Vinamra; Ortega, Alejandro; Meiron, Daniel

2017-06-01

The process of hypervelocity impact and dynamic fragmentation finds application in planetary formation, satellite design for micrometeorite impact damage mitigation, armor design and crater formations. In this work, we study high velocity impact induced dynamic fragmentation processes of brittle materials. We implement ideas of Continuum Damage Mechanics (CDM) to perform fragmentation simulations on brittle materials in various geometries. The damage formulation was implemented on an existing computational framework capable of adaptive mesh refinement that operates on an Eulerian grid, thereby avoiding problems associated with grid entanglement in large deformation processes. A damage sensitive equation of state is developed for hyperelastic materials that depends on a damage variable D, the volume fraction of micro-cracks in the brittle material. The evolution of D is governed by a modified, thermodynamically consistent Grady-Kipp model that evolves damage at points of tensile eigenvalue stresses. We simulate sphere-on-sphere and sphere-on-plate impact events with ductile and brittle materials and study the resulting damage propagation. We validate our calculations with existing literature and comment on energy dissipation and optimal design. Caltech - JPL President's and Director's Fund.

Estimation of the tritium retention in ITER tungsten divertor target using macroscopic rate equations simulations

NASA Astrophysics Data System (ADS)

Hodille, E. A.; Bernard, E.; Markelj, S.; Mougenot, J.; Becquart, C. S.; Bisson, R.; Grisolia, C.

2017-12-01

Based on macroscopic rate equation simulations of tritium migration in an actively cooled tungsten (W) plasma facing component (PFC) using the code MHIMS (migration of hydrogen isotopes in metals), an estimation has been made of the tritium retention in ITER W divertor target during a non-uniform exponential distribution of particle fluxes. Two grades of materials are considered to be exposed to tritium ions: an undamaged W and a damaged W exposed to fast fusion neutrons. Due to strong temperature gradient in the PFC, Soret effect’s impacts on tritium retention is also evaluated for both cases. Thanks to the simulation, the evolutions of the tritium retention and the tritium migration depth are obtained as a function of the implanted flux and the number of cycles. From these evolutions, extrapolation laws are built to estimate the number of cycles needed for tritium to permeate from the implantation zone to the cooled surface and to quantify the corresponding retention of tritium throughout the W PFC.

Characteristics of Creep Damage for 60Sn-40Pb Solder Material

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wei, Y.; Chow, C.L.; Fang, H.E.

This paper presents a viscoplasticity model taking into account the effects of change in grain or phase size and damage on the characterization of creep damage in 60Sn-40Pb solder. Based on the theory of damage mechanics, a two-scalar damage model is developed for isotropic materials by introducing the free energy equivalence principle. The damage evolution equations are derived in terms of the damage energy release rates. In addition, a failure criterion is developed based on the postulation that a material element is said to have ruptured when the total damage accumulated in the element reaches a critical value. The damagemore » coupled viscoplasticity model is discretized and coded in a general-purpose finite element program known as ABAQUS through its user-defined material subroutine UMAT. To illustrate the application of the model, several example cases are introduced to analyze, both numerically and experimentally, the tensile creep behaviors of the material at three stress levels. The model is then applied to predict the deformation of a notched specimen under monotonic tension at room temperature (22 C). The results demonstrate that the proposed model can successfully predict the viscoplastic behavior of the solder material.« less

Flexural testing on carbon fibre laminates taking into account their different behaviour under tension and compression

NASA Astrophysics Data System (ADS)

Serna Moreno, M. C.; Romero Gutierrez, A.; Martínez Vicente, J. L.

2016-07-01

An analytical model has been derived for describing the results of three-point-bending tests in materials with different behaviour under tension and compression. The shift of the neutral plane and the damage initiation mode and its location have been defined. The validity of the equations has been reviewed by testing carbon fibre-reinforced polymers (CFRP), typically employed in different weight-critical applications. Both unidirectional and cross-ply laminates have been studied. The initial failure mode produced depends directly on the beam span- thickness relation. Therefore, specimens with different thicknesses have been analysed for examining the damage initiation due to either the bending moment or the out-of-plane shear load. The experimental description of the damage initiation and evolution has been shown by means of optical microscopy. The good agreement between the analytical estimations and the experimental results shows the validity of the analytical model exposed.

Optimal Control for Stochastic Delay Evolution Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

Stochastic modeling of cell growth with symmetric or asymmetric division

NASA Astrophysics Data System (ADS)

Marantan, Andrew; Amir, Ariel

2016-07-01

We consider a class of biologically motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the recursive integral equation describing the evolution of the resource distribution over subsequent generations and use it to study the properties of stable resource distributions. We find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the stable distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendixes, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.

Fluid-Structure Interaction in Continuum Models of Bacterial Biofilms

NASA Astrophysics Data System (ADS)

Hicks, Jared A.

Bacterial biofilms are aggregates of cells that adhere to nearly any solid-fluid interface. While many have harmful effects, such as industrial damage and nosocomial infections, certain biofilm species are now generating renewable energy as the fundamental components of Microbial Fuel Cells (MFCs). In an MFC, bacteria consume organic waste and, as they respire, produce free electrons. To do so efficiently, the bacteria must operate at peak metabolic activity, and so require an ample supply of nutrients. But existing MFC systems face several nutrient delivery problems, including clogging and downstream depletion. Ameliorating these problems will require a better understanding of the interplay between structural development and the surrounding fluid flow. In addition to delivering nutrients that affect biofilm growth, the fluid also exerts stresses that cause erosion, detachment, and deformation. These structural changes, in turn, affect the flow and alter the nutrient distribution. To account for this feedback effect, I have developed a continuum model that couples the growth and deformation processes. My model augments an existing growth model with evolution equations derived from Morphoelasticity Theory, by showing that the growth tensor can be directly related to the biofilm velocity potential. This result helps overcome one of the major practical limitations of Morphoelasticity--there is no physical framework for specifying the growth tensor. Through further analysis of the growth tensor, I define the related adjugate and anisotropic growth tensors, which can be more meaningful measures of growth for some models. Under the assumption of small strain, I show that there exists a small correction to the biofilm growth velocity (the accommodation velocity) that represents the effect of the elastic response on the evolution of the biofilm shape. I derive a solvability condition for the accommodation velocity, and show that it leads to a novel evolution equation for stress and strain in the biofilm, which couples the growth and deformation processes. Furthermore, I show that the introduction of a vorticity allows the accommodation velocity to be described by a system of Poisson equations, and that this vorticity arises naturally from Morphoelasticity theory and is related to the velocity solvability condition. I apply the modeling approach to a one-dimensional biofilm, and show that (a) the coupled growth process affects the evolution of the biofilm shape as expected, and (b) a non-coupled approach to biofilm strain introduces an error that grows over time. Numerical analysis of the one-dimensional strain evolution equation leads to several insights that inform the development of numerical methods for the two-dimensional case, including a split-step approach that reduces the fifth-order PDE to an advection equation for strain and a biharmonic equation for stress. Finally, I discuss some useful numerical methods for the simulation of elastic biofilm growth, particularly the discretization of the strain evolution equation(s). My overall approach is to track the evolving biofilm surface using a combination of the level-set method coupled with the eXtended Finite Element Method (XFEM). The major result is a novel mixed-XFEM discretization of the clamped-plate biharmonic equation, which I show to be first-order accurate for the trace of the solution on the interface.

Strain Rate Dependant Material Model for Orthotropic Metals

NASA Astrophysics Data System (ADS)

Vignjevic, Rade

2016-08-01

In manufacturing processes anisotropic metals are often exposed to the loading with high strain rates in the range from 102 s-1 to 106 s-1 (e.g. stamping, cold spraying and explosive forming). These types of loading often involve generation and propagation of shock waves within the material. The material behaviour under such a complex loading needs to be accurately modelled, in order to optimise the manufacturing process and achieve appropriate properties of the manufactured component. The presented research is related to development and validation of a thermodynamically consistent physically based constitutive model for metals under high rate loading. The model is capable of modelling damage, failure and formation and propagation of shock waves in anisotropic metals. The model has two main parts: the strength part which defines the material response to shear deformation and an equation of state (EOS) which defines the material response to isotropic volumetric deformation [1]. The constitutive model was implemented into the transient nonlinear finite element code DYNA3D [2] and our in house SPH code. Limited model validation was performed by simulating a number of high velocity material characterisation and validation impact tests. The new damage model was developed in the framework of configurational continuum mechanics and irreversible thermodynamics with internal state variables. The use of the multiplicative decomposition of deformation gradient makes the model applicable to arbitrary plastic and damage deformations. To account for the physical mechanisms of failure, the concept of thermally activated damage initially proposed by Tuller and Bucher [3], Klepaczko [4] was adopted as the basis for the new damage evolution model. This makes the proposed damage/failure model compatible with the Mechanical Threshold Strength (MTS) model Follansbee and Kocks [5], 1988; Chen and Gray [6] which was used to control evolution of flow stress during plastic deformation. In addition the constitutive model is coupled with a vector shock equation of state which allows for modelling of shock wave propagation in orthotropic the material. Parameters for the new constitutive model are typically derived on the basis of the tensile tests (performed over a range of temperatures and strain rates), plate impact tests and Taylor anvil tests. The model was applied to simulate explosively driven fragmentation, blast loading and cold spraying impacts.

Enhanced Schapery Theory Software Development for Modeling Failure of Fiber-Reinforced Laminates

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Waas, Anthony M.

2013-01-01

Progressive damage and failure analysis (PDFA) tools are needed to predict the nonlinear response of advanced fiber-reinforced composite structures. Predictive tools should incorporate the underlying physics of the damage and failure mechanisms observed in the composite, and should utilize as few input parameters as possible. The purpose of the Enhanced Schapery Theory (EST) was to create a PDFA tool that operates in conjunction with a commercially available finite element (FE) code (Abaqus). The tool captures the physics of the damage and failure mechanisms that result in the nonlinear behavior of the material, and the failure methodology employed yields numerical results that are relatively insensitive to changes in the FE mesh. The EST code is written in Fortran and compiled into a static library that is linked to Abaqus. A Fortran Abaqus UMAT material subroutine is used to facilitate the communication between Abaqus and EST. A clear distinction between damage and failure is imposed. Damage mechanisms result in pre-peak nonlinearity in the stress strain curve. Four internal state variables (ISVs) are utilized to control the damage and failure degradation. All damage is said to result from matrix microdamage, and a single ISV marks the micro-damage evolution as it is used to degrade the transverse and shear moduli of the lamina using a set of experimentally obtainable matrix microdamage functions. Three separate failure ISVs are used to incorporate failure due to fiber breakage, mode I matrix cracking, and mode II matrix cracking. Failure initiation is determined using a failure criterion, and the evolution of these ISVs is controlled by a set of traction-separation laws. The traction separation laws are postulated such that the area under the curves is equal to the fracture toughness of the material associated with the corresponding failure mechanism. A characteristic finite element length is used to transform the traction-separation laws into stress-strain laws. The ISV evolution equations are derived in a thermodynamically consistent manner by invoking the stationary principle on the total work of the system with respect to each ISV. A novel feature is the inclusion of both pre-peak damage and appropriately scaled, post-peak strain softening failure. Also, the characteristic elements used in the failure degradation scheme are calculated using the element nodal coordinates, rather than simply the square root of the area of the element.

Core thermal response and hydrogen generation of the N Reactor hydrogen mitigation design basis accident

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, M.D.; Lombardo, N.J.; Heard, F.J.

1988-04-01

Calculations were performed to determine core heatup, core damage, and subsequent hydrogen production of a hypothetical loss-of-cooling accident at the Department of Energy's N Reactor. The thermal transient response of the reactor core was solved using the TRUMP-BD computer program. Estimates of whole-core thermal damage and hydrogen production were made by weighting the results of multiple half-length pressure tube simulations at various power levels. The Baker-Just and Wilson parabolic rate equations for the metal-water chemical reactions modeled the key phenomena of chemical energy and hydrogen evolution. Unlimited steam was assumed available for continuous oxidation of exposed Zircaloy-2 surfaces and formore » uranium metal with fuel cladding beyond the failure temperature (1038 C). Intact fuel geometry was modeled. Maximum fuel temperatures (1181 C) in the cooled central regions of the core were predicted to occur one-half hour into the accident scenario. Maximum fuel temperatures of 1447 C occurred in the core GSCS-regions at the end of the 10-h transient. After 10-h 26% of the fuel inventory was predicted to have failed. Peak hydrogen evolution equaled 42 g/s, while 10-h integrated hydrogen evolution equaled 167 kg. 12 refs., 12 figs., 2 tabs.« less

Helicity evolution at small-x

DOE PAGES

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

2016-01-13

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the g1 structure function. These evolution equations resum powers of α s ln 2(1/x) in the polarization-dependent evolution along with the powers of α s ln(1/x) in the unpolarized evolution which includes saturation efects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-N c and large-N c & N f limits. As a cross-check,more » in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for g 1 structure function derived previously by Bartels, Ermolaev and Ryskin.« less

Microscopic and macroscopic models for the onset and progression of Alzheimer's disease

NASA Astrophysics Data System (ADS)

Bertsch, Michiel; Franchi, Bruno; Carla Tesi, Maria; Tosin, Andrea

2017-10-01

In the first part of this paper we review a mathematical model for the onset and progression of Alzheimer’s disease (AD) that was developed in subsequent steps over several years. The model is meant to describe the evolution of AD in vivo. In Achdou et al (2013 J. Math. Biol. 67 1369-92) we treated the problem at a microscopic scale, where the typical length scale is a multiple of the size of the soma of a single neuron. Subsequently, in Bertsch et al (2017 Math. Med. Biol. 34 193-214) we concentrated on the macroscopic scale, where brain neurons are regarded as a continuous medium, structured by their degree of malfunctioning. In the second part of the paper we consider the relation between the microscopic and the macroscopic models. In particular we show under which assumptions the kinetic transport equation, which in the macroscopic model governs the evolution of the probability measure for the degree of malfunctioning of neurons, can be derived from a particle-based setting. The models are based on aggregation and diffusion equations for β-Amyloid (Aβ from now on), a protein fragment that healthy brains regularly produce and eliminate. In case of dementia Aβ monomers are no longer properly washed out and begin to coalesce forming eventually plaques. Two different mechanisms are assumed to be relevant for the temporal evolution of the disease: (i) diffusion and agglomeration of soluble polymers of amyloid, produced by damaged neurons; (ii) neuron-to-neuron prion-like transmission. In the microscopic model we consider mechanism (i), modelling it by a system of Smoluchowski equations for the amyloid concentration (describing the agglomeration phenomenon), with the addition of a diffusion term as well as of a source term on the neuronal membrane. At the macroscopic level instead we model processes (i) and (ii) by a system of Smoluchowski equations for the amyloid concentration, coupled to a kinetic-type transport equation for the distribution function of the degree of malfunctioning of the neurons. The transport equation contains an integral term describing the random onset of the disease as a jump process localized in particularly sensitive areas of the brain.

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

Damage Identification of Piles Based on Vibration Characteristics

PubMed Central

Zhang, Xiaozhong; Yao, Wenjuan; Chen, Bo; Liu, Dewen

2014-01-01

A method of damage identification of piles was established by using vibration characteristics. The approach focused on the application of the element strain energy and sensitive modals. A damage identification equation of piles was deduced using the structural vibration equation. The equation contained three major factors: change rate of element modal strain energy, damage factor of pile, and sensitivity factor of modal damage. The sensitive modals of damage identification were selected by using sensitivity factor of modal damage firstly. Subsequently, the indexes for early-warning of pile damage were established by applying the change rate of strain energy. Then the technology of computational analysis of wavelet transform was used to damage identification for pile. The identification of small damage of pile was completely achieved, including the location of damage and the extent of damage. In the process of identifying the extent of damage of pile, the equation of damage identification was used in many times. Finally, a stadium project was used as an example to demonstrate the effectiveness of the proposed method of damage identification for piles. The correctness and practicability of the proposed method were verified by comparing the results of damage identification with that of low strain test. The research provided a new way for damage identification of piles. PMID:25506062

Exact traveling wave solutions for system of nonlinear evolution equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

2016-01-01

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.

MESOSCALE MODELING OF DEFLAGRATION-INDUCED DECONSOLIDATION IN POLYMER-BONDED EXPLOSIVES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Springer, H K; Glascoe, E A; Reaugh, J E

Initially undamaged polymer-bonded explosives can transition from conductive burning to more violent convective burning via rapid deconsolidation at higher pressures. The pressure-dependent infiltration of cracks and pores, i.e., damage, by product gases at the burn-front is a key step in the transition to convective burning. However, the relative influence of pre-existing damage and the evolution of deflagration-induced damage during the transition to convective burning is not well understood. The objective of this study is to investigate the role of microstructure and initial pressurization on deconsolidation. We performed simulations using the multi-physics hydrocode, ALE3D. HMX-Viton A served as our model explosive.more » A Prout-Tompkins chemical kinetic model, Vielle's Law pressure-dependent burning, Gruneisen equation-of-state, and simplified strength model were used for the HMX. The propensity for deconsolidation increased with increasing defect size and decreasing initial pressurization, as measured by the increase in burning surface area. These studies are important because they enable the development of continuum-scale damage models and the design of inherently safer explosives.« less

Lie symmetries for systems of evolution equations

NASA Astrophysics Data System (ADS)

Paliathanasis, Andronikos; Tsamparlis, Michael

2018-01-01

The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined.

Damage evaluation of fiber reinforced plastic-confined circular concrete-filled steel tubular columns under cyclic loading using the acoustic emission technique

NASA Astrophysics Data System (ADS)

Li, Dongsheng; Du, Fangzhu; Ou, Jinping

2017-03-01

Glass-fiber reinforced plastic (GFRP)-confined circular concrete-filled steel tubular (CCFT) columns comprise of concrete, steel, and GFRP and show complex failure mechanics under cyclic loading. This paper investigated the failure mechanism and damage evolution of GFRP-CCFT columns by performing uniaxial cyclic loading tests that were monitored using the acoustic emission (AE) technique. Characteristic AE parameters were obtained during the damage evolution of GFRP-CCFT columns. Based on the relationship between the loading curve and these parameters, the damage evolution of GFRP-CCFT columns was classified into three stages that represented different damage degrees. Damage evolution and failure mode were investigated by analyzing the b-value and the ratio of rise time to waveform amplitude and average frequency. The damage severity of GFRP-CCFT columns were quantitatively estimated according to the modified index of damage and NDIS-2421 damage assessment criteria corresponding to each loading step. The proposed method can explain the damage evolution and failure mechanism for GFRP-CCFT columns and provide critical warning information for composite structures.

An evaluation of Computational Fluid dynamics model for flood risk analysis

NASA Astrophysics Data System (ADS)

Di Francesco, Silvia; Biscarini, Chiara; Montesarchio, Valeria

2014-05-01

This work presents an analysis of the hydrological-hydraulic engineering requisites for Risk evaluation and efficient flood damage reduction plans. Most of the research efforts have been dedicated to the scientific and technical aspects of risk assessment, providing estimates of possible alternatives and of the risk associated. In the decision making process for mitigation plan, the contribute of scientist is crucial, due to the fact that Risk-Damage analysis is based on evaluation of flow field ,of Hydraulic Risk and on economical and societal considerations. The present paper will focus on the first part of process, the mathematical modelling of flood events which is the base for all further considerations. The evaluation of potential catastrophic damage consequent to a flood event and in particular to dam failure requires modelling of the flood with sufficient detail so to capture the spatial and temporal evolutions of the event, as well of the velocity field. Thus, the selection of an appropriate mathematical model to correctly simulate flood routing is an essential step. In this work we present the application of two 3D Computational fluid dynamics models to a synthetic and real case study in order to evaluate the correct evolution of flow field and the associated flood Risk . The first model is based on a opensource CFD platform called openFoam. Water flow is schematized with a classical continuum approach based on Navier-Stokes equation coupled with Volume of fluid (VOF) method to take in account the multiphase character of river bottom-water- air systems. The second model instead is based on the Lattice Boltzmann method, an innovative numerical fluid dynamics scheme based on Boltzmann's kinetic equation that represents the flow dynamics at the macroscopic level by incorporating a microscopic kinetic approach. Fluid is seen as composed by particles that can move and collide among them. Simulation results from both models are promising and congruent to experimental results available in literature, thought the LBM model requires less computational effort respect to the NS one.

Method of Fatigue-Life Prediction for an Asphalt Mixture Based on the Plateau Value of Permanent Deformation Ratio.

PubMed

Sun, Yazhen; Fang, Chenze; Wang, Jinchang; Yuan, Xuezhong; Fan, Dong

2018-05-03

Laboratory predictions for the fatigue life of an asphalt mixture under cyclic loading based on the plateau value (PV) of the permanent deformation ratio (PDR) were carried out by three-point bending fatigue tests. The influence of test conditions on the recovery ratio of elastic deformation (RRED), the permanent deformation (PD) and PDR, and the trends of RRED, PD, and PDR were studied. The damage variable was defined by using PDR, and the relation of the fatigue life to PDR was determined by analyzing the damage evolution process. The fatigue equation was established based on the PV of PDR and the fatigue life was predicted by analyzing the relation of the fatigue life to the PV. The results show that the RRED decreases with the increase of the number of loading cycles, and the elastic recovery ability of the asphalt mixture gradually decreases. The two mathematical models proposed are based on the change laws of the RRED, and the PD can well describe the change laws. The RRED or the PD cannot well predict the fatigue life because they do not change monotonously with the fatigue life, and one part of the deformation causes the damage and the other part causes the viscoelastic deformation. The fatigue life decreases with the increase of the PDR. The average PDR in the second stage is taken as the PV, and the fatigue life decreases in a power law with the increase of the PV. The average relative error of the fatigue life predicted by the fatigue equation to the test fatigue life is 5.77%. The fatigue equation based on PV can well predict the fatigue life.

Prediction and experimental observation of damage dependent damping in laminated composite beams

NASA Technical Reports Server (NTRS)

Allen, D. H.; Harris, C. E.; Highsmith, A. L.

1987-01-01

The equations of motion are developed for laminated composite beams with load-induced matrix cracking. The damage is accounted for by utilizing internal state variables. The net result of these variables on the field equations is the introduction of both enhanced damping, and degraded stiffness. Both quantities are history dependent and spatially variable, thus resulting in nonlinear equations of motion. It is explained briefly how these equations may be quasi-linearized for laminated polymeric composites under certain types of structural loading. The coupled heat conduction equation is developed, and it is shown that an enhanced Zener damping effect is produced by the introduction of microstructural damage. The resulting equations are utilized to demonstrate how damage dependent material properties may be obtained from dynamic experiments. Finaly, experimental results are compared to model predictions for several composite layups.

Quasi-static responses and variational principles in gradient plasticity

NASA Astrophysics Data System (ADS)

Nguyen, Quoc-Son

2016-12-01

Gradient models have been much discussed in the literature for the study of time-dependent or time-independent processes such as visco-plasticity, plasticity and damage. This paper is devoted to the theory of Standard Gradient Plasticity at small strain. A general and consistent mathematical description available for common time-independent behaviours is presented. Our attention is focussed on the derivation of general results such as the description of the governing equations for the global response and the derivation of related variational principles in terms of the energy and the dissipation potentials. It is shown that the quasi-static response under a loading path is a solution of an evolution variational inequality as in classical plasticity. The rate problem and the rate minimum principle are revisited. A time-discretization by the implicit scheme of the evolution equation leads to the increment problem. An increment of the response associated with a load increment is a solution of a variational inequality and satisfies also a minimum principle if the energy potential is convex. The increment minimum principle deals with stables solutions of the variational inequality. Some numerical methods are discussed in view of the numerical simulation of the quasi-static response.

A Hybrid Approach to Composite Damage and Failure Analysis Combining Synergistic Damage Mechanics and Peridynamics

DTIC Science & Technology

2016-03-31

fiber distributions. Task 2.1 is concerned with damage evolution in a peridynamic model of poroelastic materials. Initial results for both tasks are...distributions. Task 2.1 is concerned with damage evolution in a peridynamic model of poroelastic materials. Initial results for both tasks are reported and...Task 2.1: Damage evolution in a peridynamic model of poroelastic materials. Background and Motivation In order to model the presence of pores and

Influence of sub-surface damage evolution on low-energy-plasma-driven deuterium permeation through tungsten

NASA Astrophysics Data System (ADS)

Kapser, Stefan; Balden, Martin; Fiorini da Silva, Tiago; Elgeti, Stefan; Manhard, Armin; Schmid, Klaus; Schwarz-Selinger, Thomas; von Toussaint, Udo

2018-05-01

Low-energy-plasma-driven deuterium permeation through tungsten at 300 K and 450 K has been investigated. Microstructural analysis by scanning electron microscopy, assisted by focused ion beam, revealed sub-surface damage evolution only at 300 K. This damage evolution was correlated with a significant evolution of the deuterium amount retained below the plasma-exposed surface. Although both of these phenomena were observed for 300 K exposure temperature only, the deuterium permeation flux at both exposure temperatures was indistinguishable within the experimental uncertainty. The permeation flux was used to estimate the maximum ratio of solute-deuterium to tungsten atoms during deuterium-plasma exposure at both temperatures and thus in the presence and absence of damage evolution. Diffusion-trapping simulations revealed the proximity of damage evolution to the implantation surface as the reason for an only insignificant decrease of the permeation flux.

Investigation of shear damage considering the evolution of anisotropy

NASA Astrophysics Data System (ADS)

Kweon, S.

2013-12-01

The damage that occurs in shear deformations in view of anisotropy evolution is investigated. It is widely believed in the mechanics research community that damage (or porosity) does not evolve (increase) in shear deformations since the hydrostatic stress in shear is zero. This paper proves that the above statement can be false in large deformations of simple shear. The simulation using the proposed anisotropic ductile fracture model (macro-scale) in this study indicates that hydrostatic stress becomes nonzero and (thus) porosity evolves (increases or decreases) in the simple shear deformation of anisotropic (orthotropic) materials. The simple shear simulation using a crystal plasticity based damage model (meso-scale) shows the same physics as manifested in the above macro-scale model that porosity evolves due to the grain-to-grain interaction, i.e., due to the evolution of anisotropy. Through a series of simple shear simulations, this study investigates the effect of the evolution of anisotropy, i.e., the rotation of the orthotropic axes onto the damage (porosity) evolution. The effect of the evolutions of void orientation and void shape onto the damage (porosity) evolution is investigated as well. It is found out that the interaction among porosity, the matrix anisotropy and void orientation/shape plays a crucial role in the ductile damage of porous materials.

Center manifolds for a class of degenerate evolution equations and existence of small-amplitude kinetic shocks

NASA Astrophysics Data System (ADS)

Pogan, Alin; Zumbrun, Kevin

2018-06-01

We construct center manifolds for a class of degenerate evolution equations including the steady Boltzmann equation and related kinetic models, establishing in the process existence and behavior of small-amplitude kinetic shock and boundary layers. Notably, for Boltzmann's equation, we show that elements of the center manifold decay in velocity at near-Maxwellian rate, in accord with the formal Chapman-Enskog picture of near-equilibrium flow as evolution along the manifold of Maxwellian states, or Grad moment approximation via Hermite polynomials in velocity. Our analysis is from a classical dynamical systems point of view, with a number of interesting modifications to accommodate ill-posedness of the underlying evolution equation.

The Liouville equation for flavour evolution of neutrinos and neutrino wave packets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hansen, Rasmus Sloth Lundkvist; Smirnov, Alexei Yu., E-mail: rasmus@mpi-hd.mpg.de, E-mail: smirnov@mpi-hd.mpg.de

We consider several aspects related to the form, derivation and applications of the Liouville equation (LE) for flavour evolution of neutrinos. To take into account the quantum nature of neutrinos we derive the evolution equation for the matrix of densities using wave packets instead of Wigner functions. The obtained equation differs from the standard LE by an additional term which is proportional to the difference of group velocities. We show that this term describes loss of the propagation coherence in the system. In absence of momentum changing collisions, the LE can be reduced to a single derivative equation over amore » trajectory coordinate. Additional time and spatial dependence may stem from initial (production) conditions. The transition from single neutrino evolution to the evolution of a neutrino gas is considered.« less

Efficient Meshfree Large Deformation Simulation of Rainfall Induced Soil Slope Failure

NASA Astrophysics Data System (ADS)

Wang, Dongdong; Li, Ling

2010-05-01

An efficient Lagrangian Galerkin meshfree framework is presented for large deformation simulation of rainfall-induced soil slope failure. Detailed coupled soil-rainfall seepage equations are given for the proposed formulation. This nonlinear meshfree formulation is featured by the Lagrangian stabilized conforming nodal integration method where the low cost nature of nodal integration approach is kept and at the same time the numerical stability is maintained. The initiation and evolution of progressive failure in the soil slope is modeled by the coupled constitutive equations of isotropic damage and Drucker-Prager pressure-dependent plasticity. The gradient smoothing in the stabilized conforming integration also serves as a non-local regularization of material instability and consequently the present method is capable of effectively capture the shear band failure. The efficacy of the present method is demonstrated by simulating the rainfall-induced failure of two typical soil slopes.

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Soliton evolution and radiation loss for the sine-Gordon equation.

PubMed

Smyth, N F; Worthy, A L

1999-08-01

An approximate method for describing the evolution of solitonlike initial conditions to solitons for the sine-Gordon equation is developed. This method is based on using a solitonlike pulse with variable parameters in an averaged Lagrangian for the sine-Gordon equation. This averaged Lagrangian is then used to determine ordinary differential equations governing the evolution of the pulse parameters. The pulse evolves to a steady soliton by shedding dispersive radiation. The effect of this radiation is determined by examining the linearized sine-Gordon equation and loss terms are added to the variational equations derived from the averaged Lagrangian by using the momentum and energy conservation equations for the sine-Gordon equation. Solutions of the resulting approximate equations, which include loss, are found to be in good agreement with full numerical solutions of the sine-Gordon equation.

Selection by consequences, behavioral evolution, and the price equation.

PubMed

Baum, William M

2017-05-01

Price's equation describes evolution across time in simple mathematical terms. Although it is not a theory, but a derived identity, it is useful as an analytical tool. It affords lucid descriptions of genetic evolution, cultural evolution, and behavioral evolution (often called "selection by consequences") at different levels (e.g., individual vs. group) and at different time scales (local and extended). The importance of the Price equation for behavior analysis lies in its ability to precisely restate selection by consequences, thereby restating, or even replacing, the law of effect. Beyond this, the equation may be useful whenever one regards ontogenetic behavioral change as evolutionary change, because it describes evolutionary change in abstract, general terms. As an analytical tool, the behavioral Price equation is an excellent aid in understanding how behavior changes within organisms' lifetimes. For example, it illuminates evolution of response rate, analyses of choice in concurrent schedules, negative contingencies, and dilemmas of self-control. © 2017 Society for the Experimental Analysis of Behavior.

On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations

DOE PAGES

Christov, Ivan C.

2015-08-20

We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.

Microstructural characterization and simulation of damage for geared sheet components

NASA Astrophysics Data System (ADS)

Gerstein, G.; Isik, K.; Gutknecht, F.; Sieczkarek, P.; Ewert, J.; Tekkaya, A. E.; Clausmeyer, T.; Nürnberger, F.

2017-09-01

The evolution of damage in geared components manufactured from steel sheets was investigated, to analyse the influence of damage caused by the sheet-bulk-metal forming. Due to the inhomogeneous and multi-axial deformation in the investigated parts, different aspects such as the location-dependent shape and size of voids are analysed by means of various microscopic methods. In particular, a method to characterize the state of damage evolution, i. e. void nucleation, growth and coalescence using scanning electron microscopy (SEM) is applied. The investigations reveal a strong dependence of the void area fraction, shape of voids and thus damage evolution on the loading mode. The microstructural analysis is complemented with FEM simulations using material models which consider the characteristics of the void evolution.

A note on the evolution equations from the area fraction and the thickness of a floating ice cover

NASA Astrophysics Data System (ADS)

Schulkes, R. M. S. M.

1995-03-01

In this paper, two sets of evolution equations for the area fraction and the ice thickness are investigated. First of all, a simplified alternative derivation of the evolution equations as presented by Gray and Morland (1994) is given. In addition, it is shown that with proper identification of ridging functions, there is a close connection between the derived equations and the thickness distribution model introduced by Thorndike et al. (1975).

Critical spaces for quasilinear parabolic evolution equations and applications

NASA Astrophysics Data System (ADS)

Prüss, Jan; Simonett, Gieri; Wilke, Mathias

2018-02-01

We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.

SPALLMAP

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sabau, Adrian; Wright, Ian

Boiler tubes in steam power plants experience exfoliation of oxide grown on the inner side of the tubes. In extreme cases, the exfoliation cause significant tube blockages that lead to forced power plant outages. It is thus desired to predict through modeling the propensity of exfoliation events in order to inform power plant operators of possible tube blockages. SpallMap solves for the stress-strain equations in an axisymmetric geometry, tracking the stress/strain evolution during boiler operation including outages at one-location along a boiler tube and compares it with scale damage criteria represented by Armitt diagram. The SPALLMAP code contains modules developedmore » for oxide growth, stress analysis, and classical fracture mechanics correlations by taking into account the following phenomena and features, (a) Non-uniform thermal expansion coefficient of oxides and metal substrates, (b) Plant operation schedule with periodic alternate full-load and partial-load regimes, (c) axisymmetric formulation for cylindrical tubes, (d) Multiple oxide layers, (e) oxide-growth induced stresses, and (f) damage criteria from classical fracture mechanics. The computer program is written in FORTRAN90. Its modular structure was sought for allowing the best flexibility in updating the program by implementing new constitutive equations due to availability of new material property data and/or new physical phenomena.« less

Macroscopic dielectric function within time-dependent density functional theory—Real time evolution versus the Casida approach

NASA Astrophysics Data System (ADS)

Sander, Tobias; Kresse, Georg

2017-02-01

Linear optical properties can be calculated by solving the time-dependent density functional theory equations. Linearization of the equation of motion around the ground state orbitals results in the so-called Casida equation, which is formally very similar to the Bethe-Salpeter equation. Alternatively one can determine the spectral functions by applying an infinitely short electric field in time and then following the evolution of the electron orbitals and the evolution of the dipole moments. The long wavelength response function is then given by the Fourier transformation of the evolution of the dipole moments in time. In this work, we compare the results and performance of these two approaches for the projector augmented wave method. To allow for large time steps and still rely on a simple difference scheme to solve the differential equation, we correct for the errors in the frequency domain, using a simple analytic equation. In general, we find that both approaches yield virtually indistinguishable results. For standard density functionals, the time evolution approach is, with respect to the computational performance, clearly superior compared to the solution of the Casida equation. However, for functionals including nonlocal exchange, the direct solution of the Casida equation is usually much more efficient, even though it scales less beneficial with the system size. We relate this to the large computational prefactors in evaluating the nonlocal exchange, which renders the time evolution algorithm fairly inefficient.

Cylindrical and spherical solitary waves in an electron-acoustic plasma with vortex electron distribution

NASA Astrophysics Data System (ADS)

Demiray, Hilmi; El-Zahar, Essam R.

2018-04-01

We consider the nonlinear propagation of electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical (spherical) coordinates by employing the reductive perturbation technique. The modified cylindrical (spherical) KdV equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, this evolution equation cannot be reduced to the conventional KdV equation. A new family of closed form analytical approximate solution to the evolution equation and a comparison with numerical solution are presented and the results are depicted in some 2D and 3D figures. The results reveal that both solutions are in good agreement and the method can be used to obtain a new progressive wave solution for such evolution equations. Moreover, the resulting closed form analytical solution allows us to carry out a parametric study to investigate the effect of the physical parameters on the solution behavior of the modified cylindrical (spherical) KdV equation.

General Equations of Motion for a Damaged Asymmetric Aircraft

NASA Technical Reports Server (NTRS)

Bacon, Barton J.; Gregory, Irene M.

2007-01-01

There is a renewed interest in dynamic characteristics of damaged aircraft both in order to assess survivability and to develop control laws to enhance survivability. This paper presents a set of flight dynamics equations of motion for a rigid body not necessarily referenced to the body's center of mass. Such equations can be used when the body loses a portion of its mass and it is desired to track the motion of the body s previous center of mass/reference frame now that the mass center has moved to a new position. Furthermore, results for equations presented in this paper and equations in standard aircraft simulations are compared for a scenario involving a generic transport aircraft configuration subject to wing damage.

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

PubMed Central

Motsa, S. S.; Magagula, V. M.; Sibanda, P.

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

PubMed

Motsa, S S; Magagula, V M; Sibanda, P

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

The Hartman-Grobman theorem for semilinear hyperbolic evolution equations

NASA Astrophysics Data System (ADS)

Hein, Marie-Luise; Prüss, Jan

2016-10-01

The famous Hartman-Grobman theorem for ordinary differential equations is extended to abstract semilinear hyperbolic evolution equations in Banach spaces by means of simple direct proof. It is also shown that the linearising map is Hölder continuous. Several applications to abstract and specific damped wave equations are given, to demonstrate the strength of our results.

Helicity evolution at small x : Flavor singlet and nonsinglet observables

DOE PAGES

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

2017-01-30

We extend our earlier results for the quark helicity evolution at small x to derive the small-x asymptotics of the flavor singlet and flavor nonsinglet quark helicity TMDs and PDFs and of the g 1 structure function. In the flavor singlet case we rederive the evolution equations obtained in our previous paper on the subject, performing additional cross-checks of our results. In the flavor nonsinglet case we construct new small-x evolution equations by employing the large-N c limit. Here, all evolution equations resum double-logarithmic powers of α sln 2(1/x) in the polarization-dependent evolution along with the single-logarithmic powers of αmore » sln(1/x) in the unpolarized evolution which includes saturation effects.« less

Helicity evolution at small x : Flavor singlet and nonsinglet observables

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

We extend our earlier results for the quark helicity evolution at small x to derive the small-x asymptotics of the flavor singlet and flavor nonsinglet quark helicity TMDs and PDFs and of the g 1 structure function. In the flavor singlet case we rederive the evolution equations obtained in our previous paper on the subject, performing additional cross-checks of our results. In the flavor nonsinglet case we construct new small-x evolution equations by employing the large-N c limit. Here, all evolution equations resum double-logarithmic powers of α sln 2(1/x) in the polarization-dependent evolution along with the single-logarithmic powers of αmore » sln(1/x) in the unpolarized evolution which includes saturation effects.« less

Cauchy-Jost function and hierarchy of integrable equations

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2015-11-01

We describe the properties of the Cauchy-Jost (also known as Cauchy-Baker-Akhiezer) function of the Kadomtsev-Petviashvili-II equation. Using the bar partial -method, we show that for this function, all equations of the Kadomtsev-Petviashvili-II hierarchy are given in a compact and explicit form, including equations for the Cauchy-Jost function itself, time evolutions of the Jost solutions, and evolutions of the potential of the heat equation.

A damage mechanics based approach to structural deterioration and reliability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhattcharya, B.; Ellingwood, B.

1998-02-01

Structural deterioration often occurs without perceptible manifestation. Continuum damage mechanics defines structural damage in terms of the material microstructure, and relates the damage variable to the macroscopic strength or stiffness of the structure. This enables one to predict the state of damage prior to the initiation of a macroscopic flaw, and allows one to estimate residual strength/service life of an existing structure. The accumulation of damage is a dissipative process that is governed by the laws of thermodynamics. Partial differential equations for damage growth in terms of the Helmholtz free energy are derived from fundamental thermodynamical conditions. Closed-form solutions tomore » the equations are obtained under uniaxial loading for ductile deformation damage as a function of plastic strain, for creep damage as a function of time, and for fatigue damage as function of number of cycles. The proposed damage growth model is extended into the stochastic domain by considering fluctuations in the free energy, and closed-form solutions of the resulting stochastic differential equation are obtained in each of the three cases mentioned above. A reliability analysis of a ring-stiffened cylindrical steel shell subjected to corrosion, accidental pressure, and temperature is performed.« less

Simulation of Corrosion Process for Structure with the Cellular Automata Method

NASA Astrophysics Data System (ADS)

Chen, M. C.; Wen, Q. Q.

2017-06-01

In this paper, from the mesoscopic point of view, under the assumption of metal corrosion damage evolution being a diffusive process, the cellular automata (CA) method was proposed to simulate numerically the uniform corrosion damage evolution of outer steel tube of concrete filled steel tubular columns subjected to corrosive environment, and the effects of corrosive agent concentration, dissolution probability and elapsed etching time on the corrosion damage evolution were also investigated. It was shown that corrosion damage increases nonlinearly with increasing elapsed etching time, and the longer the etching time, the more serious the corrosion damage; different concentration of corrosive agents had different impacts on the corrosion damage degree of the outer steel tube, but the difference between the impacts was very small; the heavier the concentration, the more serious the influence. The greater the dissolution probability, the more serious the corrosion damage of the outer steel tube, but with the increase of dissolution probability, the difference between its impacts on the corrosion damage became smaller and smaller. To validate present method, corrosion damage measurements for concrete filled square steel tubular columns (CFSSTCs) sealed at both their ends and immersed fully in a simulating acid rain solution were conducted, and Faraday’s law was used to predict their theoretical values. Meanwhile, the proposed CA mode was applied for the simulation of corrosion damage evolution of the CFSSTCs. It was shown by the comparisons of results from the three methods aforementioned that they were in good agreement, implying that the proposed method used for the simulation of corrosion damage evolution of concrete filled steel tubular columns is feasible and effective. It will open a new approach to study and evaluate further the corrosion damage, loading capacity and lifetime prediction of concrete filled steel tubular structures.

Analytical and experimental investigation of microstructural alterations in bearing steel in rolling contact fatigue

NASA Astrophysics Data System (ADS)

Mobasher Moghaddam, Sina

Rolling Contact Fatigue (RCF) is one the most common failure modes in bearings. RCF is usually associated with particular microstructural alterations. Such alterations (i.e. white etching cracks, butterflies, etc.) which lead to RCF failure are known to be among the most concerning matters to bearing industry. In the current work, an analytical as well as experimental approaches are used to investigate "butterfly wing" formation, crack initiation and propagation from inclusions. A new damage evolution equation coupled with a FE model is employed to account for the effect of mean stresses and alternating stresses simultaneously to investigate butterfly formation. The proposed damage evolution law matches experimentally observed butterfly orientation, shape, and size successfully. The model is used to obtain S-N results for butterfly formation at different Hertzian load levels. The results corroborate well with the experimental data available in the open literature. The model is used to predict debonding at the inclusion/matrix interface and the most vulnerable regions for crack initiation on butterfly/matrix interface. A new variable called butterfly formation index (BFI) is introduced to manifest the dependence of wing formation on depth. The value of critical damage inside the butterfly wings was obtained experimentally and was then used to simulate damage evolution. Voronoi tessellation was used to develop the FEM domains to capture the effect of microstructural randomness on butterfly wing formation, crack initiation and propagation. Then, the effects of different inclusion characteristics such as size, depth, and stiffness on RCF life are studied. The results show that stiffness of an inclusion and its location has a significant effect on the RCF life: stiffer inclusions and inclusions located at the depth of maximum shear stress reversal are more detrimental to the RCF life. Stress concentrations are not significantly affected by inclusion size for the cases investigated; however, a stereology study showed that larger inclusions have a higher chance to be located at the critical depth and cause failure. Crack maps were recorded and compared to spall geometries observed experimentally. The results show that crack initiation locations and final spall shapes are similar to what has been observed in failed bearings.

Axisymmetric thermoviscoelastoplastic state of thin laminated shells made of a damageable material

NASA Astrophysics Data System (ADS)

Galishin, A. Z.

2008-04-01

A technique for the determination of the axisymmetric thermoviscoelastoplastic state of laminated thin shells made of a damageable material is developed. The technique is based on the kinematic equations of the theory of thin shells that account for transverse shear strains. The thermoviscoplastic equations, which describe the deformation of a shell element along paths of small curvature, are used as the constitutive equations. The equivalent stress that appears in the kinetic equations of damage and creep is determined from a failure criterion that accounts for the stress mode. The thermoviscoplastic deformation of a two-layer shell that models an element of a rocket engine nozzle is considered as an example

Effective equations for the quantum pendulum from momentous quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernandez, Hector H.; Chacon-Acosta, Guillermo; Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120

In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.

Finite element analysis of notch behavior using a state variable constitutive equation

NASA Technical Reports Server (NTRS)

Dame, L. T.; Stouffer, D. C.; Abuelfoutouh, N.

1985-01-01

The state variable constitutive equation of Bodner and Partom was used to calculate the load-strain response of Inconel 718 at 649 C in the root of a notch. The constitutive equation was used with the Bodner-Partom evolution equation and with a second evolution equation that was derived from a potential function of the stress and state variable. Data used in determining constants for the constitutive models was from one-dimensional smooth bar tests. The response was calculated for a plane stress condition at the root of the notch with a finite element code using constant strain triangular elements. Results from both evolution equations compared favorably with the observed experimental response. The accuracy and efficiency of the finite element calculations also compared favorably to existing methods.

Fast wavelet based algorithms for linear evolution equations

NASA Technical Reports Server (NTRS)

Engquist, Bjorn; Osher, Stanley; Zhong, Sifen

1992-01-01

A class was devised of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin which they applied to general Calderon-Zygmund type integral operators. A modification of their idea is applied to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions.

New nonlinear evolution equations from surface theory

NASA Astrophysics Data System (ADS)

Gürses, Metin; Nutku, Yavuz

1981-07-01

We point out that the connection between surfaces in three-dimensional flat space and the inverse scattering problem provides a systematic way for constructing new nonlinear evolution equations. In particular we study the imbedding for Guichard surfaces which gives rise to the Calapso-Guichard equations generalizing the sine-Gordon (SG) equation. Further, we investigate the geometry of surfaces and their imbedding which results in the Korteweg-deVries (KdV) equation. Then by constructing a family of applicable surfaces we obtain a generalization of the KdV equation to a compressible fluid.

A study of cumulative fatigue damage in AISI 4130 steel

NASA Technical Reports Server (NTRS)

Jeelani, S.; Musial, M.

1986-01-01

Experimental data were obtained using AISI 4130 steel under stress ratios of -1 and 0. A study of cumulative fatigue damage using Miner's and Kramer's equations for stress ratios of -1 and 0 for low-high, low-high-mixed, high-low, and high-low-mixed stress sequences has revealed that there is a close agreement between the theoretical and experimental values of fatigue damage and fatigue life. Kramer's equation predicts less conservative and more realistic cumulative fatigue damage than the popularly used Miner's rule does.

Study of travelling wave solutions for some special-type nonlinear evolution equations

NASA Astrophysics Data System (ADS)

Song, Junquan; Hu, Lan; Shen, Shoufeng; Ma, Wen-Xiu

2018-07-01

The tanh-function expansion method has been improved and used to construct travelling wave solutions of the form U={\\sum }j=0n{a}j{\\tanh }jξ for some special-type nonlinear evolution equations, which have a variety of physical applications. The positive integer n can be determined by balancing the highest order linear term with the nonlinear term in the evolution equations. We improve the tanh-function expansion method with n = 0 by introducing a new transform U=-W\\prime (ξ )/{W}2. A nonlinear wave equation with source terms, and mKdV-type equations, are considered in order to show the effectiveness of the improved scheme. We also propose the tanh-function expansion method of implicit function form, and apply it to a Harry Dym-type equation as an example.

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

Generalized fractional diffusion equations for subdiffusion in arbitrarily growing domains

NASA Astrophysics Data System (ADS)

Angstmann, C. N.; Henry, B. I.; McGann, A. V.

2017-10-01

The ubiquity of subdiffusive transport in physical and biological systems has led to intensive efforts to provide robust theoretical models for this phenomena. These models often involve fractional derivatives. The important physical extension of this work to processes occurring in growing materials has proven highly nontrivial. Here we derive evolution equations for modeling subdiffusive transport in a growing medium. The derivation is based on a continuous-time random walk. The concise formulation of these evolution equations requires the introduction of a new, comoving, fractional derivative. The implementation of the evolution equation is illustrated with a simple model of subdiffusing proteins in a growing membrane.

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

A Micro-Mechanism-Based Continuum Corrosion Fatigue Damage Model for Steels

NASA Astrophysics Data System (ADS)

Sun, Bin; Li, Zhaoxia

2018-05-01

A micro-mechanism-based corrosion fatigue damage model is developed for studying the high-cycle corrosion fatigue of steel from multi-scale viewpoint. The developed physical corrosion fatigue damage model establishes micro-macro relationships between macroscopic continuum damage evolution and collective evolution behavior of microscopic pits and cracks, which can be used to describe the multi-scale corrosion fatigue process of steel. As a case study, the model is used to predict continuum damage evolution and number density of the corrosion pit and short crack of steel component in 5% NaCl water under constant stress amplitude at 20 kHz, and the numerical results are compared with experimental results. It shows that the model is effective and can be used to evaluate the continuum macroscopic corrosion fatigue damage and study microscopic corrosion fatigue mechanisms of steel.

A Micro-Mechanism-Based Continuum Corrosion Fatigue Damage Model for Steels

NASA Astrophysics Data System (ADS)

Sun, Bin; Li, Zhaoxia

2018-04-01

A micro-mechanism-based corrosion fatigue damage model is developed for studying the high-cycle corrosion fatigue of steel from multi-scale viewpoint. The developed physical corrosion fatigue damage model establishes micro-macro relationships between macroscopic continuum damage evolution and collective evolution behavior of microscopic pits and cracks, which can be used to describe the multi-scale corrosion fatigue process of steel. As a case study, the model is used to predict continuum damage evolution and number density of the corrosion pit and short crack of steel component in 5% NaCl water under constant stress amplitude at 20 kHz, and the numerical results are compared with experimental results. It shows that the model is effective and can be used to evaluate the continuum macroscopic corrosion fatigue damage and study microscopic corrosion fatigue mechanisms of steel.

Integrable Seven-Point Discrete Equations and Second-Order Evolution Chains

NASA Astrophysics Data System (ADS)

Adler, V. E.

2018-04-01

We consider differential-difference equations defining continuous symmetries for discrete equations on a triangular lattice. We show that a certain combination of continuous flows can be represented as a secondorder scalar evolution chain. We illustrate the general construction with a set of examples including an analogue of the elliptic Yamilov chain.

A life prediction model for laminated composite structural components

NASA Technical Reports Server (NTRS)

Allen, David H.

1990-01-01

A life prediction methodology for laminated continuous fiber composites subjected to fatigue loading conditions was developed. A summary is presented of research completed. A phenomenological damage evolution law was formulated for matrix cracking which is independent of stacking sequence. Mechanistic and physical support was developed for the phenomenological evolution law proposed above. The damage evolution law proposed above was implemented to a finite element computer program. And preliminary predictions were obtained for a structural component undergoing fatigue loading induced damage.

The effects of self-interstitial clusters on cascade defect evolution beyond the primary damage state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heinisch, H.L.

1997-04-01

The intracascade evolution of the defect distributions of cascades in copper is investigated using stochastic annealing simulations applied to cascades generated with molecular dynamics (MD). The temperature and energy dependencies of annihilation, clustering and free defect production are determined for individual cascades. The annealing simulation results illustrate the strong influence on intracascade evolution of the defect configuration existing in the primary damage state. Another factor significantly affecting the evolution of the defect distribution is the rapid one-dimensional diffusion of small, glissile interstitial loops produced directly in cascades. This phenomenon introduces a cascade energy dependence of defect evolution that is apparentmore » only beyond the primary damage state, amplifying the need for further study of the annealing phase of cascade evolution and for performing many more MD cascade simulations at higher energies.« less

Creep rupture analysis of a beam resting on high temperature foundation

NASA Technical Reports Server (NTRS)

Gu, Randy J.; Cozzarelli, Francis A.

1988-01-01

A simplified uniaxial strain controlled creep damage law is deduced with the use of experimental observation from a more complex strain dependent law. This creep damage law correlates the creep damage, which is interpreted as the density variation in the material, directly with the accumulated creep strain. Based on the deduced uniaxial strain controlled creep damage law, a continuum mechanical creep rupture analysis is carried out for a beam resting on a high temperature elastic (Winkler) foundation. The analysis includes the determination of the nondimensional time for initial rupture, the propagation of the rupture front with the associated thinning of the beam, and the influence of creep damage on the deflection of the beam. Creep damage starts accumulating in the beam as soon as the load is applied, and a creep rupture front develops at and propagates from the point at which the creep damage first reaches its critical value. By introducing a series of fundamental assumptions within the framework of technical Euler-Bernoulli type beam theory, a governing set of integro-differential equations is derived in terms of the nondimensional bending moment and the deflection. These governing equations are subjected to a set of interface conditions at the propagating rupture front. A numerical technique is developed to solve the governing equations together with the interface equations, and the computed results are presented and discussed in detail.

Survey of four damage models for concrete.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leelavanichkul, Seubpong; Brannon, Rebecca Moss

2009-08-01

Four conventional damage plasticity models for concrete, the Karagozian and Case model (K&C), the Riedel-Hiermaier-Thoma model (RHT), the Brannon-Fossum model (BF1), and the Continuous Surface Cap Model (CSCM) are compared. The K&C and RHT models have been used in commercial finite element programs many years, whereas the BF1 and CSCM models are relatively new. All four models are essentially isotropic plasticity models for which 'plasticity' is regarded as any form of inelasticity. All of the models support nonlinear elasticity, but with different formulations. All four models employ three shear strength surfaces. The 'yield surface' bounds an evolving set of elasticallymore » obtainable stress states. The 'limit surface' bounds stress states that can be reached by any means (elastic or plastic). To model softening, it is recognized that some stress states might be reached once, but, because of irreversible damage, might not be achievable again. In other words, softening is the process of collapse of the limit surface, ultimately down to a final 'residual surface' for fully failed material. The four models being compared differ in their softening evolution equations, as well as in their equations used to degrade the elastic stiffness. For all four models, the strength surfaces are cast in stress space. For all four models, it is recognized that scale effects are important for softening, but the models differ significantly in their approaches. The K&C documentation, for example, mentions that a particular material parameter affecting the damage evolution rate must be set by the user according to the mesh size to preserve energy to failure. Similarly, the BF1 model presumes that all material parameters are set to values appropriate to the scale of the element, and automated assignment of scale-appropriate values is available only through an enhanced implementation of BF1 (called BFS) that regards scale effects to be coupled to statistical variability of material properties. The RHT model appears to similarly support optional uncertainty and automated settings for scale-dependent material parameters. The K&C, RHT, and CSCM models support rate dependence by allowing the strength to be a function of strain rate, whereas the BF1 model uses Duvaut-Lion viscoplasticity theory to give a smoother prediction of transient effects. During softening, all four models require a certain amount of strain to develop before allowing significant damage accumulation. For the K&C, RHT, and CSCM models, the strain-to-failure is tied to fracture energy release, whereas a similar effect is achieved indirectly in the BF1 model by a time-based criterion that is tied to crack propagation speed.« less

Taking side effects into account for HIV medication.

PubMed

Costanza, Vicente; Rivadeneira, Pablo S; Biafore, Federico L; D'Attellis, Carlos E

2010-09-01

A control-theoretic approach to the problem of designing "low-side-effects" therapies for HIV patients based on highly active drugs is substantiated here. The evolution of side effects during treatment is modeled by an extra differential equation coupled to the dynamics of virions, healthy T-cells, and infected ones. The new equation reflects the dependence of collateral damages on the amount of each dose administered to the patient and on the evolution of the viral load detected by periodical blood analysis. The cost objective accounts for recommended bounds on healthy cells and virions, and also penalizes the appearance of collateral morbidities caused by the medication. The optimization problem is solved by a hybrid dynamic programming scheme that adhere to discrete-time observation and control actions, but by maintaining the continuous-time setup for predicting states and side effects. The resulting optimal strategies employ less drugs than those prescribed by previous optimization studies, but maintaining high doses at the beginning and the end of each period of six months. If an inverse discount rate is applied to favor early actions, and under a mild penalization of the final viral load, then the optimal doses are found to be high at the beginning and decrease afterward, thus causing an apparent stabilization of the main variables. But in this case, the final viral load turns higher than acceptable.

Anisotropic Damage Mechanics Modeling in Metal Matrix Composites

DTIC Science & Technology

1993-05-15

conducted on a titanium aluminide SiC-reinforced metal matrix composite. Center-cracked plates with laminate layups of (0/90) and (±45). were tested... interfacial damage mechanisms as debonding or delamination. Equations (2.14) and (2.15) represent the damage transformation equations for the stress... titanium aluminide SiC 46 continuous reinforced metal matrix composite. As a means of enforcing quality assurance, all manufacturing and cutting of the

Artificial boundary conditions for certain evolution PDEs with cubic nonlinearity for non-compactly supported initial data

NASA Astrophysics Data System (ADS)

Vaibhav, V.

2011-04-01

The paper addresses the problem of constructing non-reflecting boundary conditions for two types of one dimensional evolution equations, namely, the cubic nonlinear Schrödinger (NLS) equation, ∂tu+Lu-iχ|u|2u=0 with L≡-i∂x2, and the equation obtained by letting L≡∂x3. The usual restriction of compact support of the initial data is relaxed by allowing it to have a constant amplitude along with a linear phase variation outside a compact domain. We adapt the pseudo-differential approach developed by Antoine et al. (2006) [5] for the NLS equation to the second type of evolution equation, and further, extend the scheme to the aforementioned class of initial data for both of the equations. In addition, we discuss efficient numerical implementation of our scheme and produce the results of several numerical experiments demonstrating its effectiveness.

A Coupled Thermal–Hydrological–Mechanical Damage Model and Its Numerical Simulations of Damage Evolution in APSE

PubMed Central

Wei, Chenhui; Zhu, Wancheng; Chen, Shikuo; Ranjith, Pathegama Gamage

2016-01-01

This paper proposes a coupled thermal–hydrological–mechanical damage (THMD) model for the failure process of rock, in which coupling effects such as thermally induced rock deformation, water flow-induced thermal convection, and rock deformation-induced water flow are considered. The damage is considered to be the key factor that controls the THM coupling process and the heterogeneity of rock is characterized by the Weibull distribution. Next, numerical simulations on excavation-induced damage zones in Äspö pillar stability experiments (APSE) are carried out and the impact of in situ stress conditions on damage zone distribution is analysed. Then, further numerical simulations of damage evolution at the heating stage in APSE are carried out. The impacts of in situ stress state, swelling pressure and water pressure on damage evolution at the heating stage are simulated and analysed, respectively. The simulation results indicate that (1) the v-shaped notch at the sidewall of the pillar is predominantly controlled by the in situ stress trends and magnitude; (2) at the heating stage, the existence of confining pressure can suppress the occurrence of damage, including shear damage and tensile damage; and (3) the presence of water flow and water pressure can promote the occurrence of damage, especially shear damage. PMID:28774001

Collins-Soper equation for the energy evolution of transverse-momentum and spin dependent parton distributions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Idilbi, Ahmad; Ji Xiangdong; Yuan Feng

The hadron-energy evolution (Collins and Soper) equation for all the leading-twist transverse-momentum and spin dependent parton distributions is derived in the impact parameter space. Based on this equation, we present a resummation formulas for the spin dependent structure functions of the semi-inclusive deep-inelastic scattering.

A study of cumulative fatigue damage in titanium 6Al-4V alloy

NASA Technical Reports Server (NTRS)

Jeelani, S.; Ghebremedhin, S.; Musial, M.

1986-01-01

Experimental data were obtained using titanium 6Al-4V alloy under stress ratios of -1, 0, and negative infinity. A study of cumulative fatigue damage using Miner's (1945) and Kramer's (1974) equations for stress ratios of -1 and 0 for low-high, low-high mixed, high-low, and high-low mixed stress sequences has revealed close agreement between the theoretical and experimental values of fatigue damage and fatigue life. Kramer's equation predicts less conservative and more realistic cumulative fatigue damage than does the popularly used Miner's rule.

NLO evolution of 3-quark Wilson loop operator

DOE PAGES

Balitsky, I.; Grabovsky, A. V.

2015-01-07

It is well known that high-energy scattering of a meson from some hadronic target can be described by the interaction of that target with a color dipole formed by two Wilson lines corresponding to fast quark-antiquark pair. Moreover, the energy dependence of the scattering amplitude is governed by the evolution equation of this color dipole with respect to rapidity. Similarly, the energy dependence of scattering of a baryon can be described in terms of evolution of a three-Wilson-lines operator with respect to the rapidity of the Wilson lines. We calculate the evolution of the 3-quark Wilson loop operator in themore » next-to-leading order (NLO) and present a quasi-conformal evolution equation for a composite 3-Wilson-lines operator. Thus we also obtain the linearized version of that evolution equation describing the amplitude of the odderon exchange at high energies.« less

On the Solutions of a 2+1-Dimensional Model for Epitaxial Growth with Axial Symmetry

NASA Astrophysics Data System (ADS)

Lu, Xin Yang

2018-04-01

In this paper, we study the evolution equation derived by Xu and Xiang (SIAM J Appl Math 69(5):1393-1414, 2009) to describe heteroepitaxial growth in 2+1 dimensions with elastic forces on vicinal surfaces is in the radial case and uniform mobility. This equation is strongly nonlinear and contains two elliptic integrals and defined via Cauchy principal value. We will first derive a formally equivalent parabolic evolution equation (i.e., full equivalence when sufficient regularity is assumed), and the main aim is to prove existence, uniqueness and regularity of strong solutions. We will extensively use techniques from the theory of evolution equations governed by maximal monotone operators in Banach spaces.

Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport.

PubMed

Eu, Byung Chan

2008-09-07

In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.

Quantitative conditions for time evolution in terms of the von Neumann equation

NASA Astrophysics Data System (ADS)

Wang, WenHua; Cao, HuaiXin; Chen, ZhengLi; Wang, Lie

2018-07-01

The adiabatic theorem describes the time evolution of the pure state and gives an adiabatic approximate solution to the Schödinger equation by choosing a single eigenstate of the Hamiltonian as the initial state. In quantum systems, states are divided into pure states (unite vectors) and mixed states (density matrices, i.e., positive operators with trace one). Accordingly, mixed states have their own corresponding time evolution, which is described by the von Neumann equation. In this paper, we discuss the quantitative conditions for the time evolution of mixed states in terms of the von Neumann equation. First, we introduce the definitions for uniformly slowly evolving and δ-uniformly slowly evolving with respect to mixed states, then we present a necessary and sufficient condition for the Hamiltonian of the system to be uniformly slowly evolving and we obtain some upper bounds for the adiabatic approximate error. Lastly, we illustrate our results in an example.

Helicity Evolution at Small x

NASA Astrophysics Data System (ADS)

Sievert, Michael; Kovchegov, Yuri; Pitonyak, Daniel

2017-01-01

We construct small- x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the g1 structure function. These evolution equations resum powers of ln2(1 / x) in the polarization-dependent evolution along with the powers of ln(1 / x) in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-Nc and large-Nc &Nf limits. After solving the large-Nc equations numerically we obtain the following small- x asymptotics for the flavor-singlet g1 structure function along with quarks hPDFs and helicity TMDs (in absence of saturation effects): g1S(x ,Q2) ΔqS(x ,Q2) g1L S(x ,kT2) (1/x) > αh (1/x) 2.31√{αsNc/2 π. We also give an estimate of how much of the proton's spin may be at small x and what impact this has on the so-called ``spin crisis.'' Work supported by the U.S. DOE, Office of Science, Office of Nuclear Physics under Award Number DE-SC0004286 (YK), the RIKEN BNL Research Center, and TMD Collaboration (DP), and DOE Contract No. DE-SC0012704 (MS).

Single-Input and Multiple-Output Surface Acoustic Wave Sensing for Damage Quantification in Piezoelectric Sensors.

PubMed

Pamwani, Lavish; Habib, Anowarul; Melandsø, Frank; Ahluwalia, Balpreet Singh; Shelke, Amit

2018-06-22

The main aim of the paper is damage detection at the microscale in the anisotropic piezoelectric sensors using surface acoustic waves (SAWs). A novel technique based on the single input and multiple output of Rayleigh waves is proposed to detect the microscale cracks/flaws in the sensor. A convex-shaped interdigital transducer is fabricated for excitation of divergent SAWs in the sensor. An angularly shaped interdigital transducer (IDT) is fabricated at 0 degrees and ±20 degrees for sensing the convex shape evolution of SAWs. A precalibrated damage was introduced in the piezoelectric sensor material using a micro-indenter in the direction perpendicular to the pointing direction of the SAW. Damage detection algorithms based on empirical mode decomposition (EMD) and principal component analysis (PCA) are implemented to quantify the evolution of damage in piezoelectric sensor material. The evolution of the damage was quantified using a proposed condition indicator (CI) based on normalized Euclidean norm of the change in principal angles, corresponding to pristine and damaged states. The CI indicator provides a robust and accurate metric for detection and quantification of damage.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations.

PubMed

Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio

2014-10-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations

PubMed Central

Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio

2014-01-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530

Synergistic Effects of Frequency and Temperature on Damage Evolution and Life Prediction of Cross-Ply Ceramic Matrix Composites under Tension-Tension Fatigue Loading

NASA Astrophysics Data System (ADS)

Longbiao, Li

2017-10-01

In this paper, the synergistic effects of loading frequency and testing temperature on the fatigue damage evolution and life prediction of cross-ply SiC/MAS ceramic-matrix composite have been investigated. The damage parameters of the fatigue hysteresis modulus, fatigue hysteresis dissipated energy and the interface shear stress were used to monitor the damage evolution inside of SiC/MAS composite. The evolution of fatigue hysteresis dissipated energy, the interface shear stress and broken fibers fraction versus cycle number, and the fatigue life S-N curves of SiC/MAS composite under the loading frequency of 1 and 10 Hz at 566 °C and 1093 °C in air condition have been predicted. The synergistic effects of the loading frequency and testing temperature on the degradation rate of fatigue hysteresis dissipated energy and the interface shear stress have been analyzed.

Damage Evolution in Complex-Phase and Dual-Phase Steels during Edge Stretching.

PubMed

Pathak, Nikky; Butcher, Cliff; Worswick, Michael James; Bellhouse, Erika; Gao, Jeff

2017-03-27

The role of microstructural damage in controlling the edge stretchability of Complex-Phase (CP) and Dual-Phase (DP) steels was evaluated using hole tension experiments. The experiments considered a tensile specimen with a hole at the center of specimen that is either sheared (sheared edge condition) or drilled and then reamed (reamed edge condition). The damage mechanism and accumulation in the CP and DP steels were systematically characterized by interrupting the hole tension tests at different strain levels using scanning electron microscope (SEM) analysis and optical microscopy. Martensite cracking and decohesion of ferrite-martensite interfaces are the dominant nucleation mechanisms in the DP780. The primary source of void nucleation in the CP800 is nucleation at TiN particles, with secondary void formation at martensite/bainite interfaces near the failure strain. The rate of damage evolution is considerably higher for the sheared edge in contrast with the reamed edge since the shearing process alters the microstructure in the shear affected zone (SAZ) by introducing work-hardening and initial damage behind the sheared edge. The CP microstructures were shown to be less prone to shear-induced damage than the DP materials resulting in much higher sheared edge formability. Microstructural damage in the CP and DP steels was characterized to understand the interaction between microstructure, damage evolution and edge formability during edge stretching. An analytical model for void evolution and coalescence was developed and applied to predict the damage rate in these rather diverse microstructures.

Damage Evolution in Complex-Phase and Dual-Phase Steels during Edge Stretching

PubMed Central

Pathak, Nikky; Butcher, Cliff; Worswick, Michael James; Bellhouse, Erika; Gao, Jeff

2017-01-01

The role of microstructural damage in controlling the edge stretchability of Complex-Phase (CP) and Dual-Phase (DP) steels was evaluated using hole tension experiments. The experiments considered a tensile specimen with a hole at the center of specimen that is either sheared (sheared edge condition) or drilled and then reamed (reamed edge condition). The damage mechanism and accumulation in the CP and DP steels were systematically characterized by interrupting the hole tension tests at different strain levels using scanning electron microscope (SEM) analysis and optical microscopy. Martensite cracking and decohesion of ferrite-martensite interfaces are the dominant nucleation mechanisms in the DP780. The primary source of void nucleation in the CP800 is nucleation at TiN particles, with secondary void formation at martensite/bainite interfaces near the failure strain. The rate of damage evolution is considerably higher for the sheared edge in contrast with the reamed edge since the shearing process alters the microstructure in the shear affected zone (SAZ) by introducing work-hardening and initial damage behind the sheared edge. The CP microstructures were shown to be less prone to shear-induced damage than the DP materials resulting in much higher sheared edge formability. Microstructural damage in the CP and DP steels was characterized to understand the interaction between microstructure, damage evolution and edge formability during edge stretching. An analytical model for void evolution and coalescence was developed and applied to predict the damage rate in these rather diverse microstructures. PMID:28772707

New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

PubMed

Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

2014-01-01

In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

NASA Astrophysics Data System (ADS)

Hosseini, K.; Ayati, Z.; Ansari, R.

2018-04-01

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

Topics Associated with Nonlinear Evolution Equations and Inverse Scattering in Multidimensions,

DTIC Science & Technology

1987-03-01

significant that these concepts can be generalized to 2 spatial plus one time dimension. Here the prototype equation is the Kadomtsev - Petviashvili (K-P...O-193 32 ? T TOPICS ASSOCIATED WITH NONLINEAR E VOLUTION EQUATIONS / AND INVERSE SCATTER! .(U) CLARKSON UNIV POTSDAM NY INST...8217 - Evolution Equations and L Inverse Scattering in Multi- dimensions by _i A ,’I Mark J. Ablowi ClrsnUiest PosaNwYr/37 LaRMFOMON* .F-5 Anwo~~~d kr /ua

Basic results on the equations of magnetohydrodynamics of partially ionized inviscid plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nunez, Manuel

2009-10-15

The equations of evolution of partially ionized plasmas have been far more studied in one of their many simplifications than in its original form. They present a relation between the velocity of each species, plus the magnetic and electric fields, which yield as an analog of Ohm's law a certain elliptic equation. Therefore, the equations represent a functional evolution system, not a classical one. Nonetheless, a priori estimates and theorems of existence may be obtained in appropriate Sobolev spaces.

Modeling damage evolution in a hybrid ceramic matrix composite under static tensile load

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonora, N.; Newaz, G.

In this investigation, damage evolution in a unidirectional hybrid ceramic composite made from Nicalon and SiC fibers in a Lithium Aluminosilicate (LAS) glass matrix was studied. The static stress-strain response of the composite exhibited a linear response followed by load drop in a progressive manner. Careful experiments were conducted stopping the tests at various strain levels and using replication technique, scanning and optical microscopy to monitor the evolution of damage in these composites. It was observed that the constituents of the composite failed in a sequential manner at increasing strain levels. The matrix cracks were followed by SiC fiber failuresmore » near ultimate tensile stress. After that, the load drop was associated with progressive failure of the Nicalon fibers. Identification of these failure modes were critical to the development of a concentric cylinder model representing all three constituent phases to predict the constitutive response of the CMC computationally. The strain-to-failure of the matrix and fibers were used to progressively fail the constituents in the model and the overall experimental constitutive response of the CMC was recovered. A strain based analytical representation was developed relating stiffness loss to applied strain. Based on this formulation, damage evolution and its consequence on tensile stress-strain response was predicted for room temperature behavior of hybrid CMCs. The contribution of the current work is that the proposed strain-damage phenomenological model can capture the damage evolution and the corresponding material response for continuous fiber-reinforced CMCs. The modeling approach shows much promise for the complex damage processes observed in hybrid CMCs.« less

NLO evolution of color dipole

DOE PAGES

Balitsky, Ian; Chirilli, Giovanni A.

2008-09-01

The small-x deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles. In the next-to-leading order the BK equation gets contributions from quark and gluon loops as well as from the tree gluon diagrams with quadratic and cubic nonlinearities.

The Measurement and Cost of Removing Unexplained Gender Differences in Faculty Salaries.

ERIC Educational Resources Information Center

Becker, William E.; Toutkoushian, Robert K.

1995-01-01

In assessing sex-discrimination suit damages, debate rages over the type and number of variables included in a single-equation model of the salary-determination process. This article considers single- and multiple-equation models, providing 36 different damage calculations. For University of Minnesota data, equalization cost hinges on the…

Equation-free multiscale computation: algorithms and applications.

PubMed

Kevrekidis, Ioannis G; Samaey, Giovanni

2009-01-01

In traditional physicochemical modeling, one derives evolution equations at the (macroscopic, coarse) scale of interest; these are used to perform a variety of tasks (simulation, bifurcation analysis, optimization) using an arsenal of analytical and numerical techniques. For many complex systems, however, although one observes evolution at a macroscopic scale of interest, accurate models are only given at a more detailed (fine-scale, microscopic) level of description (e.g., lattice Boltzmann, kinetic Monte Carlo, molecular dynamics). Here, we review a framework for computer-aided multiscale analysis, which enables macroscopic computational tasks (over extended spatiotemporal scales) using only appropriately initialized microscopic simulation on short time and length scales. The methodology bypasses the derivation of macroscopic evolution equations when these equations conceptually exist but are not available in closed form-hence the term equation-free. We selectively discuss basic algorithms and underlying principles and illustrate the approach through representative applications. We also discuss potential difficulties and outline areas for future research.

Spectral evolution of weakly nonlinear random waves: kinetic description vs direct numerical simulations

NASA Astrophysics Data System (ADS)

Annenkov, Sergei; Shrira, Victor

2016-04-01

We study numerically the long-term evolution of water wave spectra without wind forcing, using three different models, aiming at understanding the role of different sets of assumptions. The first model is the classical Hasselmann kinetic equation (KE). We employ the WRT code kindly provided by G. van Vledder. Two other models are new. As the second model, we use the generalised kinetic equation (gKE), derived without the assumption of quasi-stationarity. Thus, unlike the KE, the gKE is valid in the cases when a wave spectrum is changing rapidly (e.g. at the initial stage of evolution of a narrow spectrum). However, the gKE employs the same statistical closure as the KE. The third model is based on the Zakharov integrodifferential equation for water waves and does not depend on any statistical assumptions. Since the Zakharov equation plays the role of the primitive equation of the theory of wave turbulence, we refer to this model as direct numerical simulation of spectral evolution (DNS-ZE). For initial conditions, we choose two narrow-banded spectra with the same frequency distribution (a JONSWAP spectrum with high peakedness γ = 6) and different degrees of directionality. These spectra are from the set of observations collected in a directional wave tank by Onorato et al (2009). Spectrum A is very narrow in angle (corresponding to N = 840 in the cosN directional model). Spectrum B is initially wider in angle (corresponds to N = 24). Short-term evolution of both spectra (O(102) wave periods) has been studied numerically by Xiao et al (2013) using two other approaches (broad-band modified nonlinear Schrödinger equation and direct numerical simulation based on the high-order spectral method). We use these results to verify the initial stage of our DNS-ZE simulations. However, the advantage of the DNS-ZE method is that it allows to study long-term spectral evolution (up to O(104) periods), which was previously possible only with the KE. In the short-term evolution, we find a good agreement between our DNS-ZE results and simulations by Xiao et al (2013), both for the evolution of frequency spectra and for the directional spreading. In the long term, all three approaches demonstrate very close evolution of integral characteristics of spectra, approaching for large time the theoretical asymptotes of the self-similar stage of evolution. However, the detailed comparison of the spectral evolution shows certain notable differences. Both kinetic equations give virtually identical evolution of spectrum B, but in the case of initially nearly one-dimensional spectrum A the KE overestimates the amplitude of the spectral peak. Meanwhile, the DNS-ZE results show considerably wider spectra with less pronounced peak. There is a striking difference for the rate of spectral broadening, which is much larger for the gKE and especially for the KE, than for the DNS-ZE. We show that the rates of change of the spectra obtained with the DNS-ZE are proportional to the fourth power of nonlinearity, corresponding to the dynamical timescale of evolution, rather than the statistical timescale of both kinetic equations.

Monitoring and Failure Analysis of Corroded Bridge Cables under Fatigue Loading Using Acoustic Emission Sensors

PubMed Central

Li, Dongsheng; Ou, Jinping; Lan, Chengming; Li, Hui

2012-01-01

Cables play an important role in cable-stayed systems, but are vulnerable to corrosion and fatigue damage. There is a dearth of studies on the fatigue damage evolution of corroded cable. In the present study, the acoustic emission (AE) technology is adopted to monitor the fatigue damage evolution process. First, the relationship between stress and strain is determined through a tensile test for corroded and non-corroded steel wires. Results show that the mechanical performance of corroded cables is changed considerably. The AE characteristic parameters for fatigue damage are then established. AE energy cumulative parameters can accurately describe the fatigue damage evolution of corroded cables. The failure modes in each phase as well as the type of acoustic emission source are determined based on the results of scanning electron microscopy. The waveform characteristics, damage types, and frequency distribution of the corroded cable at different damage phases are collected. Finally, the number of broken wires and breakage time of the cables are determined according to the variation in the margin index. PMID:22666009

Estimating bird damage from damage incidence in wine grape vineyards

USGS Publications Warehouse

DeHaven, R.W.; Hothem, R.L.

1981-01-01

Bird damage was measured during 1977 and 1978 at 32 wine grape vineyards in the San Joaquin Valley and North Coastal Region of California. Both the percentage bird loss (PBL) and the percentage of bunches damaged (BDI = bird damage incidence) were determined during 55 total-damage assessments, and the resulting data pairs were used to develop a regression of PBL on BDI. The final prediction equation was loge (PBL + 1) = 0.0385 BDI, for which the SE = 9.6297 10-4, and it accounted for 97% of the observed variation. We conclude that by using that equation, reasonably accurate predictions of PBL can be obtained from relatively quick and inexpensive estimates of BDI. Guidelines for the use of the prediction method and the accuracy of some PBL predictions are discussed.

Three-pattern decomposition of global atmospheric circulation: part II—dynamical equations of horizontal, meridional and zonal circulations

NASA Astrophysics Data System (ADS)

Hu, Shujuan; Cheng, Jianbo; Xu, Ming; Chou, Jifan

2018-04-01

The three-pattern decomposition of global atmospheric circulation (TPDGAC) partitions three-dimensional (3D) atmospheric circulation into horizontal, meridional and zonal components to study the 3D structures of global atmospheric circulation. This paper incorporates the three-pattern decomposition model (TPDM) into primitive equations of atmospheric dynamics and establishes a new set of dynamical equations of the horizontal, meridional and zonal circulations in which the operator properties are studied and energy conservation laws are preserved, as in the primitive equations. The physical significance of the newly established equations is demonstrated. Our findings reveal that the new equations are essentially the 3D vorticity equations of atmosphere and that the time evolution rules of the horizontal, meridional and zonal circulations can be described from the perspective of 3D vorticity evolution. The new set of dynamical equations includes decomposed expressions that can be used to explore the source terms of large-scale atmospheric circulation variations. A simplified model is presented to demonstrate the potential applications of the new equations for studying the dynamics of the Rossby, Hadley and Walker circulations. The model shows that the horizontal air temperature anomaly gradient (ATAG) induces changes in meridional and zonal circulations and promotes the baroclinic evolution of the horizontal circulation. The simplified model also indicates that the absolute vorticity of the horizontal circulation is not conserved, and its changes can be described by changes in the vertical vorticities of the meridional and zonal circulations. Moreover, the thermodynamic equation shows that the induced meridional and zonal circulations and advection transport by the horizontal circulation in turn cause a redistribution of the air temperature. The simplified model reveals the fundamental rules between the evolution of the air temperature and the horizontal, meridional and zonal components of global atmospheric circulation.

Traveling wave solutions and conservation laws for nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-02-01

In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions for the governing equation. We show that the equation is nonlinear self-adjoint by obtaining suitable substitution. Therefore, we construct conservation laws for the equation using new conservation theorem. The obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium. The constraint condition for the existence of solitons is stated. Some three dimensional figures for some of the acquired results are illustrated.

Small-x asymptotics of the quark helicity distribution: Analytic results

DOE PAGES

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

2017-06-15

In this Letter, we analytically solve the evolution equations for the small-x asymptotic behavior of the (flavor singlet) quark helicity distribution in the large- N c limit. Here, these evolution equations form a set of coupled integro-differential equations, which previously could only be solved numerically. This approximate numerical solution, however, revealed simplifying properties of the small-x asymptotics, which we exploit here to obtain an analytic solution.

Predicting knee replacement damage in a simulator machine using a computational model with a consistent wear factor.

PubMed

Zhao, Dong; Sakoda, Hideyuki; Sawyer, W Gregory; Banks, Scott A; Fregly, Benjamin J

2008-02-01

Wear of ultrahigh molecular weight polyethylene remains a primary factor limiting the longevity of total knee replacements (TKRs). However, wear testing on a simulator machine is time consuming and expensive, making it impractical for iterative design purposes. The objectives of this paper were first, to evaluate whether a computational model using a wear factor consistent with the TKR material pair can predict accurate TKR damage measured in a simulator machine, and second, to investigate how choice of surface evolution method (fixed or variable step) and material model (linear or nonlinear) affect the prediction. An iterative computational damage model was constructed for a commercial knee implant in an AMTI simulator machine. The damage model combined a dynamic contact model with a surface evolution model to predict how wear plus creep progressively alter tibial insert geometry over multiple simulations. The computational framework was validated by predicting wear in a cylinder-on-plate system for which an analytical solution was derived. The implant damage model was evaluated for 5 million cycles of simulated gait using damage measurements made on the same implant in an AMTI machine. Using a pin-on-plate wear factor for the same material pair as the implant, the model predicted tibial insert wear volume to within 2% error and damage depths and areas to within 18% and 10% error, respectively. Choice of material model had little influence, while inclusion of surface evolution affected damage depth and area but not wear volume predictions. Surface evolution method was important only during the initial cycles, where variable step was needed to capture rapid geometry changes due to the creep. Overall, our results indicate that accurate TKR damage predictions can be made with a computational model using a constant wear factor obtained from pin-on-plate tests for the same material pair, and furthermore, that surface evolution method matters only during the initial "break in" period of the simulation.

Strong oviposition preference for Bt over non-Bt maize in Spodoptera frugiperda and its implications for the evolution of resistance.

PubMed

Téllez-Rodríguez, Pilar; Raymond, Ben; Morán-Bertot, Ivis; Rodríguez-Cabrera, Lianet; Wright, Denis J; Borroto, Carlos G; Ayra-Pardo, Camilo

2014-06-16

Transgenic crops expressing Bt toxins have substantial benefits for growers in terms of reduced synthetic insecticide inputs, area-wide pest management and yield. This valuable technology depends upon delaying the evolution of resistance. The 'high dose/refuge strategy', in which a refuge of non-Bt plants is planted in close proximity to the Bt crop, is the foundation of most existing resistance management. Most theoretical analyses of the high dose/refuge strategy assume random oviposition across refugia and Bt crops. In this study we examined oviposition and survival of Spodoptera frugiperda across conventional and Bt maize and explored the impact of oviposition behavior on the evolution of resistance in simulation models. Over six growing seasons oviposition rates per plant were higher in Bt crops than in refugia. The Cry1F Bt maize variety retained largely undamaged leaves, and oviposition preference was correlated with the level of feeding damage in the refuge. In simulation models, damage-avoiding oviposition accelerated the evolution of resistance and either led to requirements for larger refugia or undermined resistance management altogether. Since larval densities affected oviposition preferences, pest population dynamics affected resistance evolution: larger refugia were weakly beneficial for resistance management if they increased pest population sizes and the concomitant degree of leaf damage. Damaged host plants have reduced attractiveness to many insect pests, and crops expressing Bt toxins are generally less damaged than conventional counterparts. Resistance management strategies should take account of this behavior, as it has the potential to undermine the effectiveness of existing practice, especially in the tropics where many pests are polyvoltinous. Efforts to bring down total pest population sizes and/or increase the attractiveness of damaged conventional plants will have substantial benefits for slowing the evolution of resistance.

A finite deformation viscoelastic-viscoplastic constitutive model for self-healing materials

NASA Astrophysics Data System (ADS)

Shahsavari, H.; Naghdabadi, R.; Baghani, M.; Sohrabpour, S.

2016-12-01

In this paper, employing the Hencky strain, viscoelastic-viscoplastic response of self-healing materials is investigated. Considering the irreversible thermodynamics and using the effective configuration in the Continuum Damage-Healing Mechanics (CDHM), a phenomenological finite strain viscoelastic-viscoplastic constitutive model is presented. Considering finite viscoelastic and viscoplastic deformations, total deformation gradient is multiplicatively decomposed into viscoelastic and viscoplastic parts. Due to mathematical advantages and physical meaning of Hencky strain, this measure of strain is employed in the constitutive model development. In this regard, defining the damage and healing variables and employing the strain equivalence hypothesis, the strain tensor is determined in the effective configuration. Satisfying the Clausius-Duhem inequality, the evolution equations are introduced for the viscoelastic and viscoplastic strains. The damage and healing variables also evolve according to two different prescribed functions. To employ the proposed model in different loading conditions, the model is discretized in the semi-implicit form. Material parameters of the model are identified employing experimental tests on asphalt mixes available in the literature. Finally, capability of the model is demonstrated comparing the model predictions in the creep-recovery and repeated creep-recovery with the experimental results available in the literature and a good agreement between predicted and test results is revealed.

Resumming double logarithms in the QCD evolution of color dipoles

DOE PAGES

Iancu, E.; Madrigal, J. D.; Mueller, A. H.; ...

2015-05-01

The higher-order perturbative corrections, beyond leading logarithmic accuracy, to the BFKL evolution in QCD at high energy are well known to suffer from a severe lack-of-convergence problem, due to radiative corrections enhanced by double collinear logarithms. Via an explicit calculation of Feynman graphs in light cone (time-ordered) perturbation theory, we show that the corrections enhanced by double logarithms (either energy-collinear, or double collinear) are associated with soft gluon emissions which are strictly ordered in lifetime. These corrections can be resummed to all orders by solving an evolution equation which is non-local in rapidity. This equation can be equivalently rewritten inmore » local form, but with modified kernel and initial conditions, which resum double collinear logs to all orders. We extend this resummation to the next-to-leading order BFKL and BK equations. The first numerical studies of the collinearly-improved BK equation demonstrate the essential role of the resummation in both stabilizing and slowing down the evolution.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bisio, Alessandro; D’Ariano, Giacomo Mauro; Tosini, Alessandro, E-mail: alessandro.tosini@unipv.it

We present a quantum cellular automaton model in one space-dimension which has the Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a lattice of quantum systems, is derived from the assumptions of homogeneity, parity and time-reversal invariance. The comparison between the automaton and the Dirac evolutions is rigorously set as a discrimination problem between unitary channels. We derive an exact lower bound for the probability of error in the discrimination as an explicit function of the mass, the number and the momentum of the particles, and the duration of the evolution. Computing this bound withmore » experimentally achievable values, we see that in that regime the QCA model cannot be discriminated from the usual Dirac evolution. Finally, we show that the evolution of one-particle states with narrow-band in momentum can be efficiently simulated by a dispersive differential equation for any regime. This analysis allows for a comparison with the dynamics of wave-packets as it is described by the usual Dirac equation. This paper is a first step in exploring the idea that quantum field theory could be grounded on a more fundamental quantum cellular automaton model and that physical dynamics could emerge from quantum information processing. In this framework, the discretization is a central ingredient and not only a tool for performing non-perturbative calculation as in lattice gauge theory. The automaton model, endowed with a precise notion of local observables and a full probabilistic interpretation, could lead to a coherent unification of a hypothetical discrete Planck scale with the usual Fermi scale of high-energy physics. - Highlights: • The free Dirac field in one space dimension as a quantum cellular automaton. • Large scale limit of the automaton and the emergence of the Dirac equation. • Dispersive differential equation for the evolution of smooth states on the automaton. • Optimal discrimination between the automaton evolution and the Dirac equation.« less

Stochastic damage evolution in textile laminates

NASA Technical Reports Server (NTRS)

Dzenis, Yuris A.; Bogdanovich, Alexander E.; Pastore, Christopher M.

1993-01-01

A probabilistic model utilizing random material characteristics to predict damage evolution in textile laminates is presented. Model is based on a division of each ply into two sublaminas consisting of cells. The probability of cell failure is calculated using stochastic function theory and maximal strain failure criterion. Three modes of failure, i.e. fiber breakage, matrix failure in transverse direction, as well as matrix or interface shear cracking, are taken into account. Computed failure probabilities are utilized in reducing cell stiffness based on the mesovolume concept. A numerical algorithm is developed predicting the damage evolution and deformation history of textile laminates. Effect of scatter of fiber orientation on cell properties is discussed. Weave influence on damage accumulation is illustrated with the help of an example of a Kevlar/epoxy laminate.

A two-scale model for dynamic damage evolution

NASA Astrophysics Data System (ADS)

Keita, Oumar; Dascalu, Cristian; François, Bertrand

2014-03-01

This paper presents a new micro-mechanical damage model accounting for inertial effect. The two-scale damage model is fully deduced from small-scale descriptions of dynamic micro-crack propagation under tensile loading (mode I). An appropriate micro-mechanical energy analysis is combined with homogenization based on asymptotic developments in order to obtain the macroscopic evolution law for damage. Numerical simulations are presented in order to illustrate the ability of the model to describe known behaviors like size effects for the structural response, strain-rate sensitivity, brittle-ductile transition and wave dispersion.

Evolution of statistical averages: An interdisciplinary proposal using the Chapman-Enskog method

NASA Astrophysics Data System (ADS)

Mariscal-Sanchez, A.; Sandoval-Villalbazo, A.

2017-08-01

This work examines the idea of applying the Chapman-Enskog (CE) method for approximating the solution of the Boltzmann equation beyond the realm of physics, using an information theory approach. Equations describing the evolution of averages and their fluctuations in a generalized phase space are established up to first-order in the Knudsen parameter which is defined as the ratio of the time between interactions (mean free time) and a characteristic macroscopic time. Although the general equations here obtained may be applied in a wide range of disciplines, in this paper, only a particular case related to the evolution of averages in speculative markets is examined.

Continuum Fatigue Damage Modeling for Use in Life Extending Control

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.

1994-01-01

This paper develops a simplified continuum (continuous wrp to time, stress, etc.) fatigue damage model for use in Life Extending Controls (LEC) studies. The work is based on zero mean stress local strain cyclic damage modeling. New nonlinear explicit equation forms of cyclic damage in terms of stress amplitude are derived to facilitate the continuum modeling. Stress based continuum models are derived. Extension to plastic strain-strain rate models are also presented. Application of these models to LEC applications is considered. Progress toward a nonzero mean stress based continuum model is presented. Also, new nonlinear explicit equation forms in terms of stress amplitude are also derived for this case.

Dynamical systems theory for nonlinear evolution equations.

PubMed

Choudhuri, Amitava; Talukdar, B; Das, Umapada

2010-09-01

We observe that the fully nonlinear evolution equations of Rosenau and Hymann, often abbreviated as K(n,m) equations, can be reduced to Hamiltonian form only on a zero-energy hypersurface belonging to some potential function associated with the equations. We treat the resulting Hamiltonian equations by the dynamical systems theory and present a phase-space analysis of their stable points. The results of our study demonstrate that the equations can, in general, support both compacton and soliton solutions. For the K(2,2) and K(3,3) cases one type of solutions can be obtained from the other by continuously varying a parameter of the equations. This is not true for the K(3,2) equation for which the parameter can take only negative values. The K(2,3) equation does not have any stable point and, in the language of mechanics, represents a particle moving with constant acceleration.

The effects of shockwave profile shape and shock obliquity on spallation in Cu and Ta: kinetic and stress-state effects on damage evolution(u)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gray, George T

2010-12-14

Widespread research over the past five decades has provided a wealth of experimental data and insight concerning shock hardening and the spallation response of materials subjected to square-topped shock-wave loading profiles. Less quantitative data have been gathered on the effect of direct, in-contact, high explosive (HE)-driven Taylor wave (or triangular-wave) loading profile shock loading on the shock hardening, damage evolution, or spallation response of materials. Explosive loading induces an impulse dubbed a 'Taylor Wave'. This is a significantly different loading history than that achieved by a square-topped impulse in terms of both the pulse duration at a fixed peak pressure,more » and a different unloading strain rate from the peak Hugoniot state achieved. The goal of this research is to quantify the influence of shockwave obliquity on the spallation response of copper and tantalum by subjecting plates of each material to HE-driven sweeping detonation-wave loading and quantify both the wave propagation and the post-mortem damage evolution. This talk will summarize our current understanding of damage evolution during sweeping detonation-wave spallation loading in Cu and Ta and show comparisons to modeling simulations. The spallation responses of Cu and Ta are both shown to be critically dependent on the shockwave profile and the stress-state of the shock. Based on variations in the specifics of the shock drive (pulse shape, peak stress, shock obliquity) and sample geometry in Cu and Ta, 'spall strength' varies by over a factor of two and the details of the mechanisms of the damage evolution is seen to vary. Simplistic models of spallation, such as P{sub min} based on 1-D square-top shock data lack the physics to capture the influence of kinetics on damage evolution such as that operative during sweeping detonation loading. Such considerations are important for the development of predictive models of damage evolution and spallation in metals and alloys.« less

Whitham modulation theory for (2  +  1)-dimensional equations of Kadomtsev–Petviashvili type

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor

2018-05-01

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev–Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin–Ono (2DBO) equation and a modified KP (m2KP) equation. A unified derivation is also provided. In the case of the m2KP equation, the corresponding Whitham modulation system exhibits features different from the other two. The approach presented here does not require integrability of the original evolution equation. Indeed, while the KP equation is known to be a completely integrable equation, the 2DBO equation and the m2KP equation are not known to be integrable. In each of the cases considered, the Whitham modulation system obtained consists of five first-order quasilinear partial differential equations. The Riemann problem (i.e. the analogue of the Gurevich–Pitaevskii problem) for the one-dimensional reduction of the m2KP equation is studied. For the m2KP equation, the system of modulation equations is used to analyze the linear stability of traveling wave solutions.

Nonlinear stability of oscillatory core-annular flow: A generalized Kuramoto-Sivashinsky equation with time periodic coefficients

NASA Technical Reports Server (NTRS)

Coward, Adrian V.; Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.

1994-01-01

In this paper the nonlinear stability of two-phase core-annular flow in a pipe is examined when the acting pressure gradient is modulated by time harmonic oscillations and viscosity stratification and interfacial tension is present. An exact solution of the Navier-Stokes equations is used as the background state to develop an asymptotic theory valid for thin annular layers, which leads to a novel nonlinear evolution describing the spatio-temporal evolution of the interface. The evolution equation is an extension of the equation found for constant pressure gradients and generalizes the Kuramoto-Sivashinsky equation with dispersive effects found by Papageorgiou, Maldarelli & Rumschitzki, Phys. Fluids A 2(3), 1990, pp. 340-352, to a similar system with time periodic coefficients. The distinct regimes of slow and moderate flow are considered and the corresponding evolution is derived. Certain solutions are described analytically in the neighborhood of the first bifurcation point by use of multiple scales asymptotics. Extensive numerical experiments, using dynamical systems ideas, are carried out in order to evaluate the effect of the oscillatory pressure gradient on the solutions in the presence of a constant pressure gradient.

Influence of Initial Correlations on Evolution of a Subsystem in a Heat Bath and Polaron Mobility

NASA Astrophysics Data System (ADS)

Los, Victor F.

2017-08-01

A regular approach to accounting for initial correlations, which allows to go beyond the unrealistic random phase (initial product state) approximation in deriving the evolution equations, is suggested. An exact homogeneous (time-convolution and time-convolutionless) equations for a relevant part of the two-time equilibrium correlation function for the dynamic variables of a subsystem interacting with a boson field (heat bath) are obtained. No conventional approximation like RPA or Bogoliubov's principle of weakening of initial correlations is used. The obtained equations take into account the initial correlations in the kernel governing their evolution. The solution to these equations is found in the second order of the kernel expansion in the electron-phonon interaction, which demonstrates that generally the initial correlations influence the correlation function's evolution in time. It is explicitly shown that this influence vanishes on a large timescale (actually at t→ ∞) and the evolution process enters an irreversible kinetic regime. The developed approach is applied to the Fröhlich polaron and the low-temperature polaron mobility (which was under a long-time debate) is found with a correction due to initial correlations.

Numerical and Experimental Validation of a New Damage Initiation Criterion

NASA Astrophysics Data System (ADS)

Sadhinoch, M.; Atzema, E. H.; Perdahcioglu, E. S.; van den Boogaard, A. H.

2017-09-01

Most commercial finite element software packages, like Abaqus, have a built-in coupled damage model where a damage evolution needs to be defined in terms of a single fracture energy value for all stress states. The Johnson-Cook criterion has been modified to be Lode parameter dependent and this Modified Johnson-Cook (MJC) criterion is used as a Damage Initiation Surface (DIS) in combination with the built-in Abaqus ductile damage model. An exponential damage evolution law has been used with a single fracture energy value. Ultimately, the simulated force-displacement curves are compared with experiments to validate the MJC criterion. 7 out of 9 fracture experiments were predicted accurately. The limitations and accuracy of the failure predictions of the newly developed damage initiation criterion will be discussed shortly.

The Evolution of Finite Amplitude Wavetrains in Plane Channel Flow

NASA Technical Reports Server (NTRS)

Hewitt, R. E.; Hall, P.

1996-01-01

We consider a viscous incompressible fluid flow driven between two parallel plates by a constant pressure gradient. The flow is at a finite Reynolds number, with an 0(l) disturbance in the form of a traveling wave. A phase equation approach is used to discuss the evolution of slowly varying fully nonlinear two dimensional wavetrains. We consider uniform wavetrains in detail, showing that the development of a wavenumber perturbation is governed by Burgers equation in most cases. The wavenumber perturbation theory, constructed using the phase equation approach for a uniform wavetrain, is shown to be distinct from an amplitude perturbation expansion about the periodic flow. In fact we show that the amplitude equation contains only linear terms and is simply the heat equation. We review, briefly, the well known dynamics of Burgers equation, which imply that both shock structures and finite time singularities of the wavenumber perturbation can occur with respect to the slow scales. Numerical computations have been performed to identify areas of the (wavenumber, Reynolds number, energy) neutral surface for which each of these possibilities can occur. We note that the evolution equations will breakdown under certain circumstances, in particular for a weakly nonlinear secondary flow. Finally we extend the theory to three dimensions and discuss the limit of a weak spanwise dependence for uniform wavetrains, showing that two functions are required to describe the evolution. These unknowns are a phase and a pressure function which satisfy a pair of linearly coupled partial differential equations. The results obtained from applying the same analysis to the fully three dimensional problem are included as an appendix.

Oblique hypervelocity impact response of dual-sheet structures

NASA Technical Reports Server (NTRS)

Schonberg, William P.; Taylor, Roy A.

1989-01-01

The results of a continuing investigation of the phenomena associated with the oblique hypervelocity impact of spherical projectiles onto multi-sheet aluminum structures are given. A series of equations that quantitatively describes these phenomena is obtained through a regression of experimental data. These equations characterize observed ricochet and penetration damage phenomena in a multi-sheet structure as functions of geometric parameters of the structure and the diameter, obliquity, and velocity of the impacting projectile. Crater damage observed on the ricochet witness plates is used to determine the sizes and speeds of the ricochet debris particles that caused the damage. It is observed that the diameter of the most damaging ricochet debris particle can be as large as 40 percent of the original particle diameter and can travel at speeds between 24 percent and 36 percent of the original projectile impact velocity. The equations necessary for the design of shielding panels that will protect external systems from such ricochet debris damage are also developed. The dimensions of these shielding panels are shown to be strongly dependent on their inclination and on their circumferential distribution around the spacecraft.

Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

2018-04-01

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

Radiation damage buildup and dislocation evolution in Ni and equiatomic multicomponent Ni-based alloys

NASA Astrophysics Data System (ADS)

Levo, E.; Granberg, F.; Fridlund, C.; Nordlund, K.; Djurabekova, F.

2017-07-01

Single-phase multicomponent alloys of equal atomic concentrations ("equiatomic") have proven to exhibit promising mechanical and corrosion resistance properties, that are sought after in materials intended for use in hazardous environments like next-generation nuclear reactors. In this article, we investigate the damage production and dislocation mobility by simulating irradiation of elemental Ni and the alloys NiCo, NiCoCr, NiCoFe and NiFe, to assess the effect of elemental composition. We compare the defect production and the evolution of dislocation networks in the simulation cells of two different sizes, for all five studied materials. We find that the trends in defect evolution are in good agreement between the different cell sizes. The damage is generally reduced with increased alloy complexity, and the dislocation evolution is specific to each material, depending on its complexity. We show that increasing complexity of the alloys does not always lead to decreased susceptibility to damage accumulation under irradiation. We show that, for instance, the NiCo alloy behaves very similarly to Ni, while presence of Fe or Cr in the alloy even as a third component reduces the saturated level of damage substantially. Moreover, we linked the defect evolution with the dislocation transformations in the alloys. Sudden drops in defect number and large defect fluctuations from the continuous irradiation can be explained from the dislocation activity.

Numerical Simulation of Rock Mass Damage Evolution During Deep-Buried Tunnel Excavation by Drill and Blast

NASA Astrophysics Data System (ADS)

Yang, Jianhua; Lu, Wenbo; Hu, Yingguo; Chen, Ming; Yan, Peng

2015-09-01

Presence of an excavation damage zone (EDZ) around a tunnel perimeter is of significant concern with regard to safety, stability, costs and overall performance of the tunnel. For deep-buried tunnel excavation by drill and blast, it is generally accepted that a combination of effects of stress redistribution and blasting is mainly responsible for development of the EDZ. However, few open literatures can be found to use numerical methods to investigate the behavior of rock damage induced by the combined effects, and it is still far from full understanding how, when and to what degree the blasting affects the behavior of the EDZ during excavation. By implementing a statistical damage evolution law based on stress criterion into the commercial software LS-DYNA through its user-subroutines, this paper presents a 3D numerical simulation of the rock damage evolution of a deep-buried tunnel excavation, with a special emphasis on the combined effects of the stress redistribution of surrounding rock masses and the blasting-induced damage. Influence of repeated blast loadings on the damage extension for practical millisecond delay blasting is investigated in the present analysis. Accompanying explosive detonation and secession of rock fragments from their initial locations, in situ stress in the immediate vicinity of the excavation face is suddenly released. The transient characteristics of the in situ stress release and induced dynamic responses in the surrounding rock masses are also highlighted. From the simulation results, some instructive conclusions are drawn with respect to the rock damage mechanism and evolution during deep-buried tunnel excavation by drill and blast.

Decoupling of the Leading Order DGLAP Evolution Equation with Spin Dependent Structure Functions

NASA Astrophysics Data System (ADS)

Azadbakht, F. Teimoury; Boroun, G. R.

2018-02-01

We propose an analytical solution for DGLAP evolution equations with polarized splitting functions at the Leading Order (LO) approximation based on the Laplace transform method. It is shown that the DGLAP evolution equations can be decoupled completely into two second order differential equations which then are solved analytically by using the initial conditions δ FS(x,Q2)=F[partial δ FS0(x), δ FS0(x)] and {δ G}(x,Q2)=G[partial δ G0(x), δ G0(x)]. We used this method to obtain the polarized structure function of the proton as well as the polarized gluon distribution function inside the proton and compared the numerical results with experimental data of COMPASS, HERMES, and AAC'08 Collaborations. It was found that there is a good agreement between our predictions and the experiments.

Constitutive equations of a tensorial model for strain-induced damage of metals based on three invariants

NASA Astrophysics Data System (ADS)

Tutyshkin, Nikolai D.; Lofink, Paul; Müller, Wolfgang H.; Wille, Ralf; Stahn, Oliver

2017-01-01

On the basis of the physical concepts of void formation, nucleation, and growth, generalized constitutive equations are formulated for a tensorial model of plastic damage in metals based on three invariants. The multiplicative decomposition of the metric transformation tensor and a thermodynamically consistent formulation of constitutive relations leads to a symmetric second-order damage tensor with a clear physical meaning. Its first invariant determines the damage related to plastic dilatation of the material due to growth of the voids. The second invariant of the deviatoric damage tensor is related to the change in void shape. The third invariant of the deviatoric tensor describes the impact of the stress state on damage (Lode angle), including the effect of rotating the principal axes of the stress tensor (Lode angle change). The introduction of three measures with related physical meaning allows for the description of kinetic processes of strain-induced damage with an equivalent parameter in a three-dimensional vector space, including the critical condition of ductile failure. Calculations were performed by using experimentally determined material functions for plastic dilatation and deviatoric strain at the mesoscale, as well as three-dimensional graphs for plastic damage of steel DC01. The constitutive parameter was determined from tests in tension, compression, and shear by using scanning electron microscopy, which allowed to vary the Lode angle over the full range of its values [InlineEquation not available: see fulltext.]. In order to construct the three-dimensional plastic damage curve for a range of triaxiality parameters -1 ≤ ST ≤ 1 and of Lode angles [InlineEquation not available: see fulltext.], we used our own, as well as systematized published experimental data. A comparison of calculations shows a significant effect of the third invariant (Lode angle) on equivalent damage. The measure of plastic damage, based on three invariants, can be useful for assessing the quality of metal mesostructure produced during metal forming processes. In many processes of metal sheet forming the material experiences, a non-proportional loading accompanied by rotating the principal axes of the stress tensor and a corresponding change of Lode angle.

LS-DYNA Simulation of Hemispherical-punch Stamping Process Using an Efficient Algorithm for Continuum Damage Based Elastoplastic Constitutive Equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Salajegheh, Nima; Abedrabbo, Nader; Pourboghrat, Farhang

An efficient integration algorithm for continuum damage based elastoplastic constitutive equations is implemented in LS-DYNA. The isotropic damage parameter is defined as the ratio of the damaged surface area over the total cross section area of the representative volume element. This parameter is incorporated into the integration algorithm as an internal variable. The developed damage model is then implemented in the FEM code LS-DYNA as user material subroutine (UMAT). Pure stretch experiments of a hemispherical punch are carried out for copper sheets and the results are compared against the predictions of the implemented damage model. Evaluation of damage parameters ismore » carried out and the optimized values that correctly predicted the failure in the sheet are reported. Prediction of failure in the numerical analysis is performed through element deletion using the critical damage value. The set of failure parameters which accurately predict the failure behavior in copper sheets compared to experimental data is reported as well.« less

Numerical study of multi-point forming of thick sheet using remeshing procedure

NASA Astrophysics Data System (ADS)

Cherouat, A.; Ma, X.; Borouchaki, H.; Zhang, Q.

2018-05-01

Multi-point forming MPF is an innovative technology of manufacturing complex thick sheet metal products without the need for solid tools. The central component of this system is a pair of the desired discrete matrices of punches, and die surface constructed by changing the positions of the tools though CAD and a control system. Because reconfigurable discrete tools are used, part-manufacturing costs are reduced and manufacturing time is shorten substantially. Firstly, in this work we develop constitutive equations which couples isotropic ductile damage into various flow stress based on the Continuum Damage Mechanic theory. The modified Johnson-Cook flow model fully coupled with an isotropic ductile damage is established using the quasi-unilateral damage evolution for considering both the open and the close of micro-cracks. During the forming processes severe mesh distortion of elements occur after a few incremental forming steps. Secondly, we introduce 3D adaptive remeshing procedure based on linear tetrahedral element and geometrical/physical errors estimation to optimize the element quality, to refine the mesh size in the whole model and to adapt the deformed mesh to the tools geometry. Simulation of the MPF process (see Fig. 1) and the unloading spring-back are carried out using adaptive remeshing scheme using the commercial finite element package ABAQUS and OPTIFORM mesher. Subsequently, influencing factors of MPF spring-back are researched to investigate the MPF spring-back tendency with the proposed remeshing procedure.

Advantages of formulating an evolution equation directly for elastic distortional deformation in finite deformation plasticity

NASA Astrophysics Data System (ADS)

Rubin, M. B.; Cardiff, P.

2017-11-01

Simo (Comput Methods Appl Mech Eng 66:199-219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1-31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61-112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation J2 plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-07-15

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the correspondingmore » growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.« less

GENERIC Integrators: Structure Preserving Time Integration for Thermodynamic Systems

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

Thermodynamically admissible evolution equations for non-equilibrium systems are known to possess a distinct mathematical structure. Within the GENERIC (general equation for the non-equilibrium reversible-irreversible coupling) framework of non-equilibrium thermodynamics, which is based on continuous time evolution, we investigate the possibility of preserving all the structural elements in time-discretized equations. Our approach, which follows Moser's [1] construction of symplectic integrators for Hamiltonian systems, is illustrated for the damped harmonic oscillator. Alternative approaches are sketched.

Nonlinear Ocean Waves

DTIC Science & Technology

1994-01-06

for all of this work is the fact that the Kadomtsev - Petviashvili equation , a1(atu + ui)xU + a.3u) + ay2u = 0, (KP) describes approximately the evolution...the contents of these two papers. (a) Numerically induced chaos The cubic-nonlinear Schrtdinger equation in one dimension, iatA +,2V + 21i,1 =0, (NLS...arises in several physical contexts, including the evolution of nearly monochromatic, one-dimensional waves in deep water. The equation is known to be

Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations.

PubMed

Gu, Yongyi; Qi, Jianming

2017-01-01

In this paper, symmetries and symmetry reduction of two higher-dimensional nonlinear evolution equations (NLEEs) are obtained by Lie group method. These NLEEs play an important role in nonlinear sciences. We derive exact solutions to these NLEEs via the [Formula: see text]-expansion method and complex method. Five types of explicit function solutions are constructed, which are rational, exponential, trigonometric, hyperbolic and elliptic function solutions of the variables in the considered equations.

The method of projected characteristics for the evolution of magnetic arches

NASA Technical Reports Server (NTRS)

Nakagawa, Y.; Hu, Y. Q.; Wu, S. T.

1987-01-01

A numerical method of solving fully nonlinear MHD equation is described. In particular, the formulation based on the newly developed method of projected characteristics (Nakagawa, 1981) suitable to study the evolution of magnetic arches due to motions of their foot-points is presented. The final formulation is given in the form of difference equations; therefore, the analysis of numerical stability is also presented. Further, the most important derivation of physically self-consistent, time-dependent boundary conditions (i.e. the evolving boundary equations) is given in detail, and some results obtained with such boundary equations are reported.

Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

NASA Astrophysics Data System (ADS)

Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

2016-12-01

Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

On the solutions of fractional order of evolution equations

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.

2017-01-01

In this paper we present a discussion of generalized Cauchy problems in a diffusion wave process, we consider bi-fractional-order evolution equations in the Riemann-Liouville, Liouville-Caputo, and Caputo-Fabrizio sense. Through Fourier transforms and Laplace transform we derive closed-form solutions to the Cauchy problems mentioned above. Similarly, we establish fundamental solutions. Finally, we give an application of the above results to the determination of decompositions of Dirac type for bi-fractional-order equations and write a formula for the moments for the fractional vibration of a beam equation. This type of decomposition allows us to speak of internal degrees of freedom in the vibration of a beam equation.

The co-evolution of microstructure features in self-ion irradiated HT9 at very high damage levels

NASA Astrophysics Data System (ADS)

Getto, E.; Vancoevering, G.; Was, G. S.

2017-02-01

Understanding the void swelling and phase evolution of reactor structural materials at very high damage levels is essential to maintaining safety and longevity of components in Gen IV fast reactors. A combination of ion irradiation and modeling was utilized to understand the microstructure evolution of ferritic-martensitic alloy HT9 at high dpa. Self-ion irradiation experiments were performed on alloy HT9 to determine the co-evolution of voids, dislocations and precipitates up to 650 dpa at 460 °C. Modeling of microstructure evolution was conducted using the modified Radiation Induced Microstructure Evolution (RIME) model, which utilizes a mean field rate theory approach with grouped cluster dynamics. Irradiations were performed with 5 MeV raster-scanned Fe2+ ions on samples pre-implanted with 10 atom parts per million He. The swelling, dislocation and precipitate evolution at very high dpa was determined using Analytical Electron Microscopy in Scanning Transmission Electron Microscopy (STEM) mode. Experimental results were then interpreted using the RIME model. A microstructure consisting only of dislocations and voids is insufficient to account for the swelling evolution observed experimentally at high damage levels in a complicated microstructure such as irradiated alloy HT9. G phase was found to have a minimal effect on either void or dislocation evolution. M2X played two roles; a variable biased sink for defects, and as a vehicle for removal of carbon from solution, thus promoting void growth. When accounting for all microstructure interactions, swelling at high damage levels is a dynamic process that continues to respond to other changes in the microstructure as long as they occur.

Optimized growth and reorientation of anisotropic material based on evolution equations

NASA Astrophysics Data System (ADS)

Jantos, Dustin R.; Junker, Philipp; Hackl, Klaus

2018-07-01

Modern high-performance materials have inherent anisotropic elastic properties. The local material orientation can thus be considered to be an additional design variable for the topology optimization of structures containing such materials. In our previous work, we introduced a variational growth approach to topology optimization for isotropic, linear-elastic materials. We solved the optimization problem purely by application of Hamilton's principle. In this way, we were able to determine an evolution equation for the spatial distribution of density mass, which can be evaluated in an iterative process within a solitary finite element environment. We now add the local material orientation described by a set of three Euler angles as additional design variables into the three-dimensional model. This leads to three additional evolution equations that can be separately evaluated for each (material) point. Thus, no additional field unknown within the finite element approach is needed, and the evolution of the spatial distribution of density mass and the evolution of the Euler angles can be evaluated simultaneously.

Damage evolution analysis of coal samples under cyclic loading based on single-link cluster method

NASA Astrophysics Data System (ADS)

Zhang, Zhibo; Wang, Enyuan; Li, Nan; Li, Xuelong; Wang, Xiaoran; Li, Zhonghui

2018-05-01

In this paper, the acoustic emission (AE) response of coal samples under cyclic loading is measured. The results show that there is good positive relation between AE parameters and stress. The AE signal of coal samples under cyclic loading exhibits an obvious Kaiser Effect. The single-link cluster (SLC) method is applied to analyze the spatial evolution characteristics of AE events and the damage evolution process of coal samples. It is found that a subset scale of the SLC structure becomes smaller and smaller when the number of cyclic loading increases, and there is a negative linear relationship between the subset scale and the degree of damage. The spatial correlation length ξ of an SLC structure is calculated. The results show that ξ fluctuates around a certain value from the second cyclic loading process to the fifth cyclic loading process, but spatial correlation length ξ clearly increases in the sixth loading process. Based on the criterion of microcrack density, the coal sample failure process is the transformation from small-scale damage to large-scale damage, which is the reason for changes in the spatial correlation length. Through a systematic analysis, the SLC method is an effective method to research the damage evolution process of coal samples under cyclic loading, and will provide important reference values for studying coal bursts.

The evolution of the small x gluon TMD

NASA Astrophysics Data System (ADS)

Zhou, Jian

2016-06-01

We study the evolution of the small x gluon transverse momentum dependent (TMD) distribution in the dilute limit. The calculation has been carried out in the Ji-Ma-Yuan scheme using a simple quark target model. As expected, we find that the resulting small x gluon TMD simultaneously satisfies both the Collins-Soper (CS) evolution equation and the Balitsky-Fadin-Kuraev-Lipatov (BFKL) evolution equation. We thus confirmed the earlier finding that the high energy factorization (HEF) and the TMD factorization should be jointly employed to resum the different type large logarithms in a process where three relevant scales are well separated.

Multiple and exact soliton solutions of the perturbed Korteweg-de Vries equation of long surface waves in a convective fluid via Painlevé analysis, factorization, and simplest equation methods.

PubMed

Selima, Ehab S; Yao, Xiaohua; Wazwaz, Abdul-Majid

2017-06-01

In this research, the surface waves of a horizontal fluid layer open to air under gravity field and vertical temperature gradient effects are studied. The governing equations of this model are reformulated and converted to a nonlinear evolution equation, the perturbed Korteweg-de Vries (pKdV) equation. We investigate the latter equation, which includes dispersion, diffusion, and instability effects, in order to examine the evolution of long surface waves in a convective fluid. Dispersion relation of the pKdV equation and its properties are discussed. The Painlevé analysis is applied not only to check the integrability of the pKdV equation but also to establish the Bäcklund transformation form. In addition, traveling wave solutions and a general form of the multiple-soliton solutions of the pKdV equation are obtained via Bäcklund transformation, the simplest equation method using Bernoulli, Riccati, and Burgers' equations as simplest equations, and the factorization method.

Non-Equilibrium Turbulence and Two-Equation Modeling

NASA Technical Reports Server (NTRS)

Rubinstein, Robert

2011-01-01

Two-equation turbulence models are analyzed from the perspective of spectral closure theories. Kolmogorov theory provides useful information for models, but it is limited to equilibrium conditions in which the energy spectrum has relaxed to a steady state consistent with the forcing at large scales; it does not describe transient evolution between such states. Transient evolution is necessarily through nonequilibrium states, which can only be found from a theory of turbulence evolution, such as one provided by a spectral closure. When the departure from equilibrium is small, perturbation theory can be used to approximate the evolution by a two-equation model. The perturbation theory also gives explicit conditions under which this model can be valid, and when it will fail. Implications of the non-equilibrium corrections for the classic Tennekes-Lumley balance in the dissipation rate equation are drawn: it is possible to establish both the cancellation of the leading order Re1/2 divergent contributions to vortex stretching and enstrophy destruction, and the existence of a nonzero difference which is finite in the limit of infinite Reynolds number.

Evolution of the equations of dynamics of the Universe: From Friedmann to the present day

NASA Astrophysics Data System (ADS)

Soloviev, V. O.

2017-05-01

Celebrating the centenary of general relativity theory, we must recall that Friedmann's discovery of the equations of evolution of the Universe became the strongest prediction of this theory. These equations currently remain the foundation of modern cosmology. Nevertheless, data from new observations stimulate a search for modified theories of gravitation. We discuss cosmological aspects of theories with two dynamical metrics and theories of massive gravity, one of which was developed by Logunov and his coworkers.

Evolution Equations of C(3)I: Cannonical Forms and Their Properties.

DTIC Science & Technology

1983-10-01

paper are all generalized Lotka - Volterra equations for two-species systems. In spite of these restric- tions, their interpretation in the C31 context...most general properties of that model exposed the fact that, unlike the earlier counter-C3 model, a four-species model is environmentally unstable...Coupled two-species evolution equations are of the general form a -F (X, Y. U) + V Y - -F (X, Y, + V(y y Fx and Fy are attrition functions. They depend

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

2018-03-01

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

On the instability of wave-fields with JONSWAP spectra to inhomogeneous disturbances, and the consequent long-time evolution

NASA Astrophysics Data System (ADS)

Ribal, A.; Stiassnie, M.; Babanin, A.; Young, I.

2012-04-01

The instability of two-dimensional wave-fields and its subsequent evolution in time are studied by means of the Alber equation for narrow-banded random surface-waves in deep water subject to inhomogeneous disturbances. A linear partial differential equation (PDE) is obtained after applying an inhomogeneous disturbance to the Alber's equation and based on the solution of this PDE, the instability of the ocean wave surface is studied for a JONSWAP spectrum, which is a realistic ocean spectrum with variable directional spreading and steepness. The steepness of the JONSWAP spectrum depends on γ and α which are the peak-enhancement factor and energy scale of the spectrum respectively and it is found that instability depends on the directional spreading, α and γ. Specifically, if the instability stops due to the directional spreading, increase of the steepness by increasing α or γ can reactivate it. This result is in qualitative agreement with the recent large-scale experiment and new theoretical results. In the instability area of α-γ plane, a long-time evolution has been simulated by integrating Alber's equation numerically and recurrent evolution is obtained which is the stochastic counterpart of the Fermi-Pasta-Ulam recurrence obtained for the cubic Schrödinger equation.

Resumming double non-global logarithms in the evolution of a jet

NASA Astrophysics Data System (ADS)

Hatta, Y.; Iancu, E.; Mueller, A. H.; Triantafyllopoulos, D. N.

2018-02-01

We consider the Banfi-Marchesini-Smye (BMS) equation which resums `non-global' energy logarithms in the QCD evolution of the energy lost by a pair of jets via soft radiation at large angles. We identify a new physical regime where, besides the energy logarithms, one has to also resum (anti)collinear logarithms. Such a regime occurs when the jets are highly collimated (boosted) and the relative angles between successive soft gluon emissions are strongly increasing. These anti-collinear emissions can violate the correct time-ordering for time-like cascades and result in large radiative corrections enhanced by double collinear logs, making the BMS evolution unstable beyond leading order. We isolate the first such a correction in a recent calculation of the BMS equation to next-to-leading order by Caron-Huot. To overcome this difficulty, we construct a `collinearly-improved' version of the leading-order BMS equation which resums the double collinear logarithms to all orders. Our construction is inspired by a recent treatment of the Balitsky-Kovchegov (BK) equation for the high-energy evolution of a space-like wavefunction, where similar time-ordering issues occur. We show that the conformal mapping relating the leading-order BMS and BK equations correctly predicts the physical time-ordering, but it fails to predict the detailed structure of the collinear improvement.

Simple Derivation of the Lindblad Equation

ERIC Educational Resources Information Center

Pearle, Philip

2012-01-01

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is…

The nonlinear evolution of modes on unstable stratified shear layers

NASA Technical Reports Server (NTRS)

Blackaby, Nicholas; Dando, Andrew; Hall, Philip

1993-01-01

The nonlinear development of disturbances in stratified shear flows (having a local Richardson number of value less than one quarter) is considered. Such modes are initially fast growing but, like related studies, we assume that the viscous, non-parallel spreading of the shear layer results in them evolving in a linear fashion until they reach a position where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. Four different basic integro-differential amplitude equations are possible, including one due to a novel mechanism; the relevant choice of amplitude equation, at a particular instance, being dependent on the relative sizes of the disturbance amplitude, the growth rate of the disturbance, its wavenumber, and the viscosity of the fluid. This richness of choice of possible nonlinearities arises mathematically from the indicial Frobenius roots of the governing linear inviscid equation (the Taylor-Goldstein equation) not, in general, differing by an integer. The initial nonlinear evolution of a mode will be governed by an integro-differential amplitude equations with a cubic nonlinearity but the resulting significant increase in the size of the disturbance's amplitude leads on to the next stage of the evolution process where the evolution of the mode is governed by an integro-differential amplitude equations with a quintic nonlinearity. Continued growth of the disturbance amplitude is expected during this stage, resulting in the effects of nonlinearity spreading to outside the critical level, by which time the flow has become fully nonlinear.

Macroscopic descriptions of rarefied gases from the elimination of fast variables

NASA Astrophysics Data System (ADS)

Dellar, Paul J.

2007-10-01

The Boltzmann equation describing a dilute monatomic gas is equivalent to an infinite hierarchy of evolution equations for successive moments of the distribution function. The five moments giving the macroscopic mass, momentum, and energy densities are unaffected by collisions between atoms, while all other moments naturally evolve on a fast collisional time scale. We show that the macroscopic equations of Chen, Rao, and Spiegel [Phys. Lett. A 271, 87 (2000)], like the familiar Navier-Stokes-Fourier equations, emerge from using a systematic procedure to eliminate the higher moments, leaving closed evolution equations for the five moments unaffected by collisions. The two equation sets differ through their treatment of contributions from the temperature to the momentum and energy fluxes. Using moment equations offers a definitive treatment of the Prandtl number problem using model collision operators, greatly reduces the labor of deriving equations for different collision operators, and clarifies the role of solvability conditions applied to the distribution function. The original Chen-Rao-Spiegel approach offers greatly improved agreement with experiments for the phase speed of ultrasound, but when corrected to match the Navier-Stokes-Fourier equations at low frequencies, it then underestimates the phase speed at high frequencies. Our introduction of a translational temperature, as in the kinetic theory of polyatomic gases, motivates a distinction in the energy flux between advection of internal energy and the work done by the pressure. Exploiting this distinction yields macroscopic equations that offer further improvement in agreement with experimental data, and arise more naturally as an approximation to the infinite hierarchy of evolution equations for moments.

Strong oviposition preference for Bt over non-Bt maize in Spodoptera frugiperda and its implications for the evolution of resistance

PubMed Central

2014-01-01

Background Transgenic crops expressing Bt toxins have substantial benefits for growers in terms of reduced synthetic insecticide inputs, area-wide pest management and yield. This valuable technology depends upon delaying the evolution of resistance. The ‘high dose/refuge strategy’, in which a refuge of non-Bt plants is planted in close proximity to the Bt crop, is the foundation of most existing resistance management. Most theoretical analyses of the high dose/refuge strategy assume random oviposition across refugia and Bt crops. Results In this study we examined oviposition and survival of Spodoptera frugiperda across conventional and Bt maize and explored the impact of oviposition behavior on the evolution of resistance in simulation models. Over six growing seasons oviposition rates per plant were higher in Bt crops than in refugia. The Cry1F Bt maize variety retained largely undamaged leaves, and oviposition preference was correlated with the level of feeding damage in the refuge. In simulation models, damage-avoiding oviposition accelerated the evolution of resistance and either led to requirements for larger refugia or undermined resistance management altogether. Since larval densities affected oviposition preferences, pest population dynamics affected resistance evolution: larger refugia were weakly beneficial for resistance management if they increased pest population sizes and the concomitant degree of leaf damage. Conclusions Damaged host plants have reduced attractiveness to many insect pests, and crops expressing Bt toxins are generally less damaged than conventional counterparts. Resistance management strategies should take account of this behavior, as it has the potential to undermine the effectiveness of existing practice, especially in the tropics where many pests are polyvoltinous. Efforts to bring down total pest population sizes and/or increase the attractiveness of damaged conventional plants will have substantial benefits for slowing the evolution of resistance. PMID:24935031

FAST TRACK COMMUNICATION: Semiclassical Klein Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential

NASA Astrophysics Data System (ADS)

Coffey, W. T.; Kalmykov, Yu P.; Titov, S. V.; Mulligan, B. P.

2007-01-01

The quantum Brownian motion of a particle in an external potential V(x) is treated using the master equation for the Wigner distribution function W(x, p, t) in phase space (x, p). A heuristic method of determination of diffusion coefficients in the master equation is proposed. The time evolution equation so obtained contains explicit quantum correction terms up to o(planck4) and in the classical limit, planck → 0, reduces to the Klein-Kramers equation. For a quantum oscillator, the method yields an evolution equation for W(x, p, t) coinciding with that of Agarwal (1971 Phys. Rev. A 4 739). In the non-inertial regime, by applying the Brinkman expansion of the momentum distribution in Weber functions (Brinkman 1956 Physica 22 29), the corresponding semiclassical Smoluchowski equation is derived.

Synergistic Effects of Temperature, Oxidation and Multicracking Modes on Damage Evolution and Life Prediction of 2D Woven Ceramic-Matrix Composites under Tension-Tension Fatigue Loading

NASA Astrophysics Data System (ADS)

Longbiao, Li

2017-08-01

In this paper, the synergistic effects of temperature, oxidation and multicracking modes on damage evolution and life prediction in 2D woven ceramic-matrix composites (CMCs) have been investigated. The damage parameter of fatigue hysteresis dissipated energy and the interface shear stress were used to monitor the damage evolution inside of CMCs. Under cyclic fatigue loading, the fibers broken fraction was determined by combining the interface/fiber oxidation model, interface wear model and fibers statistical failure model at elevated temperature, based on the assumption that the fiber strength is subjected to two-parameter Weibull distribution and the load carried by broken and intact fibers satisfy the Global Load Sharing (GLS) criterion. When the broken fibers fraction approaches to the critical value, the composite fatigue fractures. The evolution of fatigue hysteresis dissipated energy, the interface shear stress and broken fibers fraction versus cycle number, and the fatigue life S-N curves of SiC/SiC at 1000, 1200 and 1300 °C in air and steam condition have been predicted. The synergistic effects of temperature, oxidation, fatigue peak stress, and multicracking modes on the evolution of interface shear stress and fatigue hysteresis dissipated energy versus cycle numbers curves have been analyzed.

Thermography detection on the fatigue damage

NASA Astrophysics Data System (ADS)

Yang, Bing

It has always been a great temptation in finding new methods to in-situ "watch" the material fatigue-damage processes so that in-time reparations will be possible, and failures or losses can be minimized to the maximum extent. Realizing that temperature patterns may serve as fingerprints for stress-strain behaviors of materials, a state-of-art infrared (IR) thermography camera has been used to "watch" the temperature evolutions of both crystalline and amorphous materials "cycle by cycle" during fatigue experiments in the current research. The two-dimensional (2D) thermography technique records the surface-temperature evolutions of materials. Since all plastic deformations are related to heat dissipations, thermography provides an innovative method to in-situ monitor the heat-evolution processes, including plastic-deformation, mechanical-damage, and phase-transformation characteristics. With the understanding of the temperature evolutions during fatigue, thermography could provide the direct information and evidence of the stress-strain distribution, crack initiation and propagation, shear-band growth, and plastic-zone evolution, which will open up wide applications in studying the structural integrity of engineering components in service. In the current research, theoretical models combining thermodynamics and heat-conduction theory have been developed. Key issues in fatigue, such as in-situ stress-strain states, cyclic softening and hardening observations, and fatigue-life predictions, have been resolved by simply monitoring the specimen-temperature variation during fatigue. Furthermore, in-situ visulizations as well as qualitative and quantitative analyses of fatigue-damage processes, such as Luders-band evolutions, crack propagation, plastic zones, and final fracture, have been performed by thermography. As a method requiring no special sample preparation or surface contact by sensors, thermography provides an innovative and convenient method to in-situ monitor and analyze the mechanical-damage processes of materials and components.

F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation

PubMed Central

Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

2014-01-01

F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics. PMID:24672327

F-expansion method and new exact solutions of the Schrödinger-KdV equation.

PubMed

Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

2014-01-01

F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.

On the theory of Brownian motion with the Alder-Wainwright effect

NASA Astrophysics Data System (ADS)

Okabe, Yasunori

1986-12-01

The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, we obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. We are interested in whether or not it can be measured experimentally.

A linearized microstructural model for hydraulic conductivity evolution due to brittle damage: application to Hydraulic Fracturing treatments

NASA Astrophysics Data System (ADS)

Caramiello, G.; Montanino, A.; Della Vecchia, G., Sr.; Pandolfi, A., Sr.

2017-12-01

Among the features of geological structures, fractures and discontinuities play a dominant role, due to their significant influence on both the hydraulic and the mechanical behavior of the rock mass. Despite the current availability of fault and fracture mappings, the understanding of the influence of faults on fluid flow is nowadays not satisfactory, in particular when hydro-mechanical coupling is significant. In engineering technology fracture processes are often exploited. Hydraulic fracturing is one of the most important example. Hydraulic fracturing is a process characterized by the inception and propagation of fractures as a consequence of a hydraulic driven solicitation and it is used to improve the production and optimize well stimulation in low permeability reservoirs. Due to the coupling of several different phenomena (hydro-thermo-chemical coupling) there is not a reliable complete mathematical model able to simulate in a proper way the process. To design hydraulic fracturing treatments, it is necessary to predict the growth of fracture geometry as a function of treatment parameters. In this contribution we present a recently developed model of brittle damage of confined rock masses, with particular emphasis on the influence of mechanical damage on the evolution of porosity and permeability. The model is based on an explicit micromechanical construction of connected patterns of parallel equi-spaced cracks. A relevant feature of the model is that the fracture patterns are not arbitrary, but their inception, orientation and spacing follow from energetic consideration. The model, based on the Terzaghi effective stress concepts, has been then implemented into a coupled hydro-mechanical finite element code, where the linear momentum and the fluid mass balance equations are numerically solved via a staggered approach. The coupled code is used to simulate fracturing processes induced by an increase in pore pressure. The examples show the capability of the model in reproducing three-dimensional multiscale complex fracture patterns and permeability enhancement in the damaged porous medium. The numerical code, has been used to verify the influence of the distance between the different perforation slots as well of the wellbore-deviation from the minimum stress axis on the propagation of multiple.

Spontaneous electric current flow during deformation of non-piezoelectric marble samples: an indicator of stress state?

NASA Astrophysics Data System (ADS)

Cartwright-Taylor, A. L.; Sammonds, P. R.; Vallianatos, F.

2016-12-01

We recorded spontaneous electric current flow in non-piezoelectric Carrara marble samples during triaxial deformation. Mechanical data, ultrasonic velocities and acoustic emissions were acquired simultaneously with electric current to constrain the relationship between electric current flow, differential stress and damage. Under strain-controlled loading, spontaneous electric current signals (nA) were generated and sustained under all conditions tested. In dry samples, a detectable electric current arises only during dilatancy and is correlated with the damage induced by microcracking. Signal variations with confining pressure correspond to microcrack suppression, while variations with strain rate are associated with time-dependent differences in deformation mechanism across the brittle to semi-brittle transition. In the brittle regime, the signal exhibits a precursory change as damage localises and the stress drop accelerates towards failure. This change is particularly distinct at dynamic strain rates. Similar changes are seen in the semi-brittle regime although the signal is more oscillatory in nature. Current flow in dry samples is proportional to stress within 90% of peak stress. In fluid-saturated samples proportionality holds from 40% peak stress, with a significant increase in the rate of current production from 90% peak stress associated with fluid flow during dilatancy. This direct relationship demonstrates that electric current could be used as a proxy for stress, indicating when the rock is reaching the limit of its strength. The experimental power law relationship between electric current and strain rate, which mirrors the power-law creep equation, supports this observation. High-frequency fluctuations of electric current are not normally distributed - they exhibit `heavy-tails'. We model these distributions with q-Gaussian statistics and evolution of the q-parameter during deformation reveals a two-stage precursory anomaly prior to sample failure, consistent with the acoustic emissions b-value and stress intensity evolution as modelled from fracture mechanics. Our findings support the idea that electric currents in the crust can be generated purely from solid state fracture processes and that these currents may reflect the stress state within the damaged rock.

The relativistic equations of stellar structure and evolution

NASA Technical Reports Server (NTRS)

Thorne, K. S.

1975-01-01

The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. A general relativistic version of the mixing-length formalism for convection is presented. It is argued that in work on spherical systems, general relativity theorists have identified the wrong quantity as total mass-energy inside radius r.

Solutions of evolution equations associated to infinite-dimensional Laplacian

NASA Astrophysics Data System (ADS)

Ouerdiane, Habib

2016-05-01

We study an evolution equation associated with the integer power of the Gross Laplacian ΔGp and a potential function V on an infinite-dimensional space. The initial condition is a generalized function. The main technique we use is the representation of the Gross Laplacian as a convolution operator. This representation enables us to apply the convolution calculus on a suitable distribution space to obtain the explicit solution of the perturbed evolution equation. Our results generalize those previously obtained by Hochberg [K. J. Hochberg, Ann. Probab. 6 (1978) 433.] in the one-dimensional case with V=0, as well as by Barhoumi-Kuo-Ouerdiane for the case p=1 (See Ref. [A. Barhoumi, H. H. Kuo and H. Ouerdiane, Soochow J. Math. 32 (2006) 113.]).

Gaseous Viscous Peeling of Linearly Elastic Substrates

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2017-11-01

We study pressure-driven propagation of gas into a micron-scale gap between two linearly elastic substrates. Applying the lubrication approximation, the governing nonlinear evolution equation describes the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-number compressibility, characteristic to gaseous microflows. Several physical limits allow simplification of the evolution equation and enable solution by self-similarity. During the peeling process the flow-field transitions between the different limits and the respective approximate solutions. The sequence of limits occurring during the propagation dynamics can be related to the thickness of the prewetting layer of the configuration at rest, yielding an approximate description of the entire peeling dynamics. The results are validated by numerical solutions of the evolution equation. Israel Science Foundation 818/13.

On the breakup of viscous liquid threads

NASA Technical Reports Server (NTRS)

Papageorgiou, Demetrios T.

1995-01-01

A one-dimensional model evolution equation is used to describe the nonlinear dynamics that can lead to the breakup of a cylindrical thread of Newtonian fluid when capillary forces drive the motion. The model is derived from the Stokes equations by use of rational asymptotic expansions and under a slender jet approximation. The equations are solved numerically and the jet radius is found to vanish after a finite time yielding breakup. The slender jet approximation is valid throughout the evolution leading to pinching. The model admits self-similar pinching solutions which yield symmetric shapes at breakup. These solutions are shown to be the ones selected by the initial boundary value problem, for general initial conditions. Further more, the terminal state of the model equation is shown to be identical to that predicted by a theory which looks for singular pinching solutions directly from the Stokes equations without invoking the slender jet approximation throughout the evolution. It is shown quantitatively, therefore, that the one-dimensional model gives a consistent terminal state with the jet shape being locally symmetric at breakup. The asymptotic expansion scheme is also extended to include unsteady and inerticial forces in the momentum equations to derive an evolution system modelling the breakup of Navier-Stokes jets. The model is employed in extensive simulations to compute breakup times for different initial conditions; satellite drop formation is also supported by the model and the dependence of satellite drop volumes on initial conditions is studied.

Reactive transport in fractured porous media

NASA Astrophysics Data System (ADS)

Adler, P.; Jasinski, L.; Thovert, J.-F.; Mourzenko, V. V.

2012-04-01

Reactive flow through geological formations occurs in many situations due to human intervention or during natural processes. For instance, chemical dissolution and precipitation play a major role in diagenesis or in the formation of karsts. The quantitative description of the injection of a reacting fluid from a well into a fractured porous medium is also a subject of high interest. It can be provoked, as in the acidization stimulation technique for increasing well productivity, or accidental, in CO2 sequestration. Ideally, one wishes to analyze the improvements or damages caused by the fluid to the well itself and to its immediate surroundings. To this end, a coupled system of equations has to be solved. It includes the description of the flow in the porous matrix and in the fracture network by Darcy-like equations, and the description of the reactive solute transport and of the reactions which occur in the two structures. In addition, constitutive equations are required for the evolution of these two structures, such as evolution laws for permeability and reactivity as functions of porosity. Our discrete fracture numerical model involves three major steps. First, an unstructured tetrahedral mesh of the fractures and of the porous matrix is built. Second, the Darcy equations are discretized and solved, in a finite volume formulation. Third, the evolution of the solute concentration has to be calculated. This is the most difficult point if one wants to avoid numerical diffusion and accurately describe the transfers between the fractures and the matrix. A non linear flux limiting scheme of the Superbee type coupled with a systematic use of triple control volumes proved to be the most efficient. Various simple model situations have been considered, for validation purposes or to illustrate some physical points. In particular, it is shown that even when the matrix permeability is small and the flow is predominantly carried by the fracture network, convective exchanges still exist between the fractures and the matrix which can widely exceed diffusive ones and strongly affect the solute transport and its residence time distribution. Finally, simulations of passive and reactive solute transport have been performed in large samples containing percolating or non percolating fracture networks. Various parameters have been systematically investigated, including the transmissivity of the fractures, the flow regime characterized by Péclet numbers in the fractures and in the matrix, and the Damköhler numbers of the reaction process in the matrix and fractures. The passive transport behavior and the effect of the gradual clogging of the fractures and/or matrix pore space in the case of a precipitation process are analyzed.

Reactive flow in fractured porous media

NASA Astrophysics Data System (ADS)

Jasinski, L.; Thovert, J.; Mourzenko, V.; Adler, P. M.

2011-12-01

Reactive flow through geological formations occurs in many situations due to human intervention or during natural processes. For instance, chemical dissolution and precipitation play a major role in diagenesis or in the formation of karsts. The quantitative description of the injection of a reacting fluid from a well into a fractured porous medium is also a subject of high interest. It can be provoked, as in the acidization stimulation technique for increasing well productivity, or accidental, in CO2 sequestration. Ideally, one wishes to analyze the improvements or damages caused by the fluid to the well itself and to its immediate surroundings. To this end, a coupled system of equations has to be solved. It includes the description of the flow in the porous matrix and in the fracture network by Darcy-like equations, and the description of the reactive solute transport and of the reactions which occur in the two structures. In addition, constitutive equations are required for the evolution of these two structures, such as evolution laws for permeability and reactivity as functions of porosity. Our discrete fracture numerical model involves three major steps. First, an unstructured tetrahedral mesh of the fractures and of the porous matrix is built. Second, the Darcy equations are discretized and solved, in a finite volume formulation. Third, the evolution of the solute concentration has to be calculated. This is the most difficult point if one wants to avoid numerical diffusion and accurately describe the transfers between the fractures and the matrix. A non linear flux limiting scheme of the Superbee type coupled with a systematic use of triple control volumes proved to be the most efficient. Various simple model situations have been considered, for validation purposes or to illustrate some physical points. In particular, it is shown that even when the matrix permeability is small and the flow is predominantly carried by the fracture network, convective exchanges still exist between the fractures and the matrix which can widely exceed diffusive ones and strongly affect the solute transport and its residence time distribution. Finally, simulations of passive and reactive solute transport have been performed in large samples containing percolating or non percolating fracture networks. Various parameters have been systematically investigated, including the transmissivity of the fractures, the flow regime characterized by Péclet numbers in the fractures and in the matrix, and the Damköhler numbers of the reaction process in the matrix and fractures. The passive transport behavior and the effect of the gradual clogging of the fractures and/or matrix pore space in the case of a precipitation process are analyzed.

Simulations of Fluvial Landscapes

NASA Astrophysics Data System (ADS)

Cattan, D.; Birnir, B.

2013-12-01

The Smith-Bretherton-Birnir (SBB) model for fluvial landsurfaces consists of a pair of partial differential equations, one governing water flow and one governing the sediment flow. Numerical solutions of these equations have been shown to provide realistic models in the evolution of fluvial landscapes. Further analysis of these equations shows that they possess scaling laws (Hack's Law) that are known to exist in nature. However, the simulations are highly dependent on the numerical methods used; with implicit methods exhibiting the correct scaling laws, but the explicit methods fail to do so. These equations, and the resulting models, help to bridge the gap between the deterministic and the stochastic theories of landscape evolution. Slight modifications of the SBB equations make the results of the model more realistic. By modifying the sediment flow equation, the model obtains more pronounced meandering rivers. Typical landsurface with rivers.

InSitu SEM Investigation of Microstructural Damage Evolution and Strain Relaxation in a Melt Infiltrated SiC/SiC Composite

NASA Technical Reports Server (NTRS)

Sevener, Kathy; Chen, Zhe; Daly, Sam; Tracy, Jared; Kiser, Doug

2016-01-01

With CMC components poised to complete flight certification in turbine engines on commercial aircraft within the near future, there are many efforts within the aerospace community to model the mechanical and environmental degradation of CMCs. Direct observations of damage evolution are needed to support these modeling efforts and provide quantitative measures of damage parameters used in the various models. This study was performed to characterize the damage evolution during tensile loading of a melt infiltrated (MI) silicon carbide reinforced silicon carbide (SiC/SiC) composite. A SiC/SiC tensile coupon was loaded to a maximum global stress of 30 ksi in a tensile fixture within an SEM while observations were made at 5 ksi increments. Both traditional image analysis and DIC (digital image correlation) were used to quantify damage evolution. With the DIC analysis, microscale damage was observed at the fiber-matrix interfaces at stresses as low as 5 ksi. First matrix cracking took place between 20 and 25 ksi, accompanied by an observable relaxation in strain near matrix cracks. Matrix crack opening measurements at the maximum load ranged from 200 nm to 1.5 m. Crack opening along the fiber-matrix interface was also characterized as a function of load and angular position relative to the loading axis. This characterization was funded by NASA GRC and was performed to support NASA GRC modeling of SiC/SiC environmental degradation

APFEL: A PDF evolution library with QED corrections

NASA Astrophysics Data System (ADS)

Bertone, Valerio; Carrazza, Stefano; Rojo, Juan

2014-06-01

Quantum electrodynamics and electroweak corrections are important ingredients for many theoretical predictions at the LHC. This paper documents APFEL, a new PDF evolution package that allows for the first time to perform DGLAP evolution up to NNLO in QCD and to LO in QED, in the variable-flavor-number scheme and with either pole or MS bar heavy quark masses. APFEL consistently accounts for the QED corrections to the evolution of quark and gluon PDFs and for the contribution from the photon PDF in the proton. The coupled QCD ⊗ QED equations are solved in x-space by means of higher order interpolation, followed by Runge-Kutta solution of the resulting discretized evolution equations. APFEL is based on an innovative and flexible methodology for the sequential solution of the QCD and QED evolution equations and their combination. In addition to PDF evolution, APFEL provides a module that computes Deep-Inelastic Scattering structure functions in the FONLL general-mass variable-flavor-number scheme up to O(αs2) . All the functionalities of APFEL can be accessed via a Graphical User Interface, supplemented with a variety of plotting tools for PDFs, parton luminosities and structure functions. Written in FORTRAN 77, APFEL can also be used via the C/C++ and Python interfaces, and is publicly available from the HepForge repository.

Reorientational versus Kerr dark and gray solitary waves using modulation theory.

PubMed

Assanto, Gaetano; Marchant, T R; Minzoni, Antonmaria A; Smyth, Noel F

2011-12-01

We develop a modulation theory model based on a Lagrangian formulation to investigate the evolution of dark and gray optical spatial solitary waves for both the defocusing nonlinear Schrödinger (NLS) equation and the nematicon equations describing nonlinear beams, nematicons, in self-defocusing nematic liquid crystals. Since it has an exact soliton solution, the defocusing NLS equation is used as a test bed for the modulation theory applied to the nematicon equations, which have no exact solitary wave solution. We find that the evolution of dark and gray NLS solitons, as well as nematicons, is entirely driven by the emission of diffractive radiation, in contrast to the evolution of bright NLS solitons and bright nematicons. Moreover, the steady nematicon profile is nonmonotonic due to the long-range nonlocality associated with the perturbation of the optic axis. Excellent agreement is obtained with numerical solutions of both the defocusing NLS and nematicon equations. The comparisons for the nematicon solutions raise a number of subtle issues relating to the definition and measurement of the width of a dark or gray nematicon.

Transient features and growth behavior of artificial cracks during the initial damage period.

PubMed

Ma, Bin; Wang, Ke; Lu, Menglei; Zhang, Li; Zhang, Lei; Zhang, Jinlong; Cheng, Xinbin; Wang, Zhanshan

2017-02-01

The laser damage of transmission elements contains a series of complex processes and physical phenomena. The final morphology is a crater structure with different sizes and shapes. The formation and development of the crater are also accompanied by the generation, extension, and submersion of cracks. The growth characteristics of craters and cracks are important in the thermal-mechanism damage research. By using pump-probe detection and an imaging technique with a nanosecond pulsewidth probe laser, we obtained the formation time of the crack structure in the radial and circumferential directions. We carried out statistical analysis in angle, number, and crack length. We further analyzed the relationship between cracks and stress intensity or laser irradiation energy as well as the crack evolution process and the inner link between cracks and pit growth. We used an artificial indentation defect to investigate the time-domain evolution of crack growth, growth speed, transient morphology, and the characteristics of crater expansion. The results can be used to elucidate thermal stress effects on cracks, time-domain evolution of the damage structure, and the damage growth mechanism.

Asymmetrical Damage Partitioning in Bacteria: A Model for the Evolution of Stochasticity, Determinism, and Genetic Assimilation

PubMed Central

Chao, Lin; Rang, Camilla Ulla; Proenca, Audrey Menegaz; Chao, Jasper Ubirajara

2016-01-01

Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother’s old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother’s old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington’s genetic assimilation. Our model is able to quantify the evolution of the assimilation because it characterizes the fitness consequences of variation. PMID:26761487

Asymmetrical Damage Partitioning in Bacteria: A Model for the Evolution of Stochasticity, Determinism, and Genetic Assimilation.

PubMed

Chao, Lin; Rang, Camilla Ulla; Proenca, Audrey Menegaz; Chao, Jasper Ubirajara

2016-01-01

Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother's old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother's old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington's genetic assimilation. Our model is able to quantify the evolution of the assimilation because it characterizes the fitness consequences of variation.

Detection the nonlinear ultrasonic signals based on modified Duffing equations

NASA Astrophysics Data System (ADS)

Zhang, Yuhua; Mao, Hanling; Mao, Hanying; Huang, Zhenfeng

The nonlinear ultrasonic signals, like second harmonic generation (SHG) signals, could reflect the nonlinearity of material induced by fatigue damage in nonlinear ultrasonic technique which are weak nonlinear signals and usually submerged by strong background noise. In this paper the modified Duffing equations are applied to detect the SHG signals relating to the fatigue damage of material. Due to the Duffing equation could only detect the signal with specific frequency and initial phase, firstly the frequency transformation is carried on the Duffing equation which could detect the signal with any frequency. Then the influence of initial phases of to-be-detected signal and reference signal on the detection result is studied in detail, four modified Duffing equations are proposed to detect actual engineering signals with any initial phase. The relationship between the response amplitude and the total driving force is applied to estimate the amplitude of weak periodic signal. The detection results show the modified Duffing equations could effectively detect the second harmonic in SHG signals. When the SHG signals include strong background noise, the noise doesn't change the motion state of Duffing equation and the second harmonic signal could be detected until the SNR of noisy SHG signals are -26.3, yet the frequency spectrum method could only identify when the SNR is greater than 0.5. When estimation the amplitude of second harmonic signal, the estimation error of Duffing equation is obviously less than the frequency spectrum analysis method under the same noise level, which illustrates the Duffing equation has the noise immune capacity. The presence of the second harmonic signal in nonlinear ultrasonic experiments could provide an insight about the early fatigue damage of engineering components.

Multidimensional Solitons in Complex Media with Variable Dispersion: Structure and Evolution

DTIC Science & Technology

2003-07-20

the results of numerical experiments on Kadomtsev - Petviashvili (KP) equation study of structure and evolution of the nonlinear waves Sx described by...the KP equation with 13 = 3 (t,r) are con- at + auaxu + 03’u =K fAjudx, (1) sidered distracting from a concrete type of media. The -o• numerical...0i)(cot 0- mIM). It is well known that cluding the solutions of the mixed "soliton - non-soliton" the ID solutions of the KdV equation with 3 = const

A Harnack's inequality for mixed type evolution equations

NASA Astrophysics Data System (ADS)

Paronetto, Fabio

2016-03-01

We define a homogeneous parabolic De Giorgi classes of order 2 which suits a mixed type class of evolution equations whose simplest example is μ (x)∂u/∂t - Δu = 0 where μ can be positive, null and negative, so in particular elliptic-parabolic and forward-backward parabolic equations are included. For functions belonging to this class we prove local boundedness and show a Harnack inequality which, as by-products, gives Hölder-continuity, in particular in the interface I where μ changes sign, and a maximum principle.

NLO Hierarchy of Wilson Lines Evolution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balitsky, Ian

2015-03-01

The high-energy behavior of QCD amplitudes can be described in terms of the rapidity evolution of Wilson lines. I present the hierarchy of evolution equations for Wilson lines in the next-to-leading order.

On a generalized Ablowitz-Kaup-Newell-Segur hierarchy in inhomogeneities of media: soliton solutions and wave propagation influenced from coefficient functions and scattering data

NASA Astrophysics Data System (ADS)

Zhang, Sheng; Hong, Siyu

2018-07-01

In this paper, a generalized Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy in inhomogeneities of media described by variable coefficients is investigated, which includes some important nonlinear evolution equations as special cases, for example, the celebrated Korteweg-de Vries equation modeling waves on shallow water surfaces. To be specific, the known AKNS spectral problem and its time evolution equation are first generalized by embedding a finite number of differentiable and time-dependent functions. Starting from the generalized AKNS spectral problem and its generalized time evolution equation, a generalized AKNS hierarchy with variable coefficients is then derived. Furthermore, based on a systematic analysis on the time dependence of related scattering data of the generalized AKNS spectral problem, exact solutions of the generalized AKNS hierarchy are formulated through the inverse scattering transform method. In the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. It is graphically shown that the dynamical evolutions of such soliton solutions are influenced by not only the time-dependent coefficients but also the related scattering data in the process of propagations.

Direct Numerical Simulation of Fingering Instabilities in Coating Flows

NASA Astrophysics Data System (ADS)

Eres, Murat H.; Schwartz, Leonard W.

1998-11-01

We consider stability and finger formation in free surface flows. Gravity driven downhill drainage and temperature gradient driven climbing flows are two examples of such problems. The former situation occurs when a mound of viscous liquid on a vertical wall is allowed to flow. Constant surface shear stress due to temperature gradients (Marangoni stress) can initiate the latter problem. The evolution equations are derived using the lubrication approximation. We also include the effects of finite-contact angles in the evolution equations using a disjoining pressure model. Evolution equations for both problems are solved using an efficient alternating-direction-implicit method. For both problems a one-dimensional base state is established, that is steady in a moving reference frame. This base state is unstable to transverse perturbations. The transverse wavenumbers for the most rapidly growing modes are found through direct numerical solution of the nonlinear evolution equations, and are compared with published experimental results. For a range of finite equilibrium contact angles, the fingers can grow without limit leading to semi-finite steady fingers in a moving coordinate system. A computer generated movie of the nonlinear simulation results, for several sets of input parameters, will be shown.

Atomic scale modeling of defect production and microstructure evolution in irradiated metals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Diaz de la Rubia, T.; Soneda, N.; Shimomura, Y.

1997-04-01

Irradiation effects in materials depend in a complex way on the form of the as-produced primary damage state and its spatial and temporal evolution. Thus, while collision cascades produce defects on a time scale of tens of picosecond, diffusion occurs over much longer time scales, of the order of seconds, and microstructure evolution over even longer time scales. In this report the authors present work aimed at describing damage production and evolution in metals across all the relevant time and length scales. They discuss results of molecular dynamics simulations of displacement cascades in Fe and V. They show that interstitialmore » clusters are produced in cascades above 5 keV, but not vacancy clusters. Next, they discuss the development of a kinetic Monte Carlo model that enables calculations of damage evolution over much longer time scales (1000`s of s) than the picosecond lifetime of the cascade. They demonstrate the applicability of the method by presenting predictions on the fraction of freely migrating defects in {alpha}Fe during irradiation at 600 K.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krasnobaeva, L. A., E-mail: kla1983@mail.ru; Siberian State Medical University Moscowski Trakt 2, Tomsk, 634050; Shapovalov, A. V.

Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on dynamics local conformational perturbations (kink) propagating along the DNA molecule is investigated. Such waves have an important role in the regulation of important biological processes in living systems at the molecular level. As a dynamic model of DNA was used a modified sine-Gordon equation, simulating the rotational oscillations of bases in one of the chains DNA. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the frameworkmore » of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker– Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum. Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on the kink dynamics is investigated in the sine–Gordon model. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the framework of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker–Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum.« less

Energy evolution mechanism in process of Sandstone failure and energy strength criterion

NASA Astrophysics Data System (ADS)

Wang, Yunfei; Cui, Fang

2018-07-01

To reveal the inherent relation between energy change and confining pressure during the process of sandstone damage, and its characteristics of energy storage and energy dissipation in different deformation stage. Obtaining the mechanical parameters by testing the Sandstone of two1 coal seam roof under uniaxial compression in Zhaogu coalmine, using Particle Flow Code (PFC) and fish program to get the meso-mechanical parameters, studying Sandstone energy evolution mechanism under different confining pressures, and deducing energy strength criterion based on energy principle of rock failure, some main researching results are reached as follows: with the increasing of confining pressure, the Sandstone yield stage and ductility increases, but brittleness decreases; Under higher confining pressure, the elastic strain energy of Sandstone before peak approximately keeps constant in a certain strain range, and rock absorbs all the energy which converts into surface energy required for internal damage development; Under lower confining pressure, Sandstone no longer absorbs energy with increasing strain after peak under lower confining pressure, while it sequentially absorbs energy under higher confining pressure; Under lower confining pressure, the energy Sandstone before peak absorbed mainly converts into elastic strain energy, while under higher confining pressure, dissipation energy significantly increases before peak, which indicates that the degree rock strength loss is higher under higher confining pressure; with the increasing of confining pressure, the limit of elastic strain energy increases and there exists a favourable linear variation relationship; At the peak point, the ratio of elastic strain energy to total energy of Sandstone nonlinearly decreases, while the ratio of dissipation energy to total energy nonlinearly increases with the increasing of confining pressure; According to energy evolution mechanism of rock failure, an energy strength criterion is derived. The criterion equation includes lithology constants and three principal stresses, and its physical meaning is clear. This criterion has an evident advantage than Hoek-Brown and Drucker-Prager criterion in calculation accuracy and can commendably describe rock failure characteristics.

Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maccari, A.

1997-08-01

Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio{endash}temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a {open_quotes}universal{close_quotes} character, inasmuch as they may be derived from a very large classmore » of nonlinear evolution equations with a linear dispersive part. {copyright} {ital 1997 American Institute of Physics.}« less

About Tidal Evolution of Quasi-Periodic Orbits of Satellites

NASA Astrophysics Data System (ADS)

Ershkov, Sergey V.

2017-06-01

Tidal interactions between Planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. The modern ansatz in the theory of tidal dissipation in Saturn was developed previously by the international team of scientists from various countries in the field of celestial mechanics. Our applying to the theory of tidal dissipation concerns the investigating of the system of ODE-equations (ordinary differential equations) that govern the orbital evolution of the satellites; such an extremely non-linear system of 2 ordinary differential equations describes the mutual internal dynamics for the eccentricity of the orbit along with involving the semi-major axis of the proper satellite into such a monstrous equations. In our derivation, we have presented the elegant analytical solutions to the system above; so, the motivation of our ansatz is to transform the previously presented system of equations to the convenient form, in which the minimum of numerical calculations are required to obtain the final solutions. Preferably, it should be the analytical solutions; we have presented the solution as a set of quasi- periodic cycles via re-inversing of the proper ultra- elliptical integral. It means a quasi-periodic character of the evolution of the eccentricity, of the semi-major axis for the satellite orbit as well as of the quasi-periodic character of the tidal dissipation in the Planet.

Finite element method for viscoelastic medium with damage and the application to structural analysis of solid rocket motor grain

NASA Astrophysics Data System (ADS)

Deng, Bin; Shen, ZhiBin; Duan, JingBo; Tang, GuoJin

2014-05-01

This paper studies the damage-viscoelastic behavior of composite solid propellants of solid rocket motors (SRM). Based on viscoelastic theories and strain equivalent hypothesis in damage mechanics, a three-dimensional (3-D) nonlinear viscoelastic constitutive model incorporating with damage is developed. The resulting viscoelastic constitutive equations are numerically discretized by integration algorithm, and a stress-updating method is presented by solving nonlinear equations according to the Newton-Raphson method. A material subroutine of stress-updating is made up and embedded into commercial code of Abaqus. The material subroutine is validated through typical examples. Our results indicate that the finite element results are in good agreement with the analytical ones and have high accuracy, and the suggested method and designed subroutine are efficient and can be further applied to damage-coupling structural analysis of practical SRM grain.

Modeling of the spectral evolution in a narrow-linewidth fiber amplifier

NASA Astrophysics Data System (ADS)

Liu, Wei; Kuang, Wenjun; Jiang, Man; Xu, Jiangming; Zhou, Pu; Liu, Zejin

2016-03-01

Efficient numerical modeling of the spectral evolution in a narrow-linewidth fiber amplifier is presented. By describing the seeds using a statistical model and simulating the amplification process through power balanced equations combined with the nonlinear Schrödinger equations, the spectral evolution of different seeds in the fiber amplifier can be evaluated accurately. The simulation results show that the output spectra are affected by the temporal stability of the seeds and the seeds with constant amplitude in time are beneficial to maintain the linewidth of the seed in the fiber amplifier.

Numerical-experimental investigation of load paths in DP800 dual phase steel during Nakajima test

NASA Astrophysics Data System (ADS)

Bergs, Thomas; Nick, Matthias; Feuerhack, Andreas; Trauth, Daniel; Klocke, Fritz

2018-05-01

Fuel efficiency requirements demand lightweight construction of vehicle body parts. The usage of advanced high strength steels permits a reduction of sheet thickness while still maintaining the overall strength required for crash safety. However, damage, internal defects (voids, inclusions, micro fractures), microstructural defects (varying grain size distribution, precipitates on grain boundaries, anisotropy) and surface defects (micro fractures, grooves) act as a concentration point for stress and consequently as an initiation point for failure both during deep drawing and in service. Considering damage evolution in the design of car body deep drawing processes allows for a further reduction in material usage and therefore body weight. Preliminary research has shown that a modification of load paths in forming processes can help mitigate the effects of damage on the material. This paper investigates the load paths in Nakajima tests of a DP800 dual phase steel to research damage in deep drawing processes. Investigation is done via a finite element model using experimentally validated material data for a DP800 dual phase steel. Numerical simulation allows for the investigation of load paths with respect to stress states, strain rates and temperature evolution, which cannot be easily observed in physical experiments. Stress triaxiality and the Lode parameter are used to describe the stress states. Their evolution during the Nakajima tests serves as an indicator for damage evolution. The large variety of sheet metal forming specific load paths in Nakajima tests allows a comprehensive evaluation of damage for deep drawing. The results of the numerical simulation conducted in this project and further physical experiments will later be used to calibrate a damage model for simulation of deep drawing processes.

Brittleness Effect on Rock Fatigue Damage Evolution

NASA Astrophysics Data System (ADS)

Nejati, Hamid Reza; Ghazvinian, Abdolhadi

2014-09-01

The damage evolution mechanism of rocks is one of the most important aspects in studying of rock fatigue behavior. Fatigue damage evolution of three rock types (onyx marble, sandstone and soft limestone) with different brittleness were considered in the present study. Intensive experimental tests were conducted on the chosen rock samples and acoustic emission (AE) sensors were used in some of them to monitor the fracturing process. Experimental tests indicated that brittleness strongly influences damage evolution of rocks in the course of static and dynamic loading. AE monitoring revealed that micro-crack density induced by the applied loads during different stages of the failure processes increases as rock brittleness increases. Also, results of fatigue tests on the three rock types indicated that the rock with the most induced micro-cracks during loading cycles has the least fatigue life. Furthermore, the condition of failure surfaces of the studied rocks samples, subjected to dynamic and static loading, were evaluated and it was concluded that the roughness of failure surfaces is influenced by loading types and rock brittleness. Dynamic failure surfaces were rougher than static ones and low brittle rock demonstrate a smoother failure surface compared to high brittle rock.

Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach

NASA Astrophysics Data System (ADS)

Camassa, R.; Falqui, G.; Ortenzi, G.

2017-02-01

The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite two-dimensional channel. The Hamiltonian structure of the averaged equations is obtained directly from that of the Euler equations through the process of Hamiltonian reduction. Long-wave asymptotics together with the Boussinesq approximation of neglecting the fluids’ inertia is then applied to reduce the leading order vertically averaged equations to the shallow-water Airy system, albeit in a non-trivial way. The full non-Boussinesq system for the dispersionless limit can then be viewed as a deformation of this well known equation. In a perturbative study of this deformation, a family of approximate constants of the motion are explicitly constructed and used to find local solutions of the evolution equations by means of hodograph-like formulae.

Robust Maneuvering Envelope Estimation Based on Reachability Analysis in an Optimal Control Formulation

NASA Technical Reports Server (NTRS)

Lombaerts, Thomas; Schuet, Stefan R.; Wheeler, Kevin; Acosta, Diana; Kaneshige, John

2013-01-01

This paper discusses an algorithm for estimating the safe maneuvering envelope of damaged aircraft. The algorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerodynamic derivatives. Starting with an optimal control formulation, the optimization problem can be rewritten as a Hamilton- Jacobi-Bellman equation. This equation can be solved by level set methods. This approach has been applied on an aircraft example involving structural airframe damage. Monte Carlo validation tests have confirmed that this approach is successful in estimating the safe maneuvering envelope for damaged aircraft.

Simulations of Non-spherical Bubble Collapse Dynamics in Viscous and Viscoelastic Media Near a Compliant Object

NASA Astrophysics Data System (ADS)

Rodriguez, Mauro; Johnsen, Eric

2015-11-01

Understanding the dynamics of cavitation bubbles and the shock waves emitted by their collapse in and near viscoelastic media is important for various naval and medical applications, particularly in the context of cavitation damage. Two examples are histotripsy, which utilizes this phenomenon for the ablation of pathogenic tissue, and erosion to elastomeric coatings on propellers. Although not fully understood, the damage mechanism combines the effect of the incoming pulses and cavitation produced by the high tension. Additionally, the influence of the shock on the material and the response of the material to the shock are not well known. A novel numerical approach for simulating shock and acoustic wave propagation in Zener-like viscoelastic media is proposed. This Eulerian method is based on a high-order accurate weighted essentially non-oscillatory scheme for shock capturing and introduces evolution equations for the components of the shear stress tensor. Validation studies between high-fidelity two-dimensional simulations of the bubble collapse dynamics for various experimental configurations (i.e. the viscous or viscoelastic material surrounding the bubble and the nearby compliant object are varied) will be presented. This work is supported by ONR grant N00014-12-1-0751.

Model for transport and reaction of defects and carriers within displacement cascades in gallium arsenide

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wampler, William R., E-mail: wrwampl@sandia.gov; Myers, Samuel M.

A model is presented for recombination of charge carriers at evolving displacement damage in gallium arsenide, which includes clustering of the defects in atomic displacement cascades produced by neutron or ion irradiation. The carrier recombination model is based on an atomistic description of capture and emission of carriers by the defects with time evolution resulting from the migration and reaction of the defects. The physics and equations on which the model is based are presented, along with the details of the numerical methods used for their solution. The model uses a continuum description of diffusion, field-drift and reaction of carriers,more » and defects within a representative spherically symmetric cluster of defects. The initial radial defect profiles within the cluster were determined through pair-correlation-function analysis of the spatial distribution of defects obtained from the binary-collision code MARLOWE, using recoil energies for fission neutrons. Properties of the defects are discussed and values for their parameters are given, many of which were obtained from density functional theory. The model provides a basis for predicting the transient response of III-V heterojunction bipolar transistors to displacement damage from energetic particle irradiation.« less

A Damage-Dependent Finite Element Analysis for Fiber-Reinforced Composite Laminates

NASA Technical Reports Server (NTRS)

Coats, Timothy W.; Harris, Charles E.

1998-01-01

A progressive damage methodology has been developed to predict damage growth and residual strength of fiber-reinforced composite structure with through penetrations such as a slit. The methodology consists of a damage-dependent constitutive relationship based on continuum damage mechanics. Damage is modeled using volume averaged strain-like quantities known as internal state variables and is represented in the equilibrium equations as damage induced force vectors instead of the usual degradation and modification of the global stiffness matrix.

First-passage times for pattern formation in nonlocal partial differential equations

NASA Astrophysics Data System (ADS)

Cáceres, Manuel O.; Fuentes, Miguel A.

2015-10-01

We describe the lifetimes associated with the stochastic evolution from an unstable uniform state to a patterned one when the time evolution of the field is controlled by a nonlocal Fisher equation. A small noise is added to the evolution equation to define the lifetimes and to calculate the mean first-passage time of the stochastic field through a given threshold value, before the patterned steady state is reached. In order to obtain analytical results we introduce a stochastic multiscale perturbation expansion. This multiscale expansion can also be used to tackle multiplicative stochastic partial differential equations. A critical slowing down is predicted for the marginal case when the Fourier phase of the unstable initial condition is null. We carry out Monte Carlo simulations to show the agreement with our theoretical predictions. Analytic results for the bifurcation point and asymptotic analysis of traveling wave-front solutions are included to get insight into the noise-induced transition phenomena mediated by invading fronts.

First-passage times for pattern formation in nonlocal partial differential equations.

PubMed

Cáceres, Manuel O; Fuentes, Miguel A

2015-10-01

We describe the lifetimes associated with the stochastic evolution from an unstable uniform state to a patterned one when the time evolution of the field is controlled by a nonlocal Fisher equation. A small noise is added to the evolution equation to define the lifetimes and to calculate the mean first-passage time of the stochastic field through a given threshold value, before the patterned steady state is reached. In order to obtain analytical results we introduce a stochastic multiscale perturbation expansion. This multiscale expansion can also be used to tackle multiplicative stochastic partial differential equations. A critical slowing down is predicted for the marginal case when the Fourier phase of the unstable initial condition is null. We carry out Monte Carlo simulations to show the agreement with our theoretical predictions. Analytic results for the bifurcation point and asymptotic analysis of traveling wave-front solutions are included to get insight into the noise-induced transition phenomena mediated by invading fronts.

Discovering mechanisms relevant for radiation damage evolution

DOE PAGES

Uberuaga, Blas Pedro; Martinez, Enrique Saez; Perez, Danny; ...

2018-02-22

he response of a material to irradiation is a consequence of the kinetic evolution of defects produced during energetic damage events. Thus, accurate predictions of radiation damage evolution require knowing the atomic scale mechanisms associated with those defects. Atomistic simulations are a key tool in providing insight into the types of mechanisms possible. Further, by extending the time scale beyond what is achievable with conventional molecular dynamics, even greater insight can be obtained. Here, we provide examples in which such simulations have revealed new kinetic mechanisms that were not obvious before performing the simulations. We also demonstrate, through the couplingmore » with higher level models, how those mechanisms impact experimental observables in irradiated materials. Lastly, we discuss the importance of these types of simulations in the context of predicting material behavior.« less

Discovering mechanisms relevant for radiation damage evolution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Uberuaga, Blas Pedro; Martinez, Enrique Saez; Perez, Danny

he response of a material to irradiation is a consequence of the kinetic evolution of defects produced during energetic damage events. Thus, accurate predictions of radiation damage evolution require knowing the atomic scale mechanisms associated with those defects. Atomistic simulations are a key tool in providing insight into the types of mechanisms possible. Further, by extending the time scale beyond what is achievable with conventional molecular dynamics, even greater insight can be obtained. Here, we provide examples in which such simulations have revealed new kinetic mechanisms that were not obvious before performing the simulations. We also demonstrate, through the couplingmore » with higher level models, how those mechanisms impact experimental observables in irradiated materials. Lastly, we discuss the importance of these types of simulations in the context of predicting material behavior.« less

Energetic Consistency and Coupling of the Mean and Covariance Dynamics

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.

2008-01-01

The dynamical state of the ocean and atmosphere is taken to be a large dimensional random vector in a range of large-scale computational applications, including data assimilation, ensemble prediction, sensitivity analysis, and predictability studies. In each of these applications, numerical evolution of the covariance matrix of the random state plays a central role, because this matrix is used to quantify uncertainty in the state of the dynamical system. Since atmospheric and ocean dynamics are nonlinear, there is no closed evolution equation for the covariance matrix, nor for the mean state. Therefore approximate evolution equations must be used. This article studies theoretical properties of the evolution equations for the mean state and covariance matrix that arise in the second-moment closure approximation (third- and higher-order moment discard). This approximation was introduced by EPSTEIN [1969] in an early effort to introduce a stochastic element into deterministic weather forecasting, and was studied further by FLEMING [1971a,b], EPSTEIN and PITCHER [1972], and PITCHER [1977], also in the context of atmospheric predictability. It has since fallen into disuse, with a simpler one being used in current large-scale applications. The theoretical results of this article make a case that this approximation should be reconsidered for use in large-scale applications, however, because the second moment closure equations possess a property of energetic consistency that the approximate equations now in common use do not possess. A number of properties of solutions of the second-moment closure equations that result from this energetic consistency will be established.

Efficient solution of the Wigner-Liouville equation using a spectral decomposition of the force field

NASA Astrophysics Data System (ADS)

Van de Put, Maarten L.; Sorée, Bart; Magnus, Wim

2017-12-01

The Wigner-Liouville equation is reformulated using a spectral decomposition of the classical force field instead of the potential energy. The latter is shown to simplify the Wigner-Liouville kernel both conceptually and numerically as the spectral force Wigner-Liouville equation avoids the numerical evaluation of the highly oscillatory Wigner kernel which is nonlocal in both position and momentum. The quantum mechanical evolution is instead governed by a term local in space and non-local in momentum, where the non-locality in momentum has only a limited range. An interpretation of the time evolution in terms of two processes is presented; a classical evolution under the influence of the averaged driving field, and a probability-preserving quantum-mechanical generation and annihilation term. Using the inherent stability and reduced complexity, a direct deterministic numerical implementation using Chebyshev and Fourier pseudo-spectral methods is detailed. For the purpose of illustration, we present results for the time-evolution of a one-dimensional resonant tunneling diode driven out of equilibrium.

Exact harmonic solutions to Guyer-Krumhansl-type equation and application to heat transport in thin films

NASA Astrophysics Data System (ADS)

Zhukovsky, K.; Oskolkov, D.

2018-03-01

A system of hyperbolic-type inhomogeneous differential equations (DE) is considered for non-Fourier heat transfer in thin films. Exact harmonic solutions to Guyer-Krumhansl-type heat equation and to the system of inhomogeneous DE are obtained in Cauchy- and Dirichlet-type conditions. The contribution of the ballistic-type heat transport, of the Cattaneo heat waves and of the Fourier heat diffusion is discussed and compared with each other in various conditions. The application of the study to the ballistic heat transport in thin films is performed. Rapid evolution of the ballistic quasi-temperature component in low-dimensional systems is elucidated and compared with slow evolution of its diffusive counterpart. The effect of the ballistic quasi-temperature component on the evolution of the complete quasi-temperature is explored. In this context, the influence of the Knudsen number and of Cauchy- and Dirichlet-type conditions on the evolution of the temperature distribution is explored. The comparative analysis of the obtained solutions is performed.

Numerical modelling of the Madison Dynamo Experiment.

NASA Astrophysics Data System (ADS)

Bayliss, R. A.; Wright, J. C.; Forest, C. B.; O'Connell, R.; Truitt, J. L.

2000-10-01

Growth, saturation and turbulent evolution of the Madison dynamo experiment is investigated numerically using a newly developed 3-D pseudo-spectral simulation of the MHD equations; results of the simulations will be compared to the experimental results obtained from the experiment. The code, Dynamo, is in Fortran90 and allows for full evolution of the magnetic and velocity fields. The induction equation governing B and the Navier-Stokes equation governing V are solved. The code uses a spectral representation via spherical harmonic basis functions of the vector fields in longitude and latitude, and finite differences in the radial direction. The magnetic field evolution has been benchmarked against the laminar kinematic dynamo predicted by M.L. Dudley and R.W. James (M.L. Dudley and R.W. James, Time-dependant kinematic dynamos with stationary flows, Proc. R. Soc. Lond. A 425, p. 407 (1989)). Initial results on magnetic field saturation, generated by the simultaneous evolution of magnetic and velocity fields be presented using a variety of mechanical forcing terms.

NLO evolution of color dipoles in N=4 SYM

DOE PAGES

Chirilli, Giovanni A.; Balitsky, Ian

2009-07-04

Here, high-energy behavior of amplitudes in a gauge theory can be reformulated in terms of the evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the conformally invariant BK equation for the evolution of color dipoles. In QCD, the next-to-leading order BK equation has both conformal and non-conformal parts, the latter providing the running of the coupling constant. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformalmore » $${\\cal N}$$=4 SYM theory. We define the "composite dipole operator" with the rapidity cutoff preserving conformal invariance.« less

The limitation and applicability of Musher-Sturman equation to two dimensional lower hybrid wave collapse

NASA Technical Reports Server (NTRS)

Tam, Sunny W. Y.; Chang, Tom

1995-01-01

The existence of localized regions of intense lower hybrid waves in the auroral ionosphere recently observed by rocket and satellite experiments can be understood by the study of a non-linear two-timescale coupling process. In this Letter, we demonstrate that the leading non-linear term in the standard Musher-Sturman equation vanishes identically in strict two-dimensions (normal to the magnetic field). Instead, the new two-dimensional equation is characterized by a much weaker non-linear term which arises from the ponderomotive force perpendicular to the magnetic field, particularly that due to the ions. The old and new equations are compared by means of time-evolution calculations of wave fields. The results exhibit a remarkable difference in the evolution of the waves as governed by the two equations. Such dissimilar outcomes motivate our investigation of the limitation of Musher-Sturman equation in quasi-two-dimensions. Only within all these limits can Musher-Sturman equation adequately describe the collapse of lower hybrid waves.

On mechanical mechanism of damage evolution in articular cartilage.

PubMed

Men, Yu-Tao; Jiang, Yan-Long; Chen, Ling; Zhang, Chun-Qiu; Ye, Jin-Duo

2017-09-01

Superficial lesions of cartilage are the direct indication of osteoarthritis. To investigate the mechanical mechanism of cartilage with micro-defect under external loading, a new plain strain numerical model with micro-defect was proposed and damage evolution progression in cartilage over time has been simulated, the parameter were studied including load style, velocity of load and degree of damage. The new model consists of the hierarchical structure of cartilage and depth-dependent arched fibers. The numerical results have shown that not only damage of the cartilage altered the distribution of the stress but also matrix and fiber had distinct roles in affecting cartilage damage, and damage in either matrix or fiber could promote each other. It has been found that the superficial cracks in cartilage spread preferentially along the tangent direction of the fibers. It is the arched distribution form of fibers that affects the crack spread of cartilage, which has been verified by experiment. During the process of damage evolution, its extension direction and velocity varied constantly with the damage degree. The rolling load could cause larger stress and strain than sliding load. Strain values of the matrix initially increased and then decreased gradually with the increase of velocity, and velocity had a greater effect on matrix than fibers. Damage increased steadily before reaching 50%, sharply within 50 to 85%, and smoothly and slowly after 85%. The finding of the paper may help to understand the mechanical mechanism why the cracks in cartilage spread preferentially along the tangent direction of the fibers. Copyright © 2017 Elsevier B.V. All rights reserved.

Micromechanical Fatigue Visco-Damage Model for Short Glass Fiber Reinforced Polyamide-66

NASA Astrophysics Data System (ADS)

Despringre, N.; Chemisky, Y.; Robert, G.; Meraghni, F.

This work presents a micromechanical fatigue damage model developed for short glass fiber reinforced PA66. It has been developed to predict the high cycle fatigue behavior of PA66/GF30. The model is based on an extended Mori-Tanaka method which includes coated inclusions, matrix viscoelasticity and the evolution of micro-scale damage. The developed model accounts for the nonlinear matrix viscoelasticity and the reinforcement orientation. The description of the damage processes is based on the experimental investigation of damage mechanisms previously performed through in-situ SEM tests and X-ray micro-computed tomography observations. Damage chronologies have been proposed involving three different processes: interface debonding/coating, matrix micro-cracking and fiber breakages. Their occurrence strongly depends on the microstructure and the relative humidity. Each damage mechanism is introduced through an evolution law coupled to local stress fields. The developed model is implemented using a UMAT subroutine. Its experimental validation is achieved under stress or strain controlled fatigue tests.

Modeling property evolution of container materials used in nuclear waste storage

NASA Astrophysics Data System (ADS)

Li, Dongsheng; Garmestani, Hamid; Khaleel, Moe; Sun, Xin

2010-03-01

Container materials under irradiation for a long time will raise high energy in the structure to generate critical structural damage. This study investigated what kind of mesoscale microstructure will be more resistant to radiation damage. Mechanical properties evolution during irradiation was modeled using statistical continuum mechanics. Preliminary results also showed how to achieve the desired microstructure with higher resistance to radiation.

Influence of sweeping detonation-wave loading on damage evolution during spallation loading of tantalum in both a planar and curved geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gray, George Thompson III; Hull, Lawrence Mark; Livescu, Veronica

Widespread research over the past five decades has provided a wealth of experimental data and insight concerning the shock hardening, damage evolution, and the spallation response of materials subjected to square-topped shock-wave loading profiles. However, fewer quantitative studies have been conducted on the effect of direct, in-contact, high explosive (HE)-driven Taylor wave (unsupported shocks) loading on the shock hardening, damage evolution, or spallation response of materials. Systematic studies quantifying the effect of sweeping-detonation wave loading are yet sparser. In this study, the damage evolution and spallation response of Ta is shown to be critically dependent on the peak shock stress,more » the geometry of the sample (flat or curved plate geometry), and the shock obliquity during sweeping-detonation-wave shock loading. Sweepingwave loading in the flat-plate geometry is observed to: a) yield a lower spall strength than previously documented for 1-D supported-shock-wave loading, b) exhibit increased shock hardening as a function of increasing obliquity, and c) lead to an increased incidence of deformation twin formation with increasing shock obliquity. Sweeping-wave loading of a 10 cm radius curved Ta plate is observed to: a) lead to an increase in the shear stress as a function of increasing obliquity, b) display a more developed level of damage evolution, extensive voids and coalescence, and lower spall strength with obliquity in the curved plate than seen in the flat-plate sweeping-detonation wave loading for an equivalent HE loading, and c) no increased propensity for deformation twin formation with increasing obliquity as seen in the flat-plate geometry. The overall observations comparing and contrasting the flat versus curved sweeping-wave spall experiments with 1D loaded spallation behavior suggests a coupled influence of obliquity and geometry on dynamic shock-induced damage evolution and spall strength. Coupled experimental and modeling research to quantify the combined effects of sweeping-wave loading with increasingly complex sample geometries on the shockwave response of materials is clearly crucial to providing the basis for developing and thereafter validation of predictive modeling capability.« less

Decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio.

PubMed

Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan

2016-10-01

A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e., the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a one-dimensional shock tube simulation is performed. The numerical results agree with the analytical solutions very well.

Stabilization and control of distributed systems with time-dependent spatial domains

NASA Technical Reports Server (NTRS)

Wang, P. K. C.

1990-01-01

This paper considers the problem of the stabilization and control of distributed systems with time-dependent spatial domains. The evolution of the spatial domains with time is described by a finite-dimensional system of ordinary differential equations, while the distributed systems are described by first-order or second-order linear evolution equations defined on appropriate Hilbert spaces. First, results pertaining to the existence and uniqueness of solutions of the system equations are presented. Then, various optimal control and stabilization problems are considered. The paper concludes with some examples which illustrate the application of the main results.

Asymptotic Bounds for Solutions to a System of Damped Integrodifferential Equations of Electromagnetic Theory.

DTIC Science & Technology

1979-05-28

of integrodiffereiTaT~- equations governs the evolution of the components of the electric displacement field in a simple class of rigid holohedral...vacuum so that j — C and J~ — c E , H = B. In0 [3] and [4] this author has treated the evolution equations associated with the Maxwell—Hopkinsofl...F .~~~~~~‘ r - — ~~~~~ ’~~~ “~ I I be viewed as a linearized version of a more general theory introduced by Volterra in 1912 [5] to treat the case

A Factorization Approach to the Linear Regulator Quadratic Cost Problem

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

A factorization approach to the linear regulator quadratic cost problem is developed. This approach makes some new connections between optimal control, factorization, Riccati equations and certain Wiener-Hopf operator equations. Applications of the theory to systems describable by evolution equations in Hilbert space and differential delay equations in Euclidean space are presented.

Single evolution equation in a light-matter pairing system

NASA Astrophysics Data System (ADS)

Bugaychuk, S.; Tobisch, E.

2018-03-01

The coupled system including wave mixing and nonlinear dynamics of a nonlocal optical medium is usually studied (1) numerically, with the medium being regarded as a black box, or (2) experimentally, making use of some empirical assumptions. In this paper we deduce for the first time a single evolution equation describing the dynamics of the pairing system as a holistic complex. For a non-degenerate set of parameters, we obtain the nonlinear Schrödinger equation with coefficients being written out explicitly. Analytical solutions of this equation can be experimentally realized in any photorefractive medium, e.g. in photorefractive, liquid or photonic crystals. For instance, a soliton-like solution can be used in dynamical holography for designing an artificial grating with maximal amplification of an image.

The theoretical and experimental study of a material structure evolution in gigacyclic fatigue regime

NASA Astrophysics Data System (ADS)

Plekhov, Oleg; Naimark, Oleg; Narykova, Maria; Kadomtsev, Andrey; Betekhtin, Vladimir

2015-10-01

The work is devoted to the study of the metal structure evolution under gigacyclic fatigue (VHCF) regime. The study of the mechanical properties of the samples (Armco iron) with different state of life time existing was carried out on the base of the acoustic resonance method. The damage accumulation (porosity of the samples) was studied by the hydrostatic weighing method. A statistical model of damage accumulation was proposed in order to describe the damage accumulation process. The model describes the influence of the sample surface on the location of fatigue crack initiation.

The spectrum of density perturbations in an expanding universe

NASA Technical Reports Server (NTRS)

Silk, J.

1974-01-01

The basic dynamic equations that govern the evolution of perturbations in a Friedmann-Lemaitre universe are derived. General solutions describing the evolution of adiabatic perturbations in the density of matter are obtained, and the choice of the appropriate initial conditions is examined. The various perturbation modes are compared, and the effects of decoupling on the perturbation spectrum are studied. The scheme used to follow the evolution of density perturbations through decoupling is based on an extension of the Eddington approximation to the radiative transfer equation, and is strictly valid in both optically thick and thin limits.

Physical scales in the Wigner-Boltzmann equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nedjalkov, M., E-mail: mixi@iue.tuwien.ac.at; Selberherr, S.; Ferry, D.K.

2013-01-15

The Wigner-Boltzmann equation provides the Wigner single particle theory with interactions with bosonic degrees of freedom associated with harmonic oscillators, such as phonons in solids. Quantum evolution is an interplay of two transport modes, corresponding to the common coherent particle-potential processes, or to the decoherence causing scattering due to the oscillators. Which evolution mode will dominate depends on the scales of the involved physical quantities. A dimensionless formulation of the Wigner-Boltzmann equation is obtained, where these scales appear as dimensionless strength parameters. A notion called scaling theorem is derived, linking the strength parameters to the coupling with the oscillators. Itmore » is shown that an increase of this coupling is equivalent to a reduction of both the strength of the electric potential, and the coherence length. Secondly, the existence of classes of physically different, but mathematically equivalent setups of the Wigner-Boltzmann evolution is demonstrated. - Highlights: Black-Right-Pointing-Pointer Dimensionless parameters determine the ratio of quantum or classical WB evolution. Black-Right-Pointing-Pointer The scaling theorem evaluates the decoherence effect due to scattering. Black-Right-Pointing-Pointer Evolution processes are grouped into classes of equivalence.« less

Nada: A new code for studying self-gravitating tori around black holes

NASA Astrophysics Data System (ADS)

Montero, Pedro J.; Font, José A.; Shibata, Masaru

2008-09-01

We present a new two-dimensional numerical code called Nada designed to solve the full Einstein equations coupled to the general relativistic hydrodynamics equations. The code is mainly intended for studies of self-gravitating accretion disks (or tori) around black holes, although it is also suitable for regular spacetimes. Concerning technical aspects the Einstein equations are formulated and solved in the code using a formulation of the standard 3+1 Arnowitt-Deser-Misner canonical formalism system, the so-called Baumgarte-Shapiro Shibata-Nakamura approach. A key feature of the code is that derivative terms in the spacetime evolution equations are computed using a fourth-order centered finite difference approximation in conjunction with the Cartoon method to impose the axisymmetry condition under Cartesian coordinates (the choice in Nada), and the puncture/moving puncture approach to carry out black hole evolutions. Correspondingly, the general relativistic hydrodynamics equations are written in flux-conservative form and solved with high-resolution, shock-capturing schemes. We perform and discuss a number of tests to assess the accuracy and expected convergence of the code, namely, (single) black hole evolutions, shock tubes, and evolutions of both spherical and rotating relativistic stars in equilibrium, the gravitational collapse of a spherical relativistic star leading to the formation of a black hole. In addition, paving the way for specific applications of the code, we also present results from fully general relativistic numerical simulations of a system formed by a black hole surrounded by a self-gravitating torus in equilibrium.

A novel sensitivity-based method for damage detection of structures under unknown periodic excitations

NASA Astrophysics Data System (ADS)

Naseralavi, S. S.; Salajegheh, E.; Fadaee, M. J.; Salajegheh, J.

2014-06-01

This paper presents a technique for damage detection in structures under unknown periodic excitations using the transient displacement response. The method is capable of identifying the damage parameters without finding the input excitations. We first define the concept of displacement space as a linear space in which each point represents displacements of structure under an excitation and initial condition. Roughly speaking, the method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering this novel geometrical viewpoint, an equation called kernel parallelization equation (KPE) is derived for damage detection under unknown periodic excitations and a sensitivity-based algorithm for solving KPE is proposed accordingly. The method is evaluated via three case studies under periodic excitations, which confirm the efficiency of the proposed method.

Void Formation during Diffusion - Two-Dimensional Approach

NASA Astrophysics Data System (ADS)

Wierzba, Bartek

2016-06-01

The final set of equations defining the interdiffusion process in solid state is presented. The model is supplemented by vacancy evolution equation. The competition between the Kirkendall shift, backstress effect and vacancy migration is considered. The proper diffusion flux based on the Nernst-Planck formula is proposed. As a result, the comparison of the experimental and calculated evolution of the void formation in the Fe-Pd diffusion couple is shown.

Instability of isolated planar shock waves

DTIC Science & Technology

2007-06-07

Note that multi-mode perturbations can be treated by the inclusion of additional terms in Eq. (4), but owing to the linear independence of the... Volterra equation Figure 4 shows five examples of the evolution of the amplitude of a linear sinusoidal perturbation on a shock front obtained by...showing the evolution of the amplitude of a linear sinusoidal perturbation on a shock front obtained by numerically solving the Volterra equation in

Evolution equations for connected and disconnected sea parton distributions

NASA Astrophysics Data System (ADS)

Liu, Keh-Fei

2017-08-01

It has been revealed from the path-integral formulation of the hadronic tensor that there are connected sea and disconnected sea partons. The former is responsible for the Gottfried sum rule violation primarily and evolves the same way as the valence. Therefore, the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations can be extended to accommodate them separately. We discuss its consequences and implications vis-á-vis lattice calculations.

The relativistic equations of stellar structure and evolution. Stars with degenerate neutron cores. 1: Structure of equilibrium models

NASA Technical Reports Server (NTRS)

Thorne, K. S.; Zytkow, A. N.

1976-01-01

The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general relativistic version of the mixing-length formalism for convection is presented. Finally, it is argued that in previous work on spherical systems general relativity theorists have identified the wrong quantity as "total mass-energy inside radius r."

Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cruz, Hans, E-mail: hans@ciencias.unam.mx; Schuch, Dieter; Castaños, Octavio, E-mail: ocasta@nucleares.unam.mx

2015-09-15

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.

Efficient determination of the Markovian time-evolution towards a steady-state of a complex open quantum system

NASA Astrophysics Data System (ADS)

Jonsson, Thorsteinn H.; Manolescu, Andrei; Goan, Hsi-Sheng; Abdullah, Nzar Rauf; Sitek, Anna; Tang, Chi-Shung; Gudmundsson, Vidar

2017-11-01

Master equations are commonly used to describe time evolution of open systems. We introduce a general computationally efficient method for calculating a Markovian solution of the Nakajima-Zwanzig generalized master equation. We do so for a time-dependent transport of interacting electrons through a complex nano scale system in a photon cavity. The central system, described by 120 many-body states in a Fock space, is weakly coupled to the external leads. The efficiency of the approach allows us to place the bias window defined by the external leads high into the many-body spectrum of the cavity photon-dressed states of the central system revealing a cascade of intermediate transitions as the system relaxes to a steady state. The very diverse relaxation times present in the open system, reflecting radiative or non-radiative transitions, require information about the time evolution through many orders of magnitude. In our approach, the generalized master equation is mapped from a many-body Fock space of states to a Liouville space of transitions. We show that this results in a linear equation which is solved exactly through an eigenvalue analysis, which supplies information on the steady state and the time evolution of the system.

Quasi-Newton methods for parameter estimation in functional differential equations

NASA Technical Reports Server (NTRS)

Brewer, Dennis W.

1988-01-01

A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.

The Davey-Stewartson Equation on the Half-Plane

NASA Astrophysics Data System (ADS)

Fokas, A. S.

2009-08-01

The Davey-Stewartson (DS) equation is a nonlinear integrable evolution equation in two spatial dimensions. It provides a multidimensional generalisation of the celebrated nonlinear Schrödinger (NLS) equation and it appears in several physical situations. The implementation of the Inverse Scattering Transform (IST) to the solution of the initial-value problem of the NLS was presented in 1972, whereas the analogous problem for the DS equation was solved in 1983. These results are based on the formulation and solution of certain classical problems in complex analysis, namely of a Riemann Hilbert problem (RH) and of either a d-bar or a non-local RH problem respectively. A method for solving the mathematically more complicated but physically more relevant case of boundary-value problems for evolution equations in one spatial dimension, like the NLS, was finally presented in 1997, after interjecting several novel ideas to the panoply of the IST methodology. Here, this method is further extended so that it can be applied to evolution equations in two spatial dimensions, like the DS equation. This novel extension involves several new steps, including the formulation of a d-bar problem for a sectionally non-analytic function, i.e. for a function which has different non-analytic representations in different domains of the complex plane. This, in addition to the computation of a d-bar derivative, also requires the computation of the relevant jumps across the different domains. This latter step has certain similarities (but is more complicated) with the corresponding step for those initial-value problems in two dimensions which can be solved via a non-local RH problem, like KPI.

Hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit: General formalism and perturbations analysis

NASA Astrophysics Data System (ADS)

Suárez, Abril; Chavanis, Pierre-Henri

2015-07-01

Using a generalization of the Madelung transformation, we derive the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit. We consider a complex self-interacting scalar field with a λ |φ |4 potential. We study the evolution of the spatially homogeneous background in the fluid representation and derive the linearized equations describing the evolution of small perturbations in a static and in an expanding Universe. We compare the results with simplified models in which the gravitational potential is introduced by hand in the Klein-Gordon equation, and assumed to satisfy a (generalized) Poisson equation. Nonrelativistic hydrodynamic equations based on the Schrödinger-Poisson equations or on the Gross-Pitaevskii-Poisson equations are recovered in the limit c →+∞. We study the evolution of the perturbations in the matter era using the nonrelativistic limit of our formalism. Perturbations whose wavelength is below the Jeans length oscillate in time while perturbations whose wavelength is above the Jeans length grow linearly with the scale factor as in the cold dark matter model. The growth of perturbations in the scalar field model is substantially faster than in the cold dark matter model. When the wavelength of the perturbations approaches the cosmological horizon (Hubble length), a relativistic treatment is mandatory. In that case, we find that relativistic effects attenuate or even prevent the growth of perturbations. This paper exposes the general formalism and provides illustrations in simple cases. Other applications of our formalism will be considered in companion papers.

Generalized Landau Equation for a System with a Self-Consistent Mean Field - Derivation from an N-Particle Liouville Equation

NASA Astrophysics Data System (ADS)

Kandrup, H.

1981-02-01

Assume that the evolution of a system is determined by an N-particle Liouville equation. Suppose, moreover, that the particles which compose the system interact via a long range force like gravity so that the system will be spatially inhomogeneous. In this case, the mean force acting upon a test particle does not vanish, so that one wishes to isolate a self-consistent mean field and distinguish its "systematic" effects from the effects of "fluctuations." This is done here. The time-dependent projection operator formalism of Willis and Picard is used to obtain an exact equation for the time evolution of an appropriately defined one-particle probability density. If one implements the assumption that the "fluctuation" time scale is much shorter than both the relaxation and dynamical time scales, this exact equation can be approximated as a closed Markovian equation. In the limiting case of spatial homogeneity, one recovers precisely the standard Landau equation, which is customarily derived by a stochastic binary-encounter argument. This equation is contrasted with the standard heuristic equation for a mean field theory, as formulated for a Newtonian r-1 gravitational potential in stellar dynamics.

The Arrow of Time in the Collapse of Collisionless Self-gravitating Systems: Non-validity of the Vlasov-Poisson Equation during Violent Relaxation

NASA Astrophysics Data System (ADS)

Beraldo e Silva, Leandro; de Siqueira Pedra, Walter; Sodré, Laerte; Perico, Eder L. D.; Lima, Marcos

2017-09-01

The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is traditionally assumed that this evolution is governed by the Vlasov-Poisson equation, in which case entropy must be conserved. We run N-body simulations of isolated self-gravitating systems, using three simulation codes, NBODY-6 (direct summation without softening), NBODY-2 (direct summation with softening), and GADGET-2 (tree code with softening), for different numbers of particles and initial conditions. At each snapshot, we estimate the Shannon entropy of the distribution function with three different techniques: Kernel, Nearest Neighbor, and EnBiD. For all simulation codes and estimators, the entropy evolution converges to the same limit as N increases. During violent relaxation, the entropy has a fast increase followed by damping oscillations, indicating that violent relaxation must be described by a kinetic equation other than the Vlasov-Poisson equation, even for N as large as that of astronomical structures. This indicates that violent relaxation cannot be described by a time-reversible equation, shedding some light on the so-called “fundamental paradox of stellar dynamics.” The long-term evolution is well-described by the orbit-averaged Fokker-Planck model, with Coulomb logarithm values in the expected range 10{--}12. By means of NBODY-2, we also study the dependence of the two-body relaxation timescale on the softening length. The approach presented in the current work can potentially provide a general method for testing any kinetic equation intended to describe the macroscopic evolution of N-body systems.

Local structural change in zircon following radiation damage accumulation. Observation by 29Si nuclear magnetic resonance

NASA Astrophysics Data System (ADS)

Farnan, I.; Trachenko, K.

2003-04-01

29Si nuclear magnetic resonance (NMR) is a one of the most useful probes of the local structure of silicates. One of the results of recent studies of naturally radiation damaged zircons is that there is an evolution of the local structure in both crystalline and amorphous fractions of partially metamict zircon as a function of accumulated α-dose. We have examined the evolution of this local structure within the framework of several models of damage accumulation. The total number of displaced atoms produced per α-decay as function of accumulated dose, as measured by NMR, is not consistent with the idea of multiple overlap events being responsible for the evolution of the total damaged fraction. However, increased connectivity in the damaged region as the number of α-events increases is correlated to the degree of cascade overlap. The results of large scale atomistic (MD) simulations of heavy nuclei recoils at realistic energies (70keV) are consistent with the NMR quantification and also with TEM estimates of the diameters of damaged regions. The local heterogeneity (density and bonding) in the damaged area in the simulations is consistent with the existence of connected silicate tetrahedra. Detailed experiments on the annealing of damaged zircons at 500 and 600^oC have been performed. These show that a significant energetic barrier to the recrystallisation exists at these temperatures once a small fraction of damaged material has been recrystallised. This correlates well with the degree of cascade overlap. Indicating that the more connected SiO_4 tetrahedra present this barrier. A sample with very little cascade overlap can be annealed to ˜97% crystallinity at these temperatures.

Tolerance to deer herbivory and resistance to insect herbivores in the common evening primrose (Oenothera biennis).

PubMed

Puentes, A; Johnson, M T J

2016-01-01

The evolution of plant defence in response to herbivory will depend on the fitness effects of damage, availability of genetic variation and potential ecological and genetic constraints on defence. Here, we examine the potential for evolution of tolerance to deer herbivory in Oenothera biennis while simultaneously considering resistance to natural insect herbivores. We examined (i) the effects of deer damage on fitness, (ii) the presence of genetic variation in tolerance and resistance, (iii) selection on tolerance, (iv) genetic correlations with resistance that could constrain evolution of tolerance and (v) plant traits that might predict defence. In a field experiment, we simulated deer damage occurring early and late in the season, recorded arthropod abundances, flowering phenology and measured growth rate and lifetime reproduction. Our study showed that deer herbivory has a negative effect on fitness, with effects being more pronounced for late-season damage. Selection acted to increase tolerance to deer damage, yet there was low and nonsignificant genetic variation in this trait. In contrast, there was substantial genetic variation in resistance to insect herbivores. Resistance was genetically uncorrelated with tolerance, whereas positive genetic correlations in resistance to insect herbivores suggest there exists diffuse selection on resistance traits. In addition, growth rate and flowering time did not predict variation in tolerance, but flowering phenology was genetically correlated with resistance. Our results suggest that deer damage has the potential to exert selection because browsing reduces plant fitness, but limited standing genetic variation in tolerance is expected to constrain adaptive evolution in O. biennis. © 2015 European Society For Evolutionary Biology. Journal of Evolutionary Biology © 2015 European Society For Evolutionary Biology.

Solution of the Fokker-Planck equation in a wind turbine array boundary layer

NASA Astrophysics Data System (ADS)

Melius, Matthew S.; Tutkun, Murat; Cal, Raúl Bayoán

2014-07-01

Hot-wire velocity signals from a model wind turbine array boundary layer flow wind tunnel experiment are analyzed. In confirming Markovian properties, a description of the evolution of the probability density function of velocity increments via the Fokker-Planck equation is attained. Solution of the Fokker-Planck equation is possible due to the direct computation of the drift and diffusion coefficients from the experimental measurement data which were acquired within the turbine canopy. A good agreement is observed in the probability density functions between the experimental data and numerical solutions resulting from the Fokker-Planck equation, especially in the far-wake region. The results serve as a tool for improved estimation of wind velocity within the array and provide evidence that the evolution of such a complex and turbulent flow is also governed by a Fokker-Planck equation at certain scales.

Nonlinear Waves In A Stenosed Elastic Tube Filled With Viscous Fluid: Forced Perturbed Korteweg-De Vries Equation

NASA Astrophysics Data System (ADS)

Gaik*, Tay Kim; Demiray, Hilmi; Tiong, Ong Chee

In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the pro pagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By intro ducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the small-ness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.

A damage mechanics based general purpose interface/contact element

NASA Astrophysics Data System (ADS)

Yan, Chengyong

Most of the microelectronics packaging structures consist of layered substrates connected with bonding materials, such as solder or epoxy. Predicting the thermomechanical behavior of these multilayered structures is a challenging task in electronic packaging engineering. In a layered structure the most complex part is always the interfaces between the strates. Simulating the thermo-mechanical behavior of such interfaces, is the main theme of this dissertation. The most commonly used solder material, Pb-Sn alloy, has a very low melting temperature 180sp°C, so that the material demonstrates a highly viscous behavior. And, creep usually dominates the failure mechanism. Hence, the theory of viscoplasticity is adapted to describe the constitutive behavior. In a multilayered assembly each layer has a different coefficient of thermal expansion. Under thermal cycling, due to heat dissipated from circuits, interfaces and interconnects experience low cycle fatigue. Presently, the state-of-the art damage mechanics model used for fatigue life predictions is based on Kachanov (1986) continuum damage model. This model uses plastic strain as a damage criterion. Since plastic strain is a stress path dependent value, the criterion does not yield unique damage values for the same state of stress. In this dissertation a new damage evolution equation based on the second law of thermodynamic is proposed. The new criterion is based on the entropy of the system and it yields unique damage values for all stress paths to the final state of stress. In the electronics industry, there is a strong desire to develop fatigue free interconnections. The proposed interface/contact element can also simulate the behavior of the fatigue free Z-direction thin film interconnections as well as traditional layered interconnects. The proposed interface element can simulate behavior of a bonded interface or unbonded sliding interface, also called contact element. The proposed element was verified against laboratory test data presented in the literature. The results demonstrate that the proposed element and the damage law perform very well. The most important scientific contribution of this dissertation is the proposed damage criterion based on second law of thermodynamic and entropy of the system. The proposed general purpose interface/contact element is another contribution of this research. Compared to the previous adhoc interface elements proposed in the literature, the new one is, much more powerful and includes creep, plastic deformations, sliding, temperature, damage, cyclic behavior and fatigue life in a unified formulation.

Disruption avoidance by means of electron cyclotron waves

NASA Astrophysics Data System (ADS)

Esposito, B.; Granucci, G.; Maraschek, M.; Nowak, S.; Lazzaro, E.; Giannone, L.; Gude, A.; Igochine, V.; McDermott, R.; Poli, E.; Reich, M.; Sommer, F.; Stober, J.; Suttrop, W.; Treutterer, W.; Zohm, H.; ASDEX Upgrade, the; FTU Teams

2011-12-01

Disruptions are very challenging to ITER operation as they may cause damage to plasma facing components due to direct plasma heating, forces on structural components due to halo and eddy currents and the production of runaway electrons. Electron cyclotron (EC) waves have been demonstrated as a tool for disruption avoidance by a large set of recent experiments performed in ASDEX Upgrade and FTU using various disruption types, plasma operating scenarios and power deposition locations. The technique is based on the stabilization of magnetohydrodynamic (MHD) modes (mainly m/n = 2/1) through the localized injection of EC power on the resonant surface. This paper presents new results obtained in ASDEX Upgrade regarding stable operation above the Greenwald density achieved after avoidance of density limit disruptions by means of ECRH and suitable density feedback control (L-mode ohmic plasmas, Ip = 0.6 MA, Bt = 2.5 T) and NTM-driven disruptions at high-β limit delayed/avoided by means of both co-current drive (co-ECCD) and pure heating (ECRH) with power <=1.7 MW (H-mode NBI-heated plasmas, PNBI ~ 7.5 MW, Ip = 1 MA, Bt = 2.1 T, q95 ~ 3.6). The localized perpendicular injection of ECRH/ECCD onto a resonant surface leads to the delay and/or complete avoidance of disruptions. The experiments indicate the existence of a power threshold for mode stabilization to occur. An analysis of the MHD mode evolution using the generalized Rutherford equation coupled to the frequency and phase evolution equations shows that control of the modes is due to EC heating close to the resonant surface. The ECRH contribution (Δ'H term) is larger than the co-ECCD one in the initial and more important phase when the discharge is 'saved'. Future research and developments of the disruption avoidance technique are also discussed.

Solution Methods for Certain Evolution Equations

NASA Astrophysics Data System (ADS)

Vega-Guzman, Jose Manuel

Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. Such explicit construction is possible due to the relation between the diffusion-type equation studied in the first part and the time-dependent Schrodinger equation. A modication of the radiation field operators for squeezed photons in a perfect cavity is also suggested with the help of a nonstandard solution of Heisenberg's equation of motion.

Fatigue damage monitoring for basalt fiber reinforced polymer composites using acoustic emission technique

NASA Astrophysics Data System (ADS)

Wang, Wentao; Li, Hui; Qu, Zhi

2012-04-01

Basalt fiber reinforced polymer (BFRP) is a structural material with superior mechanical properties. In this study, unidirectional BFRP laminates with 14 layers are made with the hand lay-up method. Then, the acoustic emission technique (AE) combined with the scanning electronic microscope (SEM) technique is employed to monitor the fatigue damage evolution of the BFRP plates in the fatigue loading tests. Time-frequency analysis using the wavelet transform technique is proposed to analyze the received AE signal instead of the peak frequency method. A comparison between AE signals and SEM images indicates that the multi-frequency peaks picked from the time-frequency curves of AE signals reflect the accumulated fatigue damage evolution and fatigue damage patterns. Furthermore, seven damage patterns, that is, matrix cracking, delamination, fiber fracture and their combinations, are identified from the time-frequency curves of the AE signals.

Acoustic Emission Analysis of Damage during Compressive Deformation of Amorphous Zr-Based Foams with Aligned, Elongated Pores

NASA Astrophysics Data System (ADS)

Cox, Marie E.; Dunand, David C.

2013-07-01

Acoustic emission methods are used to investigate the evolution of internal microfractural damage during uniaxial compression of amorphous Zr-based foams with aligned, elongated pores. The foams are fabricated by means of densifying a blend of crystalline W powders and amorphous Zr-based powders with two oxygen contents (0.078 and 0.144 wt pct) by warm equal channel angular extrusion, followed by dissolution of the elongated W phase from the fully densified amorphous matrix. For the high-oxygen foams, prior powder boundaries in the amorphous struts promote damage that accumulates during compression, resulting in energy-absorbing properties comparable with the low-oxygen foams without stress-concentrating powder boundaries. The influence of pore orientation on the evolution of microfracture damage and the ability of the foams to accumulate damage without catastrophic failure is also investigated: pores oriented from 24 to 68 deg to the loading direction promote wall bending, resulting in foams with more diffuse damage and better energy-absorbing properties.

Physical scales in the Wigner–Boltzmann equation

PubMed Central

Nedjalkov, M.; Selberherr, S.; Ferry, D.K.; Vasileska, D.; Dollfus, P.; Querlioz, D.; Dimov, I.; Schwaha, P.

2013-01-01

The Wigner–Boltzmann equation provides the Wigner single particle theory with interactions with bosonic degrees of freedom associated with harmonic oscillators, such as phonons in solids. Quantum evolution is an interplay of two transport modes, corresponding to the common coherent particle-potential processes, or to the decoherence causing scattering due to the oscillators. Which evolution mode will dominate depends on the scales of the involved physical quantities. A dimensionless formulation of the Wigner–Boltzmann equation is obtained, where these scales appear as dimensionless strength parameters. A notion called scaling theorem is derived, linking the strength parameters to the coupling with the oscillators. It is shown that an increase of this coupling is equivalent to a reduction of both the strength of the electric potential, and the coherence length. Secondly, the existence of classes of physically different, but mathematically equivalent setups of the Wigner–Boltzmann evolution is demonstrated. PMID:23504194

Stochastic modeling of mode interactions via linear parabolized stability equations

NASA Astrophysics Data System (ADS)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

The breakdown of the weakly-nonlinear regime for kinetic instabilities

NASA Astrophysics Data System (ADS)

Sanz-Orozco, David; Berk, Herbert; Wang, Ge

2017-10-01

The evolution of marginally-unstable waves that interact resonantly with populations of energetic particles is governed by a well-known cubic integro-differential equation for the mode amplitude. One of the outcomes predicted by the equation is the so-called ``explosive'' regime, where the amplitude grows indefinitely, eventually taking the equation outside of its domain of validity. Beyond this point, only full Vlasov simulations will accurately describe the evolution of the mode amplitude. In this work, we study the breakdown of the cubic equation in detail. We find that, while the cubic equation is still valid, the distribution function of the energetic particles locally flattens or ``folds'' in phase space. This feature is unexpected in view of the assumptions of the theory that are given in. We also derive fifth-order terms in the wave equation, which not only give us a more accurate description of the marginally-unstable modes, but they also allow us to predict the breakdown of the cubic equation. Our findings allow us to better understand the transition between weakly-nonlinear modes and the long-term chirping modes that ultimately emerge.

Expanding the capability of reaction-diffusion codes using pseudo traps and temperature partitioning: Applied to hydrogen uptake and release from tungsten

DOE Office of Scientific and Technical Information (OSTI.GOV)

Simmonds, M. J.; Yu, J. H.; Wang, Y. Q.

Simulating the implantation and thermal desorption evolution in a reaction-diffusion model requires solving a set of coupled differential equations that describe the trapping and release of atomic species in Plasma Facing Materials (PFMs). These fundamental equations are well outlined by the Tritium Migration Analysis Program (TMAP) which can model systems with no more than three active traps per atomic species. To overcome this limitation, we have developed a Pseudo Trap and Temperature Partition (PTTP) scheme allowing us to lump multiple inactive traps into one pseudo trap, simplifying the system of equations to be solved. For all temperatures, we show themore » trapping of atoms from solute is exactly accounted for when using a pseudo trap. However, a single effective pseudo trap energy can not well replicate the release from multiple traps, each with its own detrapping energy. However, atoms held in a high energy trap will remain trapped at relatively low temperatures, and thus there is a temperature range in which release from high energy traps is effectively inactive. By partitioning the temperature range into segments, a pseudo trap can be defined for each segment to account for multiple high energy traps that are actively trapping but are effectively not releasing atoms. With increasing temperature, as in controlled thermal desorption, the lowest energy trap is nearly emptied and can be removed from the set of coupled equations, while the next higher energy trap becomes an actively releasing trap. Each segment is thus calculated sequentially, with the last time step of a given segment solution being used as an initial input for the next segment as only the pseudo and actively releasing traps are modeled. This PTTP scheme is then applied to experimental thermal desorption data for tungsten (W) samples damaged with heavy ions, which display six distinct release peaks during thermal desorption. Without modifying the TMAP7 source code the PTTP scheme is shown to successfully model the D retention in all six traps. In conclusion, we demonstrate the full reconstruction from the plasma implantation phase through the controlled thermal desorption phase with detrapping energies near 0.9, 1.1, 1.4, 1.7, 1.9 and 2.1 eV for a W sample damaged at room temperature.« less

Expanding the capability of reaction-diffusion codes using pseudo traps and temperature partitioning: Applied to hydrogen uptake and release from tungsten

DOE PAGES

Simmonds, M. J.; Yu, J. H.; Wang, Y. Q.; ...

2018-06-04

Simulating the implantation and thermal desorption evolution in a reaction-diffusion model requires solving a set of coupled differential equations that describe the trapping and release of atomic species in Plasma Facing Materials (PFMs). These fundamental equations are well outlined by the Tritium Migration Analysis Program (TMAP) which can model systems with no more than three active traps per atomic species. To overcome this limitation, we have developed a Pseudo Trap and Temperature Partition (PTTP) scheme allowing us to lump multiple inactive traps into one pseudo trap, simplifying the system of equations to be solved. For all temperatures, we show themore » trapping of atoms from solute is exactly accounted for when using a pseudo trap. However, a single effective pseudo trap energy can not well replicate the release from multiple traps, each with its own detrapping energy. However, atoms held in a high energy trap will remain trapped at relatively low temperatures, and thus there is a temperature range in which release from high energy traps is effectively inactive. By partitioning the temperature range into segments, a pseudo trap can be defined for each segment to account for multiple high energy traps that are actively trapping but are effectively not releasing atoms. With increasing temperature, as in controlled thermal desorption, the lowest energy trap is nearly emptied and can be removed from the set of coupled equations, while the next higher energy trap becomes an actively releasing trap. Each segment is thus calculated sequentially, with the last time step of a given segment solution being used as an initial input for the next segment as only the pseudo and actively releasing traps are modeled. This PTTP scheme is then applied to experimental thermal desorption data for tungsten (W) samples damaged with heavy ions, which display six distinct release peaks during thermal desorption. Without modifying the TMAP7 source code the PTTP scheme is shown to successfully model the D retention in all six traps. In conclusion, we demonstrate the full reconstruction from the plasma implantation phase through the controlled thermal desorption phase with detrapping energies near 0.9, 1.1, 1.4, 1.7, 1.9 and 2.1 eV for a W sample damaged at room temperature.« less

Assessment of the microstructure evolution of an austempered ductile iron during austempering process through strain hardening analysis

NASA Astrophysics Data System (ADS)

Donnini, Riccardo; Fabrizi, Alberto; Bonollo, Franco; Zanardi, Franco; Angella, Giuliano

2017-09-01

The aim of this investigation was to determine a procedure based on tensile testing to assess the critical range of austempering times for having the best ausferrite produced through austempering. The austempered ductile iron (ADI) 1050 was quenched at different times during austempering and the quenched samples were tested in tension. The dislocation-density-related constitutive equation proposed by Estrin for materials having high density of geometrical obstacles to dislocation motion, was used to model the flow curves of the tensile tested samples. On the basis of strain hardening theory, the equation parameters were related to the microstructure of the quenched samples and were used to assess the ADI microstructure evolution during austempering. The microstructure evolution was also analysed through conventional optical microscopy, electron back-scattered diffraction technique and transmission electron microscopy. The microstructure observations resulted to be consistent with the assessment based on tensile testing, so the dislocation-density-related constitutive equation was found to be a powerful tool to characterise the evolution of the solid state transformations of austempering.

Numerical modeling of the Madison Dynamo Experiment.

NASA Astrophysics Data System (ADS)

Bayliss, R. A.; Wright, J. C.; Forest, C. B.; O'Connell, R.

2002-11-01

Growth, saturation and turbulent evolution of the Madison dynamo experiment is investigated numerically using a 3-D pseudo-spectral simulation of the MHD equations; results of the simulations will be compared to results obtained from the experiment. The code, Dynamo (Fortran90), allows for full evolution of the magnetic and velocity fields. The induction equation governing B and the curl of the momentum equation governing V are separately or simultaneously solved. The code uses a spectral representation via spherical harmonic basis functions of the vector fields in longitude and latitude, and fourth order finite differences in the radial direction. The magnetic field evolution has been benchmarked against the laminar kinematic dynamo predicted by M.L. Dudley and R.W. James (M.L. Dudley and R.W. James, Time-dependent kinematic dynamos with stationary flows, Proc. R. Soc. Lond. A 425, p. 407 (1989)). Power balance in the system has been verified in both mechanically driven and perturbed hydrodynamic, kinematic, and dynamic cases. Evolution of the vacuum magnetic field has been added to facilitate comparison with the experiment. Modeling of the Madison Dynamo eXperiment will be presented.

Similarity solutions of some two-space-dimensional nonlinear wave evolution equations

NASA Technical Reports Server (NTRS)

Redekopp, L. G.

1980-01-01

Similarity reductions of the two-space-dimensional versions of the Korteweg-de Vries, modified Korteweg-de Vries, Benjamin-Davis-Ono, and nonlinear Schroedinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two-dimensional Korteweg-de Vries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painleve transcendent.

The free-electron laser - Maxwell's equations driven by single-particle currents

NASA Technical Reports Server (NTRS)

Colson, W. B.; Ride, S. K.

1980-01-01

It is shown that if single particle currents are coupled to Maxwell's equations, the resulting set of self-consistent nonlinear equations describes the evolution of the electron beam and the amplitude and phase of the free-electron-laser field. The formulation is based on the slowly varying amplitude and phase approximation, and the distinction between microscopic and macroscopic scales, which distinguishes the microscopic bunching from the macroscopic pulse propagation. The capabilities of this new theoretical approach become apparent when its predictions for the ultrashort pulse free-electron laser are compared to experimental data; the optical pulse evolution, determined simply and accurately, agrees well with observations.

Evolution of spherical cavitation bubbles: Parametric and closed-form solutions

NASA Astrophysics Data System (ADS)

Mancas, Stefan C.; Rosu, Haret C.

2016-02-01

We present an analysis of the Rayleigh-Plesset equation for a three dimensional vacuous bubble in water. In the simplest case when the effects of surface tension are neglected, the known parametric solutions for the radius and time evolution of the bubble in terms of a hypergeometric function are briefly reviewed. By including the surface tension, we show the connection between the Rayleigh-Plesset equation and Abel's equation, and obtain the parametric rational Weierstrass periodic solutions following the Abel route. In the same Abel approach, we also provide a discussion of the nonintegrable case of nonzero viscosity for which we perform a numerical integration.

FFT-based computation of the bioheat transfer equation for the HCC ultrasound surgery therapy modeling.

PubMed

Dillenseger, Jean-Louis; Esneault, Simon; Garnier, Carole

2008-01-01

This paper describes a modeling method of the tissue temperature evolution over time in hyperthermia. More precisely, this approach is used to simulate the hepatocellular carcinoma curative treatment by a percutaneous high intensity ultrasound surgery. The tissue temperature evolution over time is classically described by Pennes' bioheat transfer equation which is generally solved by a finite difference method. In this paper we will present a method where the bioheat transfer equation can be algebraically solved after a Fourier transformation over the space coordinates. The implementation and boundary conditions of this method will be shown and compared with the finite difference method.

The Optimal Capital Stock and Consumption Evolution for Non Zero Consumers Growth Rate in the Framework of Ramsey Model on Finite Horizon

NASA Astrophysics Data System (ADS)

Bonchiş, N.; Balint, Şt.

2010-09-01

In this paper the Ramsey optimal growth of the capital stock and consumption on finite horizon is analyzed when the growth rate of consumers is strictly positive. The main purpose is to establish the dependence of the optimal capital stock and consumption evolution on the growth rate of consumers. The analysis reveals: for any initial value k0≥0 there exists a unique optimal evolution path of length N+1 for the capital stock; if k0 is strictly positive then all the elements of the optimal capital stock evolution path are strictly positives except the last one which is zero; the optimal capital stock evolution of length N+1 starting from k0≥0 satisfies the Euler equation; the value function VN is strictly increasing, strictly concave and continuous on R+. The family of functions {VN-T}T = 0…N-1 satisfies the Bellman equation and it is the unique solution of this equation which is both continuous and satisfies the transversality condition. The Mangasarian Lemma is also satisfied. For N tending to infinity the optimal evolution path of length N of the capital stock tends to those on the infinite time horizon. For any k0>0 the value function in k0 decreases when the consumers growth rate increases.

Fatigue damage evaluation of short fiber CFRP based on phase information of thermoelastic temperature change

NASA Astrophysics Data System (ADS)

Sakagami, Takahide; Shiozawa, Daiki; Nakamura, Yu; Nonaka, Shinichi; Hamada, Kenichi

2017-05-01

Carbon fiber-reinforced plastic (CFRP) is widely used for structural members of transportation vehicles such as automobile, aircraft or spacecraft, utilizing its excellent specific strength and specific rigidity in contrast with the metal. Short carbon fiber composite materials are receiving a lot of attentions because of their excellent moldability and productivity, however they show complicated behaviors in fatigue fracture due to the random fibers orientation. In this study, thermoelastic stress analysis (TSA) using an infrared thermography was applied to the evaluation of fatigue damage in short carbon fiber composites. The distributions of the thermoelastic temperature change was measured during the fatigue test, as well as the phase difference between the thermoelastic temperature change and applied loading signal. Evolution of fatigue damages was detected from distributions of thermoelastic temperature change according to the thermoelastic damage analysis (TDA) procedure. It was also found that fatigue damage evolution was clearly detected than ever by the newly developed thermoelastic phase damage analysis (TPDA) in which damaged area was emphasized in the differential phase delay images utilizing the nature that carbon fiber show opposite phase thermoelastic temperature change.

Information transport in classical statistical systems

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-02-01

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

Evolution of robustness to damage in artificial 3-dimensional development.

PubMed

Joachimczak, Michał; Wróbel, Borys

2012-09-01

GReaNs is an Artificial Life platform we have built to investigate the general principles that guide evolution of multicellular development and evolution of artificial gene regulatory networks. The embryos develop in GReaNs in a continuous 3-dimensional (3D) space with simple physics. The developmental trajectories are indirectly encoded in linear genomes. The genomes are not limited in size and determine the topology of gene regulatory networks that are not limited in the number of nodes. The expression of the genes is continuous and can be modified by adding environmental noise. In this paper we evolved development of structures with a specific shape (an ellipsoid) and asymmetrical pattering (a 3D pattern inspired by the French flag problem), and investigated emergence of the robustness to damage in development and the emergence of the robustness to noise. Our results indicate that both types of robustness are related, and that including noise during evolution promotes higher robustness to damage. Interestingly, we have observed that some evolved gene regulatory networks rely on noise for proper behaviour. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Simulation of hot spots formation and evolution in HMX

NASA Astrophysics Data System (ADS)

Wang, Cheng; Yang, Tonghui

2017-06-01

In order to study the formation and evolution of hot spots under shock loading, HMX explosives were selected as the object of study for the two-dimensional finite difference numerical simulation. A fifth order finite difference weighted essentially non-oscillatory (WENO) scheme and a third order TVD Runge-Kutta method are utilized for the spatial discretization and the time advance, respectively. The governing equations are based on the fluid elasto-plastic control equations. The Mie-Gruneisen equation of state and the ideal gas equation of state are selected to use in the state equation of the solid explosives and gas material. In order to simplify the calculation of the model, the reaction can be considered to complete in one step. The calculated area is [ 3.0 ×10-5 m ] × [ 3.0 ×10-5 m ] . The radius is 0.6 ×10-5 m, and the internal gas is not involved in the reaction. The calculation area is divided into 300×300 grids and 10 grids are selected from the bottom of each column to give the particle velocity u as the initial condition. In the selected grid, different initial velocity 100m/s and 200m/s are loaded respectively to study the influence of hot spot formation and evolution in different impact intensity.

Stochastic Evolution Equations Driven by Fractional Noises

DTIC Science & Technology

2016-11-28

rate of convergence to zero or the error and the limit in distribution of the error fluctuations. We have studied time discrete numerical schemes...error fluctuations. We have studied time discrete numerical schemes based on Taylor expansions for rough differential equations and for stochastic...variations of the time discrete Taylor schemes for rough differential equations and for stochastic differential equations driven by fractional Brownian

Chandrasekhar equations for infinite dimensional systems

NASA Technical Reports Server (NTRS)

Ito, K.; Powers, R.

1985-01-01

The existence of Chandrasekhar equations for linear time-invariant systems defined on Hilbert spaces is investigated. An important consequence is that the solution to the evolutional Riccati equation is strongly differentiable in time, and that a strong solution of the Riccati differential equation can be defined. A discussion of the linear-quadratic optimal-control problem for hereditary differential systems is also included.

Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond compression and carrier envelope phase effect

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mizuta, Yo; Nagasawa, Minoru; Ohtani, Morimasa

2005-12-15

A numerical approach called Fourier direct method (FDM) is applied to nonlinear propagation of optical pulses with the central wavelength 800 nm, the width 2.67-12.00 fs, and the peak power 25-6870 kW in a fused-silica fiber. Bidirectional propagation, delayed Raman response, nonlinear dispersion (self-steepening, core dispersion), as well as correct linear dispersion are incorporated into 'bidirectional propagation equations' which are derived directly from Maxwell's equations. These equations are solved for forward and backward waves, instead of the electric-field envelope as in the nonlinear Schroedinger equation (NLSE). They are integrated as multidimensional simultaneous evolution equations evolved in space. We investigate, bothmore » theoretically and numerically, the validity and the limitation of assumptions and approximations used for deriving the NLSE. Also, the accuracy and the efficiency of the FDM are compared quantitatively with those of the finite-difference time-domain numerical approach. The time-domain size 500 fs and the number of grid points in time 2048 are chosen to investigate numerically intensity spectra, spectral phases, and temporal electric-field profiles up to the propagation distance 1.0 mm. On the intensity spectrum of a few-optical-cycle pulses, the self-steepening, core dispersion, and the delayed Raman response appear as dominant, middle, and slight effects, respectively. The delayed Raman response and the core dispersion reduce the effective nonlinearity. Correct linear dispersion is important since it affects the intensity spectrum sensitively. For the compression of femtosecond optical pulses by the complete phase compensation, the shortness and the pulse quality of compressed pulses are remarkably improved by the intense initial peak power rather than by the short initial pulse width or by the propagation distance longer than 0.1 mm. They will be compressed as short as 0.3 fs below the damage threshold of fused-silica fiber 6 MW. It is demonstrated that the carrier envelope phase (CEP) causes the difference on the temporal electric-field profile and the intensity spectrum for the initial peak power of the order of megawatts. At the propagation distance longer than the coherence length for third-order harmonics, the difference grows in the spectral components around the third-order and higher-order harmonics. The CEP can be a sensitive marker to monitor the evolution of nonlinear optical process by a few-optical-cycle electric-field wave-packet source.« less

Modelling of Damage Evolution in Braided Composites: Recent Developments

NASA Astrophysics Data System (ADS)

Wang, Chen; Roy, Anish; Silberschmidt, Vadim V.; Chen, Zhong

2017-12-01

Composites reinforced with woven or braided textiles exhibit high structural stability and excellent damage tolerance thanks to yarn interlacing. With their high stiffness-to-weight and strength-to-weight ratios, braided composites are attractive for aerospace and automotive components as well as sports protective equipment. In these potential applications, components are typically subjected to multi-directional static, impact and fatigue loadings. To enhance material analysis and design for such applications, understanding mechanical behaviour of braided composites and development of predictive capabilities becomes crucial. Significant progress has been made in recent years in development of new modelling techniques allowing elucidation of static and dynamic responses of braided composites. However, because of their unique interlacing geometric structure and complicated failure modes, prediction of damage initiation and its evolution in components is still a challenge. Therefore, a comprehensive literature analysis is presented in this work focused on a review of the state-of-the-art progressive damage analysis of braided composites with finite-element simulations. Recently models employed in the studies on mechanical behaviour, impact response and fatigue analyses of braided composites are presented systematically. This review highlights the importance, advantages and limitations of as-applied failure criteria and damage evolution laws for yarns and composite unit cells. In addition, this work provides a good reference for future research on FE simulations of braided composites.

Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows.

PubMed

Abel, I G; Plunk, G G; Wang, E; Barnes, M; Cowley, S C; Dorland, W; Schekochihin, A A

2013-11-01

This paper presents a complete theoretical framework for studying turbulence and transport in rapidly rotating tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio ε = ρi/α of the gyroradius to the equilibrium scale length. Proceeding order by order in this expansion, a set of coupled multiscale equations is developed. They describe an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the interplay between the equilibrium and the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equilibrium is obtained from the generalized Grad-Shafranov equation for a rotating plasma, determining the magnetic flux function from the mean pressure and velocity profiles of the plasma. The slow (resistive-timescale) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the 'high-flow' gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local (in space) cascade of the free energy of the fluctuations (i.e. there is no turbulence spreading). Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical and fluctuating corrections to the equilibrium Maxwellian act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived from the transport equations. Total energy, thermal, kinetic and magnetic, is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating and the equilibration of interspecies temperature differences. This equilibration is found to include both turbulent and collisional contributions. Finally, this framework is condensed, in the low-Mach-number limit, to a more concise set of equations suitable for numerical implementation.

Thermal noise in a boost-invariant matter expansion in relativistic heavy-ion collisions

NASA Astrophysics Data System (ADS)

Chattopadhyay, Chandrodoy; Bhalerao, Rajeev S.; Pal, Subrata

2018-05-01

We formulate a general theory of thermal fluctuations within causal second-order viscous hydrodynamic evolution of matter formed in relativistic heavy-ion collisions. The fluctuation is treated perturbatively on top of a boost-invariant longitudinal expansion. Numerical simulation of thermal noise is performed for a lattice quantum chromodynamics equation of state and for various second-order dissipative evolution equations. Phenomenological effects of thermal fluctuations on the two-particle rapidity correlations are studied.

Consistent Yokoya-Chen Approximation to Beamstrahlung(LCC-0010)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peskin, M

2004-04-22

I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.

Semiconductor spintronics: The full matrix approach

NASA Astrophysics Data System (ADS)

Rossani, A.

2015-12-01

A new model, based on an asymptotic procedure for solving the spinor kinetic equations of electrons and phonons is proposed, which gives naturally the displaced Fermi-Dirac distribution function at the leading order. The balance equations for the electron number, energy density and momentum, plus the Poisson’s equation, constitute now a system of six equations. Moreover, two equations for the evolution of the spin densities are added, which account for a general dispersion relation.

A Fundamental Investigation of Crack and Surrounding Damage in Stiff Clays

DTIC Science & Technology

1988-09-01

equation of state is written in terms of entropy production. A generalized flux is identified as the centroidal movement of the damage zone, and the...on the following governing equation. I I a14 ( 1.1] Ti = z ’_Xc + "_.wXrOt + a.’X ef = 0 where Si is the global entropy production, 1, , and a are...convenient to express the internal energy density u in terms of i Gibb’s potential density and the entropy density s [6.3] u = g + Ts +’ijciji Here

Approximate Micromechanics Treatise of Composite Impact

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Handler, Louis M.

2005-01-01

A formalism is described for micromechanic impact of composites. The formalism consists of numerous equations which describe all aspects of impact from impactor and composite conditions to impact contact, damage progression, and penetration or containment. The formalism is based on through-the-thickness displacement increments simulation which makes it convenient to track local damage in terms of microfailure modes and their respective characteristics. A flow chart is provided to cast the formalism (numerous equations) into a computer code for embedment in composite mechanic codes and/or finite element composite structural analysis.

Early-state damage detection, characterization, and evolution using high-resolution computed tomography

NASA Astrophysics Data System (ADS)

Grandin, Robert John

Safely using materials in high performance applications requires adequately understanding the mechanisms which control the nucleation and evolution of damage. Most of a material's operational life is spent in a state with noncritical damage, and, for example in metals only a small portion of its life falls within the classical Paris Law regime of crack growth. Developing proper structural health and prognosis models requires understanding the behavior of damage in these early stages within the material's life, and this early-stage damage occurs on length scales at which the material may be considered "granular'' in the sense that the discrete regions which comprise the whole are large enough to require special consideration. Material performance depends upon the characteristics of the granules themselves as well as the interfaces between granules. As a result, properly studying early-stage damage in complex, granular materials requires a means to characterize changes in the granules and interfaces. The granular-scale can range from tenths of microns in ceramics, to single microns in fiber-reinforced composites, to tens of millimeters in concrete. The difficulty of direct-study is often overcome by exhaustive testing of macro-scale damage caused by gross material loads and abuse. Such testing, for example optical or electron microscopy, destructive and further, is costly when used to study the evolution of damage within a material and often limits the study to a few snapshots. New developments in high-resolution computed tomography (HRCT) provide the necessary spatial resolution to directly image the granule length-scale of many materials. Successful application of HRCT with fiber-reinforced composites, however, requires extending the HRCT performance beyond current limits. This dissertation will discuss improvements made in the field of CT reconstruction which enable resolutions to be pushed to the point of being able to image the fiber-scale damage structures and the application of this new capability to the study of early-stage damage.

A Computational Efficient Physics Based Methodology for Modeling Ceramic Matrix Composites (Preprint)

DTIC Science & Technology

2011-11-01

elastic range, and with some simple forms of progressing damage . However, a general physics-based methodology to assess the initial and lifetime... damage evolution in the RVE for all possible load histories. Microstructural data on initial configuration and damage progression in CMCs were...the damaged elements will have changed, hence, a progressive damage model. The crack opening for each crack type in each element is stored as a

High-accuracy phase-field models for brittle fracture based on a new family of degradation functions

NASA Astrophysics Data System (ADS)

Sargado, Juan Michael; Keilegavlen, Eirik; Berre, Inga; Nordbotten, Jan Martin

2018-02-01

Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In the phase-field framework, the surface energy associated with crack formation is calculated by evaluating a functional defined in terms of a scalar order parameter and its gradients. These in turn describe the fractures in a diffuse sense following a prescribed regularization length scale. Imposing stationarity of the total energy leads to a coupled system of partial differential equations that enforce stress equilibrium and govern phase-field evolution. These equations are coupled through an energy degradation function that models the loss of stiffness in the bulk material as it undergoes damage. In the present work, we introduce a new parametric family of degradation functions aimed at increasing the accuracy of phase-field models in predicting critical loads associated with crack nucleation as well as the propagation of existing fractures. An additional goal is the preservation of linear elastic response in the bulk material prior to fracture. Through the analysis of several numerical examples, we demonstrate the superiority of the proposed family of functions to the classical quadratic degradation function that is used most often in the literature.

Optimization of nonlinear, non-Gaussian Bayesian filtering for diagnosis and prognosis of monotonic degradation processes

NASA Astrophysics Data System (ADS)

Corbetta, Matteo; Sbarufatti, Claudio; Giglio, Marco; Todd, Michael D.

2018-05-01

The present work critically analyzes the probabilistic definition of dynamic state-space models subject to Bayesian filters used for monitoring and predicting monotonic degradation processes. The study focuses on the selection of the random process, often called process noise, which is a key perturbation source in the evolution equation of particle filtering. Despite the large number of applications of particle filtering predicting structural degradation, the adequacy of the picked process noise has not been investigated. This paper reviews existing process noise models that are typically embedded in particle filters dedicated to monitoring and predicting structural damage caused by fatigue, which is monotonic in nature. The analysis emphasizes that existing formulations of the process noise can jeopardize the performance of the filter in terms of state estimation and remaining life prediction (i.e., damage prognosis). This paper subsequently proposes an optimal and unbiased process noise model and a list of requirements that the stochastic model must satisfy to guarantee high prognostic performance. These requirements are useful for future and further implementations of particle filtering for monotonic system dynamics. The validity of the new process noise formulation is assessed against experimental fatigue crack growth data from a full-scale aeronautical structure using dedicated performance metrics.

Dynamic modeling of photothermal interactions for laser-induced interstitial thermotherapy: parameter sensitivity analysis.

PubMed

Jiang, S C; Zhang, X X

2005-12-01

A two-dimensional model was developed to model the effects of dynamic changes in the physical properties on tissue temperature and damage to simulate laser-induced interstitial thermotherapy (LITT) treatment procedures with temperature monitoring. A modified Monte Carlo method was used to simulate photon transport in the tissue in the non-uniform optical property field with the finite volume method used to solve the Pennes bioheat equation to calculate the temperature distribution and the Arrhenius equation used to predict the thermal damage extent. The laser light transport and the heat transfer as well as the damage accumulation were calculated iteratively at each time step. The influences of different laser sources, different applicator sizes, and different irradiation modes on the final damage volume were analyzed to optimize the LITT treatment. The numerical results showed that damage volume was the smallest for the 1,064-nm laser, with much larger, similar damage volumes for the 980- and 850-nm lasers at normal blood perfusion rates. The damage volume was the largest for the 1,064-nm laser with significantly smaller, similar damage volumes for the 980- and 850-nm lasers with temporally interrupted blood perfusion. The numerical results also showed that the variations in applicator sizes, laser powers, heating durations and temperature monitoring ranges significantly affected the shapes and sizes of the thermal damage zones. The shapes and sizes of the thermal damage zones can be optimized by selecting different applicator sizes, laser powers, heating duration times, temperature monitoring ranges, etc.

Solutions of the KPI equation with smooth initial data

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A.

1994-06-01

The solution $u(t,x,y)$ of the Kadomtsev--Petviashvili I (KPI) equation with given initial data $u(0,x,y)$ belonging to the Schwartz space is considered. No additional special constraints, usually considered in literature, as $\\int\\!dx\\,u(0,x,y)=0$ are required to be satisfied by the initial data. The problem is completely solved in the framework of the spectral transform theory and it is shown that $u(t,x,y)$ satisfies a special evolution version of the KPI equation and that, in general, $\\partial_t u(t,x,y)$ has different left and right limits at the initial time $t=0$. The conditions of the type $\\int\\!dx\\,u(t,x,y)=0$, $\\int\\!dx\\,xu_y(t,x,y)=0$ and so on (first, second, etc. `constraints') are dynamically generated by the evolution equation for $t\

Initial value formulation of dynamical Chern-Simons gravity

NASA Astrophysics Data System (ADS)

Delsate, Térence; Hilditch, David; Witek, Helvi

2015-01-01

We derive an initial value formulation for dynamical Chern-Simons gravity, a modification of general relativity involving parity-violating higher derivative terms. We investigate the structure of the resulting system of partial differential equations thinking about linearization around arbitrary backgrounds. This type of consideration is necessary if we are to establish well-posedness of the Cauchy problem. Treating the field equations as an effective field theory we find that weak necessary conditions for hyperbolicity are satisfied. For the full field equations we find that there are states from which subsequent evolution is not determined. Generically the evolution system closes, but is not hyperbolic in any sense that requires a first order pseudodifferential reduction. In a cursory mode analysis we find that the equations of motion contain terms that may cause ill-posedness of the initial value problem.

Nonlinear Waves

DTIC Science & Technology

1989-06-15

Hamiltonian Formulation of the Kadomtsev - Petviashvili and Benjamin-Ono Equations , A.S. Fokas and P.M. Santini, J. Math. Phys. 29 (3) 604-617 (1988...Prototypes are the so-called Kadomtsev -Petviashvilli and Davey-Stewartson equations . These equations arise in a variety of physical instances such as water...plasma physics. Moreover the study of solutions to some of the underlying nonlinear evolution equations has led naturally to the investigation and new

Chandrasekhar equations for infinite dimensional systems

NASA Technical Reports Server (NTRS)

Ito, K.; Powers, R. K.

1985-01-01

Chandrasekhar equations are derived for linear time invariant systems defined on Hilbert spaces using a functional analytic technique. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a strong solution of the Riccati differential equation. A detailed discussion on the linear quadratic optimal control problem for hereditary differential systems is also included.

Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution.

PubMed

Djordjevic, Ivan B

2015-08-24

Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually coupled.

Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution

PubMed Central

Djordjevic, Ivan B.

2015-01-01

Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually coupled. PMID:26305258

Partition-free approach to open quantum systems in harmonic environments: An exact stochastic Liouville equation

NASA Astrophysics Data System (ADS)

McCaul, G. M. G.; Lorenz, C. D.; Kantorovich, L.

2017-03-01

We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional formalism combined with a two-time Hubbard-Stratonovich transformation allows us to derive a set of exact differential equations for the reduced density matrix of an open system, termed the extended stochastic Liouville-von Neumann equation. Our approach generalizes previous work based on Caldeira-Leggett models and a partitioned initial density matrix. This provides a simple, yet exact, closed-form description for the evolution of open systems from equilibriated initial conditions. The applicability of this model and the potential for numerical implementations are also discussed.

Qubit models of weak continuous measurements: markovian conditional and open-system dynamics

NASA Astrophysics Data System (ADS)

Gross, Jonathan A.; Caves, Carlton M.; Milburn, Gerard J.; Combes, Joshua

2018-04-01

In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.

Rosenzweig instability in a thin layer of a magnetic fluid

NASA Astrophysics Data System (ADS)

Korovin, V. M.

2013-12-01

A simple mathematical model of the initial stage of nonlinear evolution of the Rosenzweig instability in a thin layer of a nonlinearly magnetized viscous ferrofluid coating a horizontal nonmagnetizable plate is constructed on the basis of the system of equations and boundary conditions of ferrofluid dynamics. A dispersion relation is derived and analyzed using the linearized equations of this model. The critical magnetization of the initial layer with a flat free surface, the threshold wavenumber, and the characteristic time of evolution of the most rapidly growing mode are determined. The equation for the neutral stability curve, which is applicable for any physically admissible law of magnetization of a ferrofluid, is derived analytically.

Instability of Poiseuille flow at extreme Mach numbers: linear analysis and simulations.

PubMed

Xie, Zhimin; Girimaji, Sharath S

2014-04-01

We develop the perturbation equations to describe instability evolution in Poiseuille flow at the limit of very high Mach numbers. At this limit the equation governing the flow is the pressure-released Navier-Stokes equation. The ensuing semianalytical solution is compared against simulations performed using the gas-kinetic method (GKM), resulting in excellent agreement. A similar comparison between analytical and computational results of small perturbation growth is performed at the incompressible (zero Mach number) limit, again leading to excellent agreement. The study accomplishes two important goals: it (i) contrasts the small perturbation evolution in Poiseuille flows at extreme Mach numbers and (ii) provides important verification of the GKM simulation scheme.

Ring Current Ion Coupling with Electromagnetic Ion Cyclotron Waves

NASA Technical Reports Server (NTRS)

Khazanov. G. V.; Gamayunov, K. V.; Jordanova, V. K.; Six, N. Frank (Technical Monitor)

2002-01-01

A new ring current global model has been developed that couples the system of two kinetic equations: one equation describes the ring current (RC) ion dynamic, and another equation describes wave evolution of electromagnetic ion cyclotron waves (EMIC). The coupled model is able to simulate, for the first time self-consistently calculated RC ion kinetic and evolution of EMIC waves that propagate along geomagnetic field lines and reflect from the ionosphere. Ionospheric properties affect the reflection index through the integral Pedersen and Hall conductivities. The structure and dynamics of the ring current proton precipitating flux regions, intensities of EMIC global RC energy balance, and some other parameters will be studied in detail for the selected geomagnetic storms.

Alleviating inequality in climate policy costs: an integrated perspective on mitigation, damage and adaptation

NASA Astrophysics Data System (ADS)

De Cian, E.; Hof, A. F.; Marangoni, G.; Tavoni, M.; van Vuuren, D. P.

2016-07-01

Equity considerations play an important role in international climate negotiations. While policy analysis has often focused on equity as it relates to mitigation costs, there are large regional differences in adaptation costs and the level of residual damage. This paper illustrates the relevance of including adaptation and residual damage in equity considerations by determining how the allocation of emission allowances would change to counteract regional differences in total climate costs, defined as the costs of mitigation, adaptation, and residual damage. We compare emission levels resulting from a global carbon tax with two allocations of emission allowances under a global cap-and-trade system: one equating mitigation costs and one equating total climate costs as share of GDP. To account for uncertainties in both mitigation and adaptation, we use a model-comparison approach employing two alternative modeling frameworks with different damage, adaptation cost, and mitigation cost estimates, and look at two different climate goals. Despite the identified model uncertainties, we derive unambiguous results on the change in emission allowance allocation that could lessen the unequal distribution of adaptation costs and residual damages through the financial transfers associated with emission trading.

The Approach to Equilibrium: Detailed Balance and the Master Equation

ERIC Educational Resources Information Center

Alexander, Millard H.; Hall, Gregory E.; Dagdigian, Paul J.

2011-01-01

The approach to the equilibrium (Boltzmann) distribution of populations of internal states of a molecule is governed by inelastic collisions in the gas phase and with surfaces. The set of differential equations governing the time evolution of the internal state populations is commonly called the master equation. An analytic solution to the master…

Switching probability of all-perpendicular spin valve nanopillars

NASA Astrophysics Data System (ADS)

Tzoufras, M.

2018-05-01

In all-perpendicular spin valve nanopillars the probability density of the free-layer magnetization is independent of the azimuthal angle and its evolution equation simplifies considerably compared to the general, nonaxisymmetric geometry. Expansion of the time-dependent probability density to Legendre polynomials enables analytical integration of the evolution equation and yields a compact expression for the practically relevant switching probability. This approach is valid when the free layer behaves as a single-domain magnetic particle and it can be readily applied to fitting experimental data.

Perturbative dynamics of thin-shell wormholes beyond general relativity: An alternative approach

NASA Astrophysics Data System (ADS)

Rubín de Celis, Emilio; Tomasini, Cecilia; Simeone, Claudio

Recent studies relating the approximations for the equations-of-state for thin shells and their consequent perturbative evolution are extended to thin-shell wormholes in theories beyond general relativity and more than four spacetime dimensions. The assumption of equations-of-state of the same form for static and slowly evolving shells appears as a strong restriction excluding the possibility of oscillatory evolutions. Then the new results considerably differ from previous ones obtained within the usual linearized approach.

An Equation-Free Reduced-Order Modeling Approach to Tropical Pacific Simulation

NASA Astrophysics Data System (ADS)

Wang, Ruiwen; Zhu, Jiang; Luo, Zhendong; Navon, I. M.

2009-03-01

The “equation-free” (EF) method is often used in complex, multi-scale problems. In such cases it is necessary to know the closed form of the required evolution equations about oscopic variables within some applied fields. Conceptually such equations exist, however, they are not available in closed form. The EF method can bypass this difficulty. This method can obtain oscopic information by implementing models at a microscopic level. Given an initial oscopic variable, through lifting we can obtain the associated microscopic variable, which may be evolved using Direct Numerical Simulations (DNS) and by restriction, we can obtain the necessary oscopic information and the projective integration to obtain the desired quantities. In this paper we apply the EF POD-assisted method to the reduced modeling of a large-scale upper ocean circulation in the tropical Pacific domain. The computation cost is reduced dramatically. Compared with the POD method, the method provided more accurate results and it did not require the availability of any explicit equations or the right-hand side (RHS) of the evolution equation.

Monitoring of temperature fatigue failure mechanism for polyvinyl alcohol fiber concrete using acoustic emission sensors.

PubMed

Li, Dongsheng; Cao, Hai

2012-01-01

The applicability of acoustic emission (AE) techniques to monitor the mechanism of evolution of polyvinyl alcohol (PVA) fiber concrete damage under temperature fatigue loading is investigated. Using the temperature fatigue test, real-time AE monitoring data of PVA fiber concrete is achieved. Based on the AE signal characteristics of the whole test process and comparison of AE signals of PVA fiber concretes with different fiber contents, the damage evolution process of PVA fiber concrete is analyzed. Finally, a qualitative evaluation of the damage degree is obtained using the kurtosis index and b-value of AE characteristic parameters. The results obtained using both methods are discussed.

Monitoring of Temperature Fatigue Failure Mechanism for Polyvinyl Alcohol Fiber Concrete Using Acoustic Emission Sensors

PubMed Central

Li, Dongsheng; Cao, Hai

2012-01-01

The applicability of acoustic emission (AE) techniques to monitor the mechanism of evolution of polyvinyl alcohol (PVA) fiber concrete damage under temperature fatigue loading is investigated. Using the temperature fatigue test, real-time AE monitoring data of PVA fiber concrete is achieved. Based on the AE signal characteristics of the whole test process and comparison of AE signals of PVA fiber concretes with different fiber contents, the damage evolution process of PVA fiber concrete is analyzed. Finally, a qualitative evaluation of the damage degree is obtained using the kurtosis index and b-value of AE characteristic parameters. The results obtained using both methods are discussed. PMID:23012555

Parametric resonant triad interactions in a free shear layer

NASA Technical Reports Server (NTRS)

Mallier, R.; Maslowe, S. A.

1993-01-01

We investigate the weakly nonlinear evolution of a triad of nearly-neutral modes superimposed on a mixing layer with velocity profile u bar equals Um + tanh y. The perturbation consists of a plane wave and a pair of oblique waves each inclined at approximately 60 degrees to the mean flow direction. Because the evolution occurs on a relatively fast time scale, the critical layer dynamics dominate the process and the amplitude evolution of the oblique waves is governed by an integro-differential equation. The long-time solution of this equation predicts very rapid (exponential of an exponential) amplification and we discuss the pertinence of this result to vortex pairing phenomena in mixing layers.

Chaotic evolution of arms races

NASA Astrophysics Data System (ADS)

Tomochi, Masaki; Kono, Mitsuo

1998-12-01

A new set of model equations is proposed to describe the evolution of the arms race, by extending Richardson's model with special emphases that (1) power dependent defensive reaction or historical enmity could be a motive force to promote armaments, (2) a deterrent would suppress the growth of armaments, and (3) the defense reaction of one nation against the other nation depends nonlinearly on the difference in armaments between two. The set of equations is numerically solved to exhibit stationary, periodic, and chaotic behavior depending on the combinations of parameters involved. The chaotic evolution is realized when the economic situation of each country involved in the arms race is quite different, which is often observed in the real world.

The effect of viscoelasticity on the stability of a pulmonary airway liquid layer

NASA Astrophysics Data System (ADS)

Halpern, David; Fujioka, Hideki; Grotberg, James B.

2010-01-01

The lungs consist of a network of bifurcating airways that are lined with a thin liquid film. This film is a bilayer consisting of a mucus layer on top of a periciliary fluid layer. Mucus is a non-Newtonian fluid possessing viscoelastic characteristics. Surface tension induces flows within the layer, which may cause the lung's airways to close due to liquid plug formation if the liquid film is sufficiently thick. The stability of the liquid layer is also influenced by the viscoelastic nature of the liquid, which is modeled using the Oldroyd-B constitutive equation or as a Jeffreys fluid. To examine the role of mucus alone, a single layer of a viscoelastic fluid is considered. A system of nonlinear evolution equations is derived using lubrication theory for the film thickness and the film flow rate. A uniform film is initially perturbed and a normal mode analysis is carried out that shows that the growth rate g for a viscoelastic layer is larger than for a Newtonian fluid with the same viscosity. Closure occurs if the minimum core radius, Rmin(t), reaches zero within one breath. Solutions of the nonlinear evolution equations reveal that Rmin normally decreases to zero faster with increasing relaxation time parameter, the Weissenberg number We. For small values of the dimensionless film thickness parameter ɛ, the closure time, tc, increases slightly with We, while for moderate values of ɛ, ranging from 14% to 18% of the tube radius, tc decreases rapidly with We provided the solvent viscosity is sufficiently small. Viscoelasticity was found to have little effect for ɛ >0.18, indicating the strong influence of surface tension. The film thickness parameter ɛ and the Weissenberg number We also have a significant effect on the maximum shear stress on tube wall, max(τw), and thus, potentially, an impact on cell damage. Max(τw) increases with ɛ for fixed We, and it decreases with increasing We for small We provided the solvent viscosity parameter is sufficiently small. For large ɛ ≈0.2, there is no significant difference between the Newtonian flow case and the large We cases.

A comparison of neutron and gamma damage effects on silica glass in a nuclear reactor radiation environment

NASA Astrophysics Data System (ADS)

Holcomb, David E.; Miller, Don W.

1993-08-01

A study of the relative damage effects of neutrons and gamma rays on silica glass in a nuclear reactor radiation environment is reported. The neutron and gamma energy spectra of the Ohio State University Research Reactor beam port #1 were applied to silica glass to obtain primary knock-on charged particle energy spectra. The resultant charged particle spectra were then applied to the polyatomic forms of the Lindhard et al. integrodifferential equation for damage energy and the Parkin and Coulter integrodifferential equation for net atomic displacement. The results show that near a nuclear reactor core the vast majority of the dose to silica is due to gamma rays (factor of roughly 40) and that neutrons cause much more displacement damage than gamma rays (35 times the oxygen displacement rate and 500 times the silicon displacement rate). However, pure silica core optical fibers irradiated in a nuclear reactor's mixed neutron/gamma environment exhibit little difference in transmission loss on an equal dose basis compared to fibers irradiated in a gamma only environment, indicating that atomic displacement is not a significant damage mechanism.

The Role of Deformation Energetics in Long-Term Tectonic Modeling

NASA Astrophysics Data System (ADS)

Ahamed, S.; Choi, E.

2017-12-01

The deformation-related energy budget is usually considered in the simplest form or even entirely omitted from the energy balance equation. We derive a full energy balance equation that accounts not only for heat energy but also for mechanical (elastic, plastic and viscous) work. The derived equation is implemented in DES3D, an unstructured finite element solver for long-term tectonic deformation. We verify the implementation by comparing numerical solutions to the corresponding semi-analytic solutions in three benchmarks extended from the classical oedometer test. We also investigate the long-term effects of deformation energetics on the evolution of large offset normal faults. We find that the models considering the full energy balance equation tend to produce more secondary faults and an elongated core complex. Our results for the normal fault system confirm that persistent inelastic deformation has a significant impact on the long-term evolution of faults, motivating further exploration of the role of the full energy balance equation in other geodynamic systems.

Bell-polynomial approach and Wronskian determinant solutions for three sets of differential-difference nonlinear evolution equations with symbolic computation

NASA Astrophysics Data System (ADS)

Qin, Bo; Tian, Bo; Wang, Yu-Feng; Shen, Yu-Jia; Wang, Ming

2017-10-01

Under investigation in this paper are the Belov-Chaltikian (BC), Leznov and Blaszak-Marciniak (BM) lattice equations, which are associated with the conformal field theory, UToda(m_1,m_2) system and r-matrix, respectively. With symbolic computation, the Bell-polynomial approach is developed to directly bilinearize those three sets of differential-difference nonlinear evolution equations (NLEEs). This Bell-polynomial approach does not rely on any dependent variable transformation, which constitutes the key step and main difficulty of the Hirota bilinear method, and thus has the advantage in the bilinearization of the differential-difference NLEEs. Based on the bilinear forms obtained, the N-soliton solutions are constructed in terms of the N × N Wronskian determinant. Graphic illustrations demonstrate that those solutions, more general than the existing results, permit some new properties, such as the solitonic propagation and interactions for the BC lattice equations, and the nonnegative dark solitons for the BM lattice equations.

On a model of electromagnetic field propagation in ferroelectric media

NASA Astrophysics Data System (ADS)

Picard, Rainer

2007-04-01

The Maxwell system in an anisotropic, inhomogeneous medium with non-linear memory effect produced by a Maxwell type system for the polarization is investigated under low regularity assumptions on data and domain. The particular form of memory in the system is motivated by a model for electromagnetic wave propagation in ferromagnetic materials suggested by Greenberg, MacCamy and Coffman [J.M. Greenberg, R.C. MacCamy, C.V. Coffman, On the long-time behavior of ferroelectric systems, Phys. D 134 (1999) 362-383]. To avoid unnecessary regularity requirements the problem is approached as a system of space-time operator equation in the framework of extrapolation spaces (Sobolev lattices), a theoretical framework developed in [R. Picard, Evolution equations as space-time operator equations, Math. Anal. Appl. 173 (2) (1993) 436-458; R. Picard, Evolution equations as operator equations in lattices of Hilbert spaces, Glasnik Mat. 35 (2000) 111-136]. A solution theory for a large class of ferromagnetic materials confined to an arbitrary open set (with suitably generalized boundary conditions) is obtained.

Spherically symmetric Einstein-aether perfect fluid models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coley, Alan A.; Latta, Joey; Leon, Genly

We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysicalmore » objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in (β−) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.« less

Quantum trajectories for time-dependent adiabatic master equations

NASA Astrophysics Data System (ADS)

Yip, Ka Wa; Albash, Tameem; Lidar, Daniel A.

2018-02-01

We describe a quantum trajectories technique for the unraveling of the quantum adiabatic master equation in Lindblad form. By evolving a complex state vector of dimension N instead of a complex density matrix of dimension N2, simulations of larger system sizes become feasible. The cost of running many trajectories, which is required to recover the master equation evolution, can be minimized by running the trajectories in parallel, making this method suitable for high performance computing clusters. In general, the trajectories method can provide up to a factor N advantage over directly solving the master equation. In special cases where only the expectation values of certain observables are desired, an advantage of up to a factor N2 is possible. We test the method by demonstrating agreement with direct solution of the quantum adiabatic master equation for 8-qubit quantum annealing examples. We also apply the quantum trajectories method to a 16-qubit example originally introduced to demonstrate the role of tunneling in quantum annealing, which is significantly more time consuming to solve directly using the master equation. The quantum trajectories method provides insight into individual quantum jump trajectories and their statistics, thus shedding light on open system quantum adiabatic evolution beyond the master equation.

Recursion equations in predicting band width under gradient elution.

PubMed

Liang, Heng; Liu, Ying

2004-06-18

The evolution of solute zone under gradient elution is a typical problem of non-linear continuity equation since the local diffusion coefficient and local migration velocity of the mass cells of solute zones are the functions of position and time due to space- and time-variable mobile phase composition. In this paper, based on the mesoscopic approaches (Lagrangian description, the continuity theory and the local equilibrium assumption), the evolution of solute zones in space- and time-dependent fields is described by the iterative addition of local probability density of the mass cells of solute zones. Furthermore, on macroscopic levels, the recursion equations have been proposed to simulate zone migration and spreading in reversed-phase high-performance liquid chromatography (RP-HPLC) through directly relating local retention factor and local diffusion coefficient to local mobile phase concentration. This new approach differs entirely from the traditional theories on plate concept with Eulerian description, since band width recursion equation is actually the accumulation of local diffusion coefficients of solute zones to discrete-time slices. Recursion equations and literature equations were used in dealing with same experimental data in RP-HPLC, and the comparison results show that the recursion equations can accurately predict band width under gradient elution.

A unified phase-field theory for the mechanics of damage and quasi-brittle failure

NASA Astrophysics Data System (ADS)

Wu, Jian-Ying

2017-06-01

Being one of the most promising candidates for the modeling of localized failure in solids, so far the phase-field method has been applied only to brittle fracture with very few exceptions. In this work, a unified phase-field theory for the mechanics of damage and quasi-brittle failure is proposed within the framework of thermodynamics. Specifically, the crack phase-field and its gradient are introduced to regularize the sharp crack topology in a purely geometric context. The energy dissipation functional due to crack evolution and the stored energy functional of the bulk are characterized by a crack geometric function of polynomial type and an energetic degradation function of rational type, respectively. Standard arguments of thermodynamics then yield the macroscopic balance equation coupled with an extra evolution law of gradient type for the crack phase-field, governed by the aforesaid constitutive functions. The classical phase-field models for brittle fracture are recovered as particular examples. More importantly, the constitutive functions optimal for quasi-brittle failure are determined such that the proposed phase-field theory converges to a cohesive zone model for a vanishing length scale. Those general softening laws frequently adopted for quasi-brittle failure, e.g., linear, exponential, hyperbolic and Cornelissen et al. (1986) ones, etc., can be reproduced or fit with high precision. Except for the internal length scale, all the other model parameters can be determined from standard material properties (i.e., Young's modulus, failure strength, fracture energy and the target softening law). Some representative numerical examples are presented for the validation. It is found that both the internal length scale and the mesh size have little influences on the overall global responses, so long as the former can be well resolved by sufficiently fine mesh. In particular, for the benchmark tests of concrete the numerical results of load versus displacement curve and crack paths both agree well with the experimental data, showing validity of the proposed phase-field theory for the modeling of damage and quasi-brittle failure in solids.

Molecular dynamics study of radiation damage and microstructure evolution of zigzag single-walled carbon nanotubes under carbon ion incidence

NASA Astrophysics Data System (ADS)

Li, Huan; Tang, Xiaobin; Chen, Feida; Huang, Hai; Liu, Jian; Chen, Da

2016-07-01

The radiation damage and microstructure evolution of different zigzag single-walled carbon nanotubes (SWCNTs) were investigated under incident carbon ion by molecular dynamics (MD) simulations. The radiation damage of SWCNTs under incident carbon ion with energy ranging from 25 eV to 1 keV at 300 K showed many differences at different incident sites, and the defect production increased to the maximum value with the increase in incident ion energy, and slightly decreased but stayed fairly stable within the majority of the energy range. The maximum damage of SWCNTs appeared when the incident ion energy reached 200 eV and the level of damage was directly proportional to incident ion fluence. The radiation damage was also studied at 100 K and 700 K and the defect production decreased distinctly with rising temperature because radiation-induced defects would anneal and recombine by saturating dangling bonds and reconstructing carbon network at the higher temperature. Furthermore, the stability of a large-diameter tube surpassed that of a thin one under the same radiation environments.

Transient thermal driven bubble's surface and its potential ultrasound-induced damage

NASA Astrophysics Data System (ADS)

Movahed, Pooya; Freund, Jonathan B.

2017-11-01

Ultrasound-induced bubble activity in soft tissues is well-known to be a potential injury mechanism in therapeutic ultrasound treatments. We consider damage by transient thermal effects, including a hypothetical mechanism based on transient thermal phenomena, including viscous dissipation. A spherically symmetric compressible Navier-Stokes discretization is developed to solve the full governing equations, both inside and outside of the bubble, without the usual simplifications in the Rayleigh-Plesset bubble dynamics approach. Equations are solved in the Lagrangian framework, which provides a sharp and accurate representation of the interface as well as the viscous dissipation and thermal transport effects, which preclude reduction to the usual Rayleigh-Plesset ordinary differential equation. This method is used to study transient thermal effects at different frequencies and pressure amplitudes relevant to therapeutic ultrasound treatments. High temperatures achieved in the surrounding medium during the violent bubble collapse phase due to the viscous dissipation in the surrounding medium and thermal conduction from the bubble are expected to cause damage. This work was supported by NIH NIDDK Grant P01-DK043881.

A Numerical Method for Simulating the Microscopic Damage Evolution in Composites Under Uniaxial Transverse Tension

NASA Astrophysics Data System (ADS)

Zhi, Jie; Zhao, Libin; Zhang, Jianyu; Liu, Zhanli

2016-06-01

In this paper, a new numerical method that combines a surface-based cohesive model and extended finite element method (XFEM) without predefining the crack paths is presented to simulate the microscopic damage evolution in composites under uniaxial transverse tension. The proposed method is verified to accurately capture the crack kinking into the matrix after fiber/matrix debonding. A statistical representative volume element (SRVE) under periodic boundary conditions is used to approximate the microstructure of the composites. The interface parameters of the cohesive models are investigated, in which the initial interface stiffness has a great effect on the predictions of the fiber/matrix debonding. The detailed debonding states of SRVE with strong and weak interfaces are compared based on the surface-based and element-based cohesive models. The mechanism of damage in composites under transverse tension is described as the appearance of the interface cracks and their induced matrix micro-cracking, both of which coalesce into transversal macro-cracks. Good agreement is found between the predictions of the model and the in situ experimental observations, demonstrating the efficiency of the presented model for simulating the microscopic damage evolution in composites.

Prediction of failure in notched carbon-fibre-reinforced-polymer laminates under multi-axial loading.

PubMed

Tan, J L Y; Deshpande, V S; Fleck, N A

2016-07-13

A damage-based finite-element model is used to predict the fracture behaviour of centre-notched quasi-isotropic carbon-fibre-reinforced-polymer laminates under multi-axial loading. Damage within each ply is associated with fibre tension, fibre compression, matrix tension and matrix compression. Inter-ply delamination is modelled by cohesive interfaces using a traction-separation law. Failure envelopes for a notch and a circular hole are predicted for in-plane multi-axial loading and are in good agreement with the observed failure envelopes from a parallel experimental study. The ply-by-ply (and inter-ply) damage evolution and the critical mechanisms of ultimate failure also agree with the observed damage evolution. It is demonstrated that accurate predictions of notched compressive strength are obtained upon employing the band broadening stress for microbuckling, highlighting the importance of this damage mode in compression. This article is part of the themed issue 'Multiscale modelling of the structural integrity of composite materials'. © 2016 The Author(s).

Breaking Off of Large Ice Masses From Hanging Glaciers

NASA Astrophysics Data System (ADS)

Pralong, A.; Funk, M.

In order to reduce damage to settlements or other installations (roads, railway, etc) and avoid loss of life, a forecast of the final failure time of ice masses is required. At present, the most promising approach for such a prediction is based on the regularity by which certain large ice masses accelerate prior to the instant of collapse. The lim- itation of this forecast lies in short-term irregularities and in the difficulties to obtain sufficiently accurate data. A better physical understanding of the breaking off process is required, in order to improve the forecasting method. Previous analyze has shown that a stepwise crack extension coupling with a viscous flow leads to the observed acceleration function. We propose another approach by considering a local damage evolution law (gener- alized Kachanow's law) coupled with Glen's flow law to simulate the spatial evolu- tion of damage in polycristalline ice, using a finite element computational model. The present study focuses on the transition from a diffuse to a localised damage reparti- tion occurring during the damage evolution. The influence of inhomogeneous initial conditions (inhomogeneity of the mechanical properties of ice, damage inhomogene- ity) and inhomogeneous boundary conditions on the damage repartition are especially investigated.

Fatigue Damage Evaluation of Short Carbon Fiber Reinforced Plastics Based on Phase Information of Thermoelastic Temperature Change.

PubMed

Shiozawa, Daiki; Sakagami, Takahide; Nakamura, Yu; Nonaka, Shinichi; Hamada, Kenichi

2017-12-06

Carbon fiber-reinforced plastic (CFRP) is widely used for structural members of transportation vehicles such as automobile, aircraft, or spacecraft, utilizing its excellent specific strength and specific rigidity in contrast with the metal. Short carbon fiber composite materials are receiving a lot of attentions because of their excellent moldability and productivity, however they show complicated behaviors in fatigue fracture due to the random fibers orientation. In this study, thermoelastic stress analysis (TSA) using an infrared thermography was applied to evaluate fatigue damage in short carbon fiber composites. The distribution of the thermoelastic temperature change was measured during the fatigue test, as well as the phase difference between the thermoelastic temperature change and applied loading signal. Evolution of fatigue damage was detected from the distribution of thermoelastic temperature change according to the thermoelastic damage analysis (TDA) procedure. It was also found that fatigue damage evolution was more clearly detected than before by the newly developed thermoelastic phase damage analysis (TPDA) in which damaged area was emphasized in the differential phase delay images utilizing the property that carbon fiber shows opposite phase thermoelastic temperature change.

Pair correlation function and nonlinear kinetic equation for a spatially uniform polarizable nonideal plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Belyi, V.V.; Kukharenko, Y.A.; Wallenborn, J.

Taking into account the first non-Markovian correction to the Balescu-Lenard equation, we have derived an expression for the pair correlation function and a nonlinear kinetic equation valid for a nonideal polarized classical plasma. This last equation allows for the description of the correlational energy evolution and shows the global conservation of energy with dynamical polarization. {copyright} {ital 1996 The American Physical Society.}

Role of nonlinear refraction in the generation of terahertz field pulses by light fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zabolotskii, A. A., E-mail: zabolotskii@iae.nsk.su

2013-07-15

The generation of microwave (terahertz) pulses without any envelope in a four-level quasi-resonant medium is considered. Two intense quasi-monochromatic laser fields lead to a partial upper-level population. Microwave field pulses cause the transition between these levels. For appropriately chosen scales, the evolution of the fields is shown to be described by the pseudo-spin evolution equations in a microwave field with the inclusion of nonlinear refraction caused by an adiabatic upper-level population. The evolution of terahertz field pulses is described outside the scope of the slow-envelope approximation. When a number of standard approximations are taken into account, this system of equationsmore » is shown to be equivalent to an integrable version of the generalized reduced Maxwell-Bloch equations or to the generalized three-wave mixing equations. The soliton solution found by the inverse scattering transform method is used as an example to show that nonlinear refraction leads to a strong compression of the microwave (terahertz) field soliton.« less

Dynamics of vector dark solitons propagation and tunneling effect in the variable coefficient coupled nonlinear Schrödinger equation.

PubMed

Musammil, N M; Porsezian, K; Subha, P A; Nithyanandan, K

2017-02-01

We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.

Mapping quantum-classical Liouville equation: projectors and trajectories.

PubMed

Kelly, Aaron; van Zon, Ramses; Schofield, Jeremy; Kapral, Raymond

2012-02-28

The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility, and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.

The Minimum-Mass Surface Density of the Solar Nebula using the Disk Evolution Equation

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

2005-01-01

The Hayashi minimum-mass power law representation of the pre-solar nebula (Hayashi 1981, Prog. Theo. Phys.70,35) is revisited using analytic solutions of the disk evolution equation. A new cumulative-planetary-mass-model (an integrated form of the surface density) is shown to predict a smoother surface density compared with methods based on direct estimates of surface density from planetary data. First, a best-fit transcendental function is applied directly to the cumulative planetary mass data with the surface density obtained by direct differentiation. Next a solution to the time-dependent disk evolution equation is parametrically adapted to the planetary data. The latter model indicates a decay rate of r -1/2 in the inner disk followed by a rapid decay which results in a sharper outer boundary than predicted by the minimum mass model. The model is shown to be a good approximation to the finite-size early Solar Nebula and by extension to extra solar protoplanetary disks.

Outer boundary as arrested history in general relativity

NASA Astrophysics Data System (ADS)

Lau, Stephen R.

2002-06-01

We present explicit outer boundary conditions for the canonical variables of general relativity. The conditions are associated with the causal evolution of a finite Cauchy domain, a so-called quasilocal boost, and they suggest a consistent scheme for modelling such an evolution numerically. The scheme involves a continuous boost in the spacetime orthogonal complement ⊥Tp(B) of the tangent space Tp(B) belonging to each point p on the system boundary B. We show how the boost rate may be computed numerically via equations similar to those appearing in canonical investigations of black-hole thermodynamics (although here holding at an outer two-surface rather than the bifurcate two-surface of a Killing horizon). We demonstrate the numerical scheme on a model example, the quasilocal boost of a spherical three-ball in Minkowski spacetime. Developing our general formalism with recent hyperbolic formulations of the Einstein equations in mind, we use Anderson and York's 'Einstein-Christoffel' hyperbolic system as the evolution equations for our numerical simulation of the model.

Cracking evolution behaviors of lightweight materials based on in situ synchrotron X-ray tomography: A review

NASA Astrophysics Data System (ADS)

Luo, Y.; Wu, S. C.; Hu, Y. N.; Fu, Y. N.

2018-03-01

Damage accumulation and failure behaviors are crucial concerns during the design and service of a critical component, leading researchers and engineers to thoroughly identifying the crack evolution. Third-generation synchrotron radiation X-ray computed microtomography can be used to detect the inner damage evolution of a large-density material or component. This paper provides a brief review of studying the crack initiation and propagation inside lightweight materials with advanced synchrotron three-dimensional (3D) X-ray imaging, such as aluminum materials. Various damage modes under both static and dynamic loading are elucidated for pure aluminum, aluminum alloy matrix, aluminum alloy metal matrix composite, and aluminum alloy welded joint. For aluminum alloy matrix, metallurgical defects (porosity, void, inclusion, precipitate, etc.) or artificial defects (notch, scratch, pit, etc.) strongly affect the crack initiation and propagation. For aluminum alloy metal matrix composites, the fracture occurs either from the particle debonding or voids at the particle/matrix interface, and the void evolution is closely related with fatigued cycles. For the hybrid laser welded aluminum alloy, fatigue cracks usually initiate from gas pores located at the surface or sub-surface and gradually propagate to a quarter ellipse or a typical semi-ellipse profile.

Note on Solutions to a Class of Nonlinear Singular Integro-Differential Equations,

DTIC Science & Technology

1986-08-01

KdV) ut + 2uu x +Uxx x a 0, (1) the sine-Gordon equation Uxt a sin u, (2) and the Kadomtsev - Petviashvili (KP) equation (Ut + 2uu x + UXXx)x -3a 2u yy...SOUIN OA LSFNN ! /" / M.. \\boiz A.S ::-:- and ,M.O.. .- :1/1 / NOTE ON SOLUTIONS TO A CLASS OF NON \\ / LINEAR SINGULAR INTEGRO-DIFFERENTIA[ EQUATIONS by...important nonlinear evolution equations which can be linearized. Many of these equations fall into the category of linearization via soliton theory and

Group-kinetic theory of turbulence

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1986-01-01

The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.

Evolution families of conformal mappings with fixed points and the Löwner-Kufarev equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goryainov, V V

2015-01-31

The paper is concerned with evolution families of conformal mappings of the unit disc to itself that fix an interior point and a boundary point. Conditions are obtained for the evolution families to be differentiable, and an existence and uniqueness theorem for an evolution equation is proved. A convergence theorem is established which describes the topology of locally uniform convergence of evolution families in terms of infinitesimal generating functions. The main result in this paper is the embedding theorem which shows that any conformal mapping of the unit disc to itself with two fixed points can be embedded into a differentiable evolution familymore » of such mappings. This result extends the range of the parametric method in the theory of univalent functions. In this way the problem of the mutual change of the derivative at an interior point and the angular derivative at a fixed point on the boundary is solved for a class of mappings of the unit disc to itself. In particular, the rotation theorem is established for this class of mappings. Bibliography: 27 titles.« less

Uncertainty in Damage Detection, Dynamic Propagation and Just-in-Time Networks

DTIC Science & Technology

2015-08-03

estimated parameter uncertainty in dynamic data sets; high order compact finite difference schemes for Helmholtz equations with discontinuous wave numbers...delay differential equations with a Gamma distributed delay. We found that with the same population size the histogram plots for the solution to the...schemes for Helmholtz equations with discontinuous wave numbers across interfaces. • We carried out numerical sensitivity analysis with respect to

Modelling of hyperconcentrated flood and channel evolution in a braided reach using a dynamically coupled one-dimensional approach

NASA Astrophysics Data System (ADS)

Xia, Junqiang; Zhang, Xiaolei; Wang, Zenghui; Li, Jie; Zhou, Meirong

2018-06-01

Hyperconcentrated sediment-laden floods often occur in a braided reach of the Lower Yellow River, usually leading to significant channel evolution. A one-dimensional (1D) morphodynamic model using a dynamically coupled solution approach is developed to simulate hyperconcentrated flood and channel evolution in the braided reach with an extremely irregular cross-sectional geometry. In the model, the improved equations for hydrodynamics account for the effects of sediment concentration and bed evolution, which are coupled with the equations of non-equilibrium sediment transport and bed evolution. The model was validated using measurements from the 1977 and 2004 hyperconcentrated floods. Furthermore, the effects were investigated of different cross-sectional spacings and allocation modes of channel deformation area on the model results. It was found that a suitable cross-sectional distance of less than 3 km should be adopted when simulating hyperconcentrated floods, and the results using the uniform allocation mode can agree better with measurements than other two allocation modes.

Selected Aspects of Markovian and Non-Markovian Quantum Master Equations

NASA Astrophysics Data System (ADS)

Lendi, K.

A few particular marked properties of quantum dynamical equations accounting for general relaxation and dissipation are selected and summarized in brief. Most results derive from the universal concept of complete positivity. The considerations mainly regard genuinely irreversible processes as characterized by a unique asymptotically stationary final state for arbitrary initial conditions. From ordinary Markovian master equations and associated quantum dynamical semigroup time-evolution, derivations of higher order Onsager coefficients and related entropy production are discussed. For general processes including non-faithful states a regularized version of quantum relative entropy is introduced. Further considerations extend to time-dependent infinitesimal generators of time-evolution and to a possible description of propagation of initial states entangled between open system and environment. In the coherence-vector representation of the full non-Markovian equations including entangled initial states, first results are outlined towards identifying mathematical properties of a restricted class of trial integral-kernel functions suited to phenomenological applications.

Two-dimensional coupled mathematical modeling of fluvial processes with intense sediment transport and rapid bed evolution

NASA Astrophysics Data System (ADS)

Yue, Zhiyuan; Cao, Zhixian; Li, Xin; Che, Tao

2008-09-01

Alluvial rivers may experience intense sediment transport and rapid bed evolution under a high flow regime, for which traditional decoupled mathematical river models based on simplified conservation equations are not applicable. A two-dimensional coupled mathematical model is presented, which is generally applicable to the fluvial processes with either intense or weak sediment transport. The governing equations of the model comprise the complete shallow water hydrodynamic equations closed with Manning roughness for boundary resistance and empirical relationships for sediment exchange with the erodible bed. The second-order Total-Variation-Diminishing version of the Weighted-Average-Flux method, along with the HLLC approximate Riemann Solver, is adapted to solve the governing equations, which can properly resolve shock waves and contact discontinuities. The model is applied to the pilot study of the flooding due to a sudden outburst of a real glacial-lake.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Chuchu, E-mail: chenchuchu@lsec.cc.ac.cn; Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn; Zhang, Liying, E-mail: lyzhang@lsec.cc.ac.cn

Stochastic Maxwell equations with additive noise are a system of stochastic Hamiltonian partial differential equations intrinsically, possessing the stochastic multi-symplectic conservation law. It is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic Maxwell equations with additive noise preserves the divergence in the sense of expectation. Moreover, we propose three novel stochastic multi-symplectic methods to discretize stochastic Maxwell equations in order to investigate the preservation of these properties numerically. We make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the correspondingmore » discrete version of the averaged divergence. Meanwhile, we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method. Especially, the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case. Numerical experiments are performed to verify our theoretical results.« less

New solitary wave and multiple soliton solutions for fifth order nonlinear evolution equation with time variable coefficients

NASA Astrophysics Data System (ADS)

Jaradat, H. M.; Syam, Muhammed; Jaradat, M. M. M.; Mustafa, Zead; Moman, S.

2018-03-01

In this paper, we investigate the multiple soliton solutions and multiple singular soliton solutions of a class of the fifth order nonlinear evolution equation with variable coefficients of t using the simplified bilinear method based on a transformation method combined with the Hirota's bilinear sense. In addition, we present analysis for some parameters such as the soliton amplitude and the characteristic line. Several equation in the literature are special cases of the class which we discuss such as Caudrey-Dodd-Gibbon equation and Sawada-Kotera. Comparison with several methods in the literature, such as Helmholtz solution of the inverse variational problem, rational exponential function method, tanh method, homotopy perturbation method, exp-function method, and coth method, are made. From these comparisons, we conclude that the proposed method is efficient and our solutions are correct. It is worth mention that the proposed solution can solve many physical problems.

The evolution of energetic particles and the emitted radiation in solar flares. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Lu, Edward Tsang

1989-01-01

The evolution of accelerated particle distributions in a magnetized plasma and the resulting radiation are calculated, and the results are applied to solar flares. To study the radiation on timescales of order the particle lifetimes, the evolution of the particle distribution is determined by the use of the Fokker-Planck equation including Coulomb collisions and magnetic mirroring. Analytic solution to the equations are obtained for limiting cases such as homogeneous injection in a homogeneous plasma, and for small pitch angle. These analytic solutions are then used to place constraints on flare parameters such as density, loop length, and the injection timescale for very short implusive solar flares. For general particle distributions in arbitrary magnetic field and background density, the equation is solved numerically. The relative timing of microwaves and X-rays during individual flares is investigated. A number of possible sources for excessive microwave flux are discussed including a flattening in the electron spectrum above hard X-ray energies, thermal synchrotron emission, and trapping of electron by converging magnetic fields. Over shorter timescales, the Fokker-Planck equation is solved numerically to calculate the temporal evolution of microwaves and X-rays from nonthermal thick target models. It is shown that magnetic trapping will not account for the observed correlation of microwaves of approximately 0.15 seconds behind X-rays in flares with rapid time variation, and thus higher energy electrons must be accelerated later than lower energy electrons.

General relativistic treatment of the thermal, magnetic and rotational evolution of isolated neutron stars with crustal magnetic fields

NASA Astrophysics Data System (ADS)

Page, D.; Geppert, U.; Zannias, T.

2000-08-01

We investigate the thermal, magnetic and rotational evolution of isolated neutron stars assuming that the dipolar magnetic field is confined to the crust. Our treatment, for the first time, uses a fully general relativistic formalism not only for the thermal but also for the magnetic part, and includes partial general relativistic effects in the rotational part. Due to the fact that the combined evolution depends crucially upon the compactness of the star, three different equations of state have been employed in the calculations. In the absence of general relativistic effects, while upon increasing compactness a decrease of the crust thickness takes place leading into an accelerating field decay, the inclusion of general relativistic effects intend to "decelerate this acceleration". As a consequence we find that, within the crustal field hypothesis, a given equation of state is compatible with the observed distribution of pulsar periods P and period derivative &mathaccent "705Frelax dot; provided the initial field strength and current location as well as the magnitude of the impurity content are appropriately constrained. Finally, we access the flexibility of the soft, medium and stiff classes of equations of state as candidates in describing the state of the matter in the neutron star interiors. The comparison of our model calculations with observations, together with the consideration of independent information about neutron star evolution, suggests that a not too soft equation of state describes neutron star interiors and its cooling proceeds along the `standard' scenario.

Modelling of squall with the generalised kinetic equation

NASA Astrophysics Data System (ADS)

Annenkov, Sergei; Shrira, Victor

2014-05-01

We study the long-term evolution of random wind waves using the new generalised kinetic equation (GKE). The GKE derivation [1] does not assume the quasi-stationarity of a random wave field. In contrast with the Hasselmann kinetic equation, the GKE can describe fast spectral changes occurring when a wave field is driven out of a quasi-equilibrium state by a fast increase or decrease of wind, or by other factors. In these cases, a random wave field evolves on the dynamic timescale typical of coherent wave processes, rather than on the kinetic timescale predicted by the conventional statistical theory. Besides that, the generalised theory allows to trace the evolution of higher statistical moments of the field, notably the kurtosis, which is important for assessing the risk of freak waves and other applications. A new efficient and highly parallelised algorithm for the numerical simulation of the generalised kinetic equation is presented and discussed. Unlike in the case of the Hasselmann equation, the algorithm takes into account all (resonant and non-resonant) nonlinear wave interactions, but only approximately resonant interactions contribute to the spectral evolution. However, counter-intuitively, all interactions contribute to the kurtosis. Without forcing or dissipation, the algorithm is shown to conserve the relevant integrals. We show that under steady wind forcing the wave field evolution predicted by the GKE is close to the predictions of the conventional statistical theory, which is applicable in this case. In particular, we demonstrate the known long-term asymptotics for the evolution of the spectrum. When the wind forcing is not steady (in the simplest case, an instant increase or decrease of wind occurs), the generalised theory is the only way to study the spectral evolution, apart from the direct numerical simulation. The focus of the work is a detailed analysis of the fast evolution after an instant change of forcing, and of the subsequent transition to the new quasi-stationary state of a wave field. It is shown that both increase and decrease of wind lead to a significant transient increase of the dynamic kurtosis, although these changes remain small compared to the changes of the other component of the kurtosis, which is due to bound harmonics. A special consideration is given to the case of the squall, i.e. an instant and large (by a factor of 2-4) increase of wind, which lasts for O(102) characteristic wave periods. We show that fast adjustment processes lead to the formation of a transient spectrum, which has a considerably narrower peak than the spectra developed under a steady forcing. These transient spectra differ qualitatively from those predicted by the Hasselmann kinetic equation under the squall with the same parameters. 1. S.Annenkov, V.Shrira (2006) Role of non-resonant interactions in evolution of nonlinear random water wave fields, J. Fluid Mech. 561, 181-207.

Characteristics of temporal evolution of particle density and electron temperature in helicon discharge

NASA Astrophysics Data System (ADS)

Yang, Xiong; Cheng, Mousen; Guo, Dawei; Wang, Moge; Li, Xiaokang

2017-10-01

On the basis of considering electrochemical reactions and collision relations in detail, a direct numerical simulation model of a helicon plasma discharge with three-dimensional two-fluid equations was employed to study the characteristics of the temporal evolution of particle density and electron temperature. With the assumption of weak ionization, the Maxwell equations coupled with the plasma parameters were directly solved in the whole computational domain. All of the partial differential equations were solved by the finite element solver in COMSOL MultiphysicsTM with a fully coupled method. In this work, the numerical cases were calculated with an Ar working medium and a Shoji-type antenna. The numerical results indicate that there exist two distinct modes of temporal evolution of the electron and ground atom density, which can be explained by the ion pumping effect. The evolution of the electron temperature is controlled by two schemes: electromagnetic wave heating and particle collision cooling. The high RF power results in a high peak electron temperature while the high gas pressure leads to a low steady temperature. In addition, an OES experiment using nine Ar I lines was conducted using a modified CR model to verify the validity of the results by simulation, showing that the trends of temporal evolution of electron density and temperature are well consistent with the numerically simulated ones.

Thermal Damage Analysis in Biological Tissues Under Optical Irradiation: Application to the Skin

NASA Astrophysics Data System (ADS)

Fanjul-Vélez, Félix; Ortega-Quijano, Noé; Solana-Quirós, José Ramón; Arce-Diego, José Luis

2009-07-01

The use of optical sources in medical praxis is increasing nowadays. In this study, different approaches using thermo-optical principles that allow us to predict thermal damage in irradiated tissues are analyzed. Optical propagation is studied by means of the radiation transport theory (RTT) equation, solved via a Monte Carlo analysis. Data obtained are included in a bio-heat equation, solved via a numerical finite difference approach. Optothermal properties are considered for the model to be accurate and reliable. Thermal distribution is calculated as a function of optical source parameters, mainly optical irradiance, wavelength and exposition time. Two thermal damage models, the cumulative equivalent minutes (CEM) 43 °C approach and the Arrhenius analysis, are used. The former is appropriate when dealing with dosimetry considerations at constant temperature. The latter is adequate to predict thermal damage with arbitrary temperature time dependence. Both models are applied and compared for the particular application of skin thermotherapy irradiation.

Semistable extremal ground states for nonlinear evolution equations in unbounded domains

NASA Astrophysics Data System (ADS)

Rodríguez-Bernal, Aníbal; Vidal-López, Alejandro

2008-02-01

In this paper we show that dissipative reaction-diffusion equations in unbounded domains posses extremal semistable ground states equilibria, which bound asymptotically the global dynamics. Uniqueness of such positive ground state and their approximation by extremal equilibria in bounded domains is also studied. The results are then applied to the important case of logistic equations.

Feedbacks Between Topographic Stress and Drainage Basin Evolution

NASA Astrophysics Data System (ADS)

Perron, J.; Martel, S. J.; Singha, K.; Slim, M. I.

2013-12-01

Theoretical calculations imply that stresses produced by gravity acting on topography may be large enough in some scenarios to fracture rock. Predicted stress fields beneath ridges and valleys can differ dramatically, which has led several authors to hypothesize feedbacks between topographic stress, rock fracture and landscape evolution. However, there have been few attempts to explore these feedbacks. We use a coupled model to identify possible feedbacks between topographic stress and drainage basin evolution. The domain is a cross-section of a valley consisting of a bedrock channel and adjacent soil-mantled hillslopes. The bedrock surface evolves due to channel incision, soil production, and rock uplift, and soil thickness evolves due to soil production and transport. Plane stresses at and below the bedrock surface are calculated with a boundary element method that accounts for both ambient tectonic stress and topographic stress. We assume that the stress field experienced by rock as it is exhumed influences the likelihood that it will develop fractures, which make the rock more susceptible to weathering, disaggregation and erosion. A measure of susceptibility to shear fracture, the most likely failure mode under regional compression, serves as a proxy for rock damage. We couple the landscape evolution model to the stress model by assuming that rock damage accelerates the rates of soil production and channel incision, with two endmember cases: rates scale with the magnitude of the damage proxy at the bedrock surface, or with cumulative damage acquired during rock exhumation. The stress-induced variations in soil production and channel incision alter the soil thickness and topography, which in turn alter the stress field. Comparing model simulations with and without these feedbacks, we note several predicted consequences of topographic stress for drainage basin evolution. Rock damage is typically focused at or near the foot of hillslopes, which creates thicker soils near the valley bottom than near the ridgetop. This gradient in soil thickness is largest, and the thickest soil furthest downslope, if most rock damage is assumed to occur near the surface. Ambient tectonic stress also has a strong effect on hillslopes, with more compressive horizontal stress steepening the soil thickness gradient and displacing the thickest soil farther downslope. Rock damage in the valley bottom scales with valley depth, creating a positive feedback between relief and channel incision. This produces higher relief during transient channel incision, but steady-state relief is insensitive to stress effects because the positive feedback is limited by reduction of the channel slope. However, the fact that valleys are typically deepest in the middle of a drainage basin implies that channel profiles will be more concave if stresses enhance channel incision. Observational tests of these qualitative predictions will help evaluate the significance of suspected feedbacks between topographic stress and landscape evolution.

Exemplar for simulation challenges: Large-deformation micromechanics of Sylgard 184/glass microballoon syntactic foams.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Judith Alice; Long, Kevin Nicholas

2018-05-01

Sylgard® 184/Glass Microballoon (GMB) potting material is currently used in many NW systems. Analysts need a macroscale constitutive model that can predict material behavior under complex loading and damage evolution. To address this need, ongoing modeling and experimental efforts have focused on study of damage evolution in these materials. Micromechanical finite element simulations that resolve individual GMB and matrix components promote discovery and better understanding of the material behavior. With these simulations, we can study the role of the GMB volume fraction, time-dependent damage, behavior under confined vs. unconfined compression, and the effects of partial damage. These simulations are challengingmore » and push the boundaries of capability even with the high performance computing tools available at Sandia. We summarize the major challenges and the current state of this modeling effort, as an exemplar of micromechanical modeling needs that can motivate advances in future computing efforts.« less

An experimental investigation of damage evolution in a ceramic matrix composite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Walter, M.E.; Ravichandran, G.

The mechanical behavior of a glass-ceramic matrix composite, SiC/CAS (calcium aluminosilicate reinforced with unidirectional SiC fibers), is studied. Results based on uniaxial tension experiments are presented for specimens with fibers aligned in the loading direction. Axial and transverse strain gages on all four gage section surfaces and in situ acoustic emission and ultrasonic wave speed measurements were used to monitor the evolution of damage. All measurements were made with high-resolution, continuous data acquisition. Post-test optical and scanning electron microscopy was also used to identify the various micromechanisms of damage. The experimental results demonstrate the existence of zones of deformation'' whichmore » are associated with the onset of different damage mechanisms. It is shown that the observed stress-strain behavior can be explained in terms of the material properties of the matrix and the fiber, the material processing, and the postulated zones of deformation.« less

Mesoscale analysis of failure in quasi-brittle materials: comparison between lattice model and acoustic emission data.

PubMed

Grégoire, David; Verdon, Laura; Lefort, Vincent; Grassl, Peter; Saliba, Jacqueline; Regoin, Jean-Pierre; Loukili, Ahmed; Pijaudier-Cabot, Gilles

2015-10-25

The purpose of this paper is to analyse the development and the evolution of the fracture process zone during fracture and damage in quasi-brittle materials. A model taking into account the material details at the mesoscale is used to describe the failure process at the scale of the heterogeneities. This model is used to compute histograms of the relative distances between damaged points. These numerical results are compared with experimental data, where the damage evolution is monitored using acoustic emissions. Histograms of the relative distances between damage events in the numerical calculations and acoustic events in the experiments exhibit good agreement. It is shown that the mesoscale model provides relevant information from the point of view of both global responses and the local failure process. © 2015 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.

Constrained evolution in numerical relativity

NASA Astrophysics Data System (ADS)

Anderson, Matthew William

The strongest potential source of gravitational radiation for current and future detectors is the merger of binary black holes. Full numerical simulation of such mergers can provide realistic signal predictions and enhance the probability of detection. Numerical simulation of the Einstein equations, however, is fraught with difficulty. Stability even in static test cases of single black holes has proven elusive. Common to unstable simulations is the growth of constraint violations. This work examines the effect of controlling the growth of constraint violations by solving the constraints periodically during a simulation, an approach called constrained evolution. The effects of constrained evolution are contrasted with the results of unconstrained evolution, evolution where the constraints are not solved during the course of a simulation. Two different formulations of the Einstein equations are examined: the standard ADM formulation and the generalized Frittelli-Reula formulation. In most cases constrained evolution vastly improves the stability of a simulation at minimal computational cost when compared with unconstrained evolution. However, in the more demanding test cases examined, constrained evolution fails to produce simulations with long-term stability in spite of producing improvements in simulation lifetime when compared with unconstrained evolution. Constrained evolution is also examined in conjunction with a wide variety of promising numerical techniques, including mesh refinement and overlapping Cartesian and spherical computational grids. Constrained evolution in boosted black hole spacetimes is investigated using overlapping grids. Constrained evolution proves to be central to the host of innovations required in carrying out such intensive simulations.

The weak coupling limit as a quantum functional central limit

NASA Astrophysics Data System (ADS)

Accardi, L.; Frigerio, A.; Lu, Y. G.

1990-08-01

We show that, in the weak coupling limit, the laser model process converges weakly in the sense of the matrix elements to a quantum diffusion whose equation is explicitly obtained. We prove convergence, in the same sense, of the Heisenberg evolution of an observable of the system to the solution of a quantum Langevin equation. As a corollary of this result, via the quantum Feynman-Kac technique, one can recover previous results on the quantum master equation for reduced evolutions of open systems. When applied to some particular model (e.g. the free Boson gas) our results allow to interpret the Lamb shift as an Ito correction term and to express the pumping rates in terms of quantities related to the original Hamiltonian model.

Impacts and the origin of life

NASA Technical Reports Server (NTRS)

Oberbeck, Verne R.; Fogleman, Guy

1989-01-01

Consideration is given to the estimate of Maher and Stevenson (1988) of the time at which life could have developed on earth through chemical evolution within a time interval between impact events, assuming chemical or prebiotic evolution times of 100,000 to 10,000,000 yrs. An error in the equations used to determine the time periods between impact events in estimating this time is noted. A revised equation is presented and used to calculate the point in time at which impact events became infrequent enough for life to form. By using this equation, the finding of Maher and Stevenson that life could have first originated between 4,100 and 4,300 million years ago is changed to 3,700 to 4,000 million years ago.

Model dynamics for quantum computing

NASA Astrophysics Data System (ADS)

Tabakin, Frank

2017-08-01

A model master equation suitable for quantum computing dynamics is presented. In an ideal quantum computer (QC), a system of qubits evolves in time unitarily and, by virtue of their entanglement, interfere quantum mechanically to solve otherwise intractable problems. In the real situation, a QC is subject to decoherence and attenuation effects due to interaction with an environment and with possible short-term random disturbances and gate deficiencies. The stability of a QC under such attacks is a key issue for the development of realistic devices. We assume that the influence of the environment can be incorporated by a master equation that includes unitary evolution with gates, supplemented by a Lindblad term. Lindblad operators of various types are explored; namely, steady, pulsed, gate friction, and measurement operators. In the master equation, we use the Lindblad term to describe short time intrusions by random Lindblad pulses. The phenomenological master equation is then extended to include a nonlinear Beretta term that describes the evolution of a closed system with increasing entropy. An external Bath environment is stipulated by a fixed temperature in two different ways. Here we explore the case of a simple one-qubit system in preparation for generalization to multi-qubit, qutrit and hybrid qubit-qutrit systems. This model master equation can be used to test the stability of memory and the efficacy of quantum gates. The properties of such hybrid master equations are explored, with emphasis on the role of thermal equilibrium and entropy constraints. Several significant properties of time-dependent qubit evolution are revealed by this simple study.

General relativistic screening in cosmological simulations

NASA Astrophysics Data System (ADS)

Hahn, Oliver; Paranjape, Aseem

2016-10-01

We revisit the issue of interpreting the results of large volume cosmological simulations in the context of large-scale general relativistic effects. We look for simple modifications to the nonlinear evolution of the gravitational potential ψ that lead on large scales to the correct, fully relativistic description of density perturbations in the Newtonian gauge. We note that the relativistic constraint equation for ψ can be cast as a diffusion equation, with a diffusion length scale determined by the expansion of the Universe. Exploiting the weak time evolution of ψ in all regimes of interest, this equation can be further accurately approximated as a Helmholtz equation, with an effective relativistic "screening" scale ℓ related to the Hubble radius. We demonstrate that it is thus possible to carry out N-body simulations in the Newtonian gauge by replacing Poisson's equation with this Helmholtz equation, involving a trivial change in the Green's function kernel. Our results also motivate a simple, approximate (but very accurate) gauge transformation—δN(k )≈δsim(k )×(k2+ℓ-2)/k2 —to convert the density field δsim of standard collisionless N -body simulations (initialized in the comoving synchronous gauge) into the Newtonian gauge density δN at arbitrary times. A similar conversion can also be written in terms of particle positions. Our results can be interpreted in terms of a Jeans stability criterion induced by the expansion of the Universe. The appearance of the screening scale ℓ in the evolution of ψ , in particular, leads to a natural resolution of the "Jeans swindle" in the presence of superhorizon modes.

Markovian Monte Carlo program EvolFMC v.2 for solving QCD evolution equations

NASA Astrophysics Data System (ADS)

Jadach, S.; Płaczek, W.; Skrzypek, M.; Stokłosa, P.

2010-02-01

We present the program EvolFMC v.2 that solves the evolution equations in QCD for the parton momentum distributions by means of the Monte Carlo technique based on the Markovian process. The program solves the DGLAP-type evolution as well as modified-DGLAP ones. In both cases the evolution can be performed in the LO or NLO approximation. The quarks are treated as massless. The overall technical precision of the code has been established at 5×10. This way, for the first time ever, we demonstrate that with the Monte Carlo method one can solve the evolution equations with precision comparable to the other numerical methods. New version program summaryProgram title: EvolFMC v.2 Catalogue identifier: AEFN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including binary test data, etc.: 66 456 (7407 lines of C++ code) No. of bytes in distributed program, including test data, etc.: 412 752 Distribution format: tar.gz Programming language: C++ Computer: PC, Mac Operating system: Linux, Mac OS X RAM: Less than 256 MB Classification: 11.5 External routines: ROOT ( http://root.cern.ch/drupal/) Nature of problem: Solution of the QCD evolution equations for the parton momentum distributions of the DGLAP- and modified-DGLAP-type in the LO and NLO approximations. Solution method: Monte Carlo simulation of the Markovian process of a multiple emission of partons. Restrictions:Limited to the case of massless partons. Implemented in the LO and NLO approximations only. Weighted events only. Unusual features: Modified-DGLAP evolutions included up to the NLO level. Additional comments: Technical precision established at 5×10. Running time: For the 10 6 events at 100 GeV: DGLAP NLO: 27s; C-type modified DGLAP NLO: 150s (MacBook Pro with Mac OS X v.10.5.5, 2.4 GHz Intel Core 2 Duo, gcc 4.2.4, single thread).

The evolution of dispersal in a Levins' type metapopulation model.

PubMed

Jansen, Vincent A A; Vitalis, Renaud

2007-10-01

We study the evolution of the dispersal rate in a metapopulation model with extinction and colonization dynamics, akin to the model as originally described by Levins. To do so we extend the metapopulation model with a description of the within patch dynamics. By means of a separation of time scales we analytically derive a fitness expression from first principles for this model. The fitness function can be written as an inclusive fitness equation (Hamilton's rule). By recasting this equation in a form that emphasizes the effects of competition we show the effect of the local competition and the local population size on the evolution of dispersal. We find that the evolution of dispersal cannot be easily interpreted in terms of avoidance of kin competition, but rather that increased dispersal reduces the competitive ability. Our model also yields a testable prediction in term of relatedness and life-history parameters.

Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics.

PubMed

Glavatskiy, K S

2015-05-28

We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such that there exists an "integral of evolution" which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

PubMed

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

PubMed Central

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method. PMID:25973605

Evolution equation for quantum coherence

PubMed Central

Hu, Ming-Liang; Fan, Heng

2016-01-01

The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures. PMID:27382933

Ionizing doses and displacement damage testing of COTS CMOS imagers

NASA Astrophysics Data System (ADS)

Bernard, Frédéric; Petit, Sophie; Courtade, Sophie

2017-11-01

CMOS sensors begin to be a credible alternative to CCD sensors in some space missions. However, technology evolution of CMOS sensors is much faster than CCD one's. So a continuous technology evaluation is needed for CMOS imagers. Many of commercial COTS (Components Off The Shelf) CMOS sensors use organic filters, micro-lenses and non rad-hard technologies. An evaluation of the possibilities offered by such technologies is interesting before any custom development. This can be obtained by testing commercial COTS imagers. This article will present electro-optical performances evolution of off the shelves CMOS imagers after Ionizing Doses until 50kRad(Si) and Displacement Damage environment tests (until 1011 p/cm2 at 50 MeV). Dark current level and non uniformity evolutions are compared and discussed. Relative spectral response measurement and associated evolution with irradiation will also be presented and discussed. Tests have been performed on CNES detection benches.

Geometrothermodynamic model for the evolution of the Universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gruber, Christine; Quevedo, Hernando, E-mail: christine.gruber@correo.nucleares.unam.mx, E-mail: quevedo@nucleares.unam.mx

Using the formalism of geometrothermodynamics to derive a fundamental thermodynamic equation, we construct a cosmological model in the framework of relativistic cosmology. In a first step, we describe a system without thermodynamic interaction, and show it to be equivalent to the standard ΛCDM paradigm. The second step includes thermodynamic interaction and produces a model consistent with the main features of inflation. With the proposed fundamental equation we are thus able to describe all the known epochs in the evolution of our Universe, starting from the inflationary phase.

Symmetric factorization of the conformation tensor in viscoelastic fluid models

NASA Astrophysics Data System (ADS)

Thomases, Becca; Balci, Nusret; Renardy, Michael; Doering, Charles

2010-11-01

The positive definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the velocity field and the symmetric square root of the conformation tensor, these models' equations of motion formally constitute an evolution in a Hilbert space with a total energy functional that defines a norm. Moreover, this formulation is easily implemented in direct numerical simulations resulting in significant practical advantages in terms of both accuracy and stability.

Controlled Quantum Packets

NASA Technical Reports Server (NTRS)

DeMartino, Salvatore; DeSiena, Silvio

1996-01-01

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

Evolution of Degenerate Space-Time from Non-Degenerate Initial Value in Ashtekar's Formalism

NASA Astrophysics Data System (ADS)

Ma, Yongge; Liang, Canbin

1998-09-01

The possibility of evolving a degenerate space-time from non-degenerate initial value in Ashtekar's formalism is considered in a constructed example. It is found that this possibility could be realized in the time evolution given by Ashtekar's equations, but the topology change of space makes it fail to be a Cauchy evolution.

Properties of bright solitons in averaged and unaveraged models for SDG fibres

NASA Astrophysics Data System (ADS)

Kumar, Ajit; Kumar, Atul

1996-04-01

Using the slowly varying envelope approximation and averaging over the fibre cross-section the evolution equation for optical pulses in semiconductor-doped glass (SDG) fibres is derived from the nonlinear wave equation. Bright soliton solutions of this equation are obtained numerically and their properties are studied and compared with those of the bright solitons in the unaveraged model.

Gyrofluid turbulence models with kinetic effects

NASA Astrophysics Data System (ADS)

Dorland, W.; Hammett, G. W.

1993-03-01

Nonlinear gyrofluid equations are derived by taking moments of the nonlinear, electrostatic gyrokinetic equation. The principal model presented includes evolution equations for the guiding center n, u∥, T∥, and T⊥ along with an equation expressing the quasineutrality constraint. Additional evolution equations for higher moments are derived that may be used if greater accuracy is desired. The moment hierarchy is closed with a Landau damping model [G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64, 3019 (1990)], which is equivalent to a multipole approximation to the plasma dispersion function, extended to include finite Larmor radius effects (FLR). In particular, new dissipative, nonlinear terms are found that model the perpendicular phase mixing of the distribution function along contours of constant electrostatic potential. These ``FLR phase-mixing'' terms introduce a hyperviscositylike damping ∝k⊥2‖Φkk×k'‖, which should provide a physics-based damping mechanism at high k⊥ρ which is potentially as important as the usual polarization drift nonlinearity. The moments are taken in guiding center space to pick up the correct nonlinear FLR terms and the gyroaveraging of the shear. The equations are solved with a nonlinear, three-dimensional initial value code. Linear results are presented, showing excellent agreement with linear gyrokinetic theory.

Dynamics of a differential-difference integrable (2+1)-dimensional system.

PubMed

Yu, Guo-Fu; Xu, Zong-Wei

2015-06-01

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled (2+1)-dimensional system which is related to the KP equation and the Zakharov equation. N-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

The Kadomtsev{endash}Petviashvili equation as a source of integrable model equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maccari, A.

1996-12-01

A new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained, by an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, from the Kadomtsev{endash}Petviashvili equation. The integrability property is explicitly demonstrated, by exhibiting the corresponding Lax pair, that is obtained by applying the reduction technique to the Lax pair of the Kadomtsev{endash}Petviashvili equation. This model equation is likely to be of applicative relevance, because it may be considered a consistent approximation of a large class of nonlinear evolution PDEs. {copyright} {ital 1996 American Institute of Physics.}

Effect of annealing on the laser induced damage of polished and CO2 laser-processed fused silica surfaces

NASA Astrophysics Data System (ADS)

Doualle, T.; Gallais, L.; Cormont, P.; Donval, T.; Lamaignère, L.; Rullier, J. L.

2016-06-01

We investigate the effect of different heat treatments on the laser-induced damage probabilities of fused silica samples. Isothermal annealing in a furnace is applied, with different temperatures in the range 700-1100 °C and 12 h annealing time, to super-polished fused silica samples. The surface flatness and laser damage probabilities at 3 ns, 351 nm are measured before and after the different annealing procedures. We have found a significant improvement of the initial laser damage probabilities of the silica surface after annealing at 1050 °C for 12 h. A similar study has been conducted on CO2 laser-processed sites on the surface of the samples. Before and after annealing, we have studied the morphology of the sites, the evolution of residual stress, and the laser-induced damage threshold measured at 351 nm, 3 ns. In this case, we observe that the laser damage resistance of the laser created craters can reach the damage level of the bare fused silica surface after the annealing process, with a complete stress relieve. The obtained results are then compared to the case of local annealing process by CO2 laser irradiation during 1 s, and we found similar improvements in both cases. The different results obtained in the study are compared to numerical simulations made with a thermo-mechanical model based on finite-element method that allows the simulation of the isothermal or the local annealing process, the evolution of stress and fictive temperature. The simulation results were found to be very consistent with experimental observations for the stresses evolution after annealing and estimation of the heat affected area during laser-processing based on the density dependence with fictive temperature. Following this work, the temperature for local annealing should reach 1330-1470 °C for an optimized reduction of damage probability and be below the threshold for material removal, whereas furnace annealing should be kept below the annealing point to avoid sample deformation.

Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Islam, S M Rayhanul

2014-01-01

In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact solutions-hyperbolic and trigonometric solutions of the associated equations are characterized with some free parameters. Then these exact solutions correspond to solitary waves for particular values of the parameters. 02.30.Jr; 02.70.Wz; 05.45.Yv; 94.05.Fg.

The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts

NASA Astrophysics Data System (ADS)

Neill, Duff

2017-01-01

We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.

The genetic architecture of sexual conflict: male harm and female resistance in Callosobruchus maculatus.

PubMed

Gay, L; Brown, E; Tregenza, T; Pincheira-Donoso, D; Eady, P E; Vasudev, R; Hunt, J; Hosken, D J

2011-02-01

Males harm females during mating in a range of species. This harm is thought to evolve because it is directly or indirectly beneficial to the male, despite being costly to his mate. The resulting sexually antagonistic selection can cause sexual arms races. For sexually antagonistic co-evolution to occur, there must be genetic variation for traits involved in female harming and susceptibility to harm, but even then intersexual genetic correlations could facilitate or impede sexual co-evolution. Male Callosobruchus maculatus harm their mates during copulation by damaging the female's reproductive tract. However, there have been no investigations of the genetic variation in damage or in female susceptibility to damage, nor has the genetic covariance between these characters been assessed. Here, we use a full-sib/half-sib breeding design to show that male damage is heritable, whereas female susceptibility to damage is much less so. There is also a substantial positive genetic correlation between the two, suggesting that selection favouring damaging males will increase the prevalence of susceptible females. We also provide evidence consistent with intralocus sexual conflict in this species. © 2010 The Authors. Journal of Evolutionary Biology © 2010 European Society For Evolutionary Biology.

Cluster analysis of stress corrosion mechanisms for steel wires used in bridge cables through acoustic emission particle swarm optimization.

PubMed

Li, Dongsheng; Yang, Wei; Zhang, Wenyao

2017-05-01

Stress corrosion is the major failure type of bridge cable damage. The acoustic emission (AE) technique was applied to monitor the stress corrosion process of steel wires used in bridge cable structures. The damage evolution of stress corrosion in bridge cables was obtained according to the AE characteristic parameter figure. A particle swarm optimization cluster method was developed to determine the relationship between the AE signal and stress corrosion mechanisms. Results indicate that the main AE sources of stress corrosion in bridge cables included four types: passive film breakdown and detachment of the corrosion product, crack initiation, crack extension, and cable fracture. By analyzing different types of clustering data, the mean value of each damage pattern's AE characteristic parameters was determined. Different corrosion damage source AE waveforms and the peak frequency were extracted. AE particle swarm optimization cluster analysis based on principal component analysis was also proposed. This method can completely distinguish the four types of damage sources and simplifies the determination of the evolution process of corrosion damage and broken wire signals. Copyright © 2017. Published by Elsevier B.V.

The cubic-quintic-septic complex Ginzburg-Landau equation formulation of optical pulse propagation in 3D doped Kerr media with higher-order dispersions

NASA Astrophysics Data System (ADS)

Djoko, Martin; Kofane, T. C.

2018-06-01

We investigate the propagation characteristics and stabilization of generalized-Gaussian pulse in highly nonlinear homogeneous media with higher-order dispersion terms. The optical pulse propagation has been modeled by the higher-order (3+1)-dimensional cubic-quintic-septic complex Ginzburg-Landau [(3+1)D CQS-CGL] equation. We have used the variational method to find a set of differential equations characterizing the variation of the pulse parameters in fiber optic-links. The variational equations we obtained have been integrated numerically by the means of the fourth-order Runge-Kutta (RK4) method, which also allows us to investigate the evolution of the generalized-Gaussian beam and the pulse evolution along an optical doped fiber. Then, we have solved the original nonlinear (3+1)D CQS-CGL equation with the split-step Fourier method (SSFM), and compare the results with those obtained, using the variational approach. A good agreement between analytical and numerical methods is observed. The evolution of the generalized-Gaussian beam has shown oscillatory propagation, and bell-shaped dissipative optical bullets have been obtained under certain parameter values in both anomalous and normal chromatic dispersion regimes. Using the natural control parameter of the solution as it evolves, named the total energy Q, our numerical simulations reveal the existence of 3D stable vortex dissipative light bullets, 3D stable spatiotemporal optical soliton, stationary and pulsating optical bullets, depending on the used initial input condition (symmetric or elliptic).

Dynamic Evolution Of Off-Fault Medium During An Earthquake: A Micromechanics Based Model

NASA Astrophysics Data System (ADS)

Thomas, Marion Y.; Bhat, Harsha S.

2018-05-01

Geophysical observations show a dramatic drop of seismic wave speeds in the shallow off-fault medium following earthquake ruptures. Seismic ruptures generate, or reactivate, damage around faults that alter the constitutive response of the surrounding medium, which in turn modifies the earthquake itself, the seismic radiation, and the near-fault ground motion. We present a micromechanics based constitutive model that accounts for dynamic evolution of elastic moduli at high-strain rates. We consider 2D in-plane models, with a 1D right lateral fault featuring slip-weakening friction law. The two scenarios studied here assume uniform initial off-fault damage and an observationally motivated exponential decay of initial damage with fault normal distance. Both scenarios produce dynamic damage that is consistent with geological observations. A small difference in initial damage actively impacts the final damage pattern. The second numerical experiment, in particular, highlights the complex feedback that exists between the evolving medium and the seismic event. We show that there is a unique off-fault damage pattern associated with supershear transition of an earthquake rupture that could be potentially seen as a geological signature of this transition. These scenarios presented here underline the importance of incorporating the complex structure of fault zone systems in dynamic models of earthquakes.

Dynamic Evolution Of Off-Fault Medium During An Earthquake: A Micromechanics Based Model

NASA Astrophysics Data System (ADS)

Thomas, M. Y.; Bhat, H. S.

2017-12-01

Geophysical observations show a dramatic drop of seismic wave speeds in the shallow off-fault medium following earthquake ruptures. Seismic ruptures generate, or reactivate, damage around faults that alter the constitutive response of the surrounding medium, which in turn modifies the earthquake itself, the seismic radiation, and the near-fault ground motion. We present a micromechanics based constitutive model that accounts for dynamic evolution of elastic moduli at high-strain rates. We consider 2D in-plane models, with a 1D right lateral fault featuring slip-weakening friction law. The two scenarios studied here assume uniform initial off-fault damage and an observationally motivated exponential decay of initial damage with fault normal distance. Both scenarios produce dynamic damage that is consistent with geological observations. A small difference in initial damage actively impacts the final damage pattern. The second numerical experiment, in particular, highlights the complex feedback that exists between the evolving medium and the seismic event. We show that there is a unique off-fault damage pattern associated with supershear transition of an earthquake rupture that could be potentially seen as a geological signature of this transition. These scenarios presented here underline the importance of incorporating the complex structure of fault zone systems in dynamic models of earthquakes.

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Nonlinear inhomogeneous Fokker-Planck equations: Entropy and free-energy time evolution.

PubMed

Sicuro, Gabriele; Rapčan, Peter; Tsallis, Constantino

2016-12-01

We extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck equations. In our approach, the free-energy functional is expressed in terms of an entropic functional and an auxiliary potential, both derived from the coefficients of the equation. With reference to the introduced entropic functional, we discuss the entropy production in a relaxation process towards equilibrium. The properties of the stationary solutions of the considered Fokker-Planck equations are also discussed.

Evolution of magnetic field and atmospheric response. I - Three-dimensional formulation by the method of projected characteristics. II - Formulation of proper boundary equations. [stellar magnetohydrodynamics

NASA Technical Reports Server (NTRS)

Nakagawa, Y.

1981-01-01

The method described as the method of nearcharacteristics by Nakagawa (1980) is renamed the method of projected characteristics. Making full use of properties of the projected characteristics, a new and simpler formulation is developed. As a result, the formulation for the examination of the general three-dimensional problems is presented. It is noted that since in practice numerical solutions must be obtained, the final formulation is given in the form of difference equations. The possibility of including effects of viscous and ohmic dissipations in the formulation is considered, and the physical interpretation is discussed. A systematic manner is then presented for deriving physically self-consistent, time-dependent boundary equations for MHD initial boundary problems. It is demonstrated that the full use of the compatibility equations (differential equations relating variations at two spatial locations and times) is required in determining the time-dependent boundary conditions. In order to provide a clear physical picture as an example, the evolution of axisymmetric global magnetic field by photospheric differential rotation is considered.

The general relativistic thin disc evolution equation

NASA Astrophysics Data System (ADS)

Balbus, Steven A.

2017-11-01

In the classical theory of thin disc accretion discs, the constraints of mass and angular momentum conservation lead to a diffusion-like equation for the turbulent evolution of the surface density. Here, we revisit this problem, extending the Newtonian analysis to the regime of Kerr geometry relevant to black holes. A diffusion-like equation once again emerges, but now with a singularity at the radius at which the effective angular momentum gradient passes through zero. The equation may be analysed using a combination of Wentzel-Kramers-Brillouin techniques, local techniques and matched asymptotic expansions. It is shown that imposing the boundary condition of a vanishing stress tensor (more precisely the radial-azimuthal component thereof) allows smooth stable modes to exist external to the angular momentum singularity, the innermost stable circular orbit, while smoothly vanishing inside this location. The extension of the disc diffusion equation to the domain of general relativity introduces a new tool for numerical and phenomenological studies of accretion discs, and may prove to be a useful technique for understanding black hole X-ray transients.

Evolution of density and velocity profiles of dark matter and dark energy in spherical voids

NASA Astrophysics Data System (ADS)

Novosyadlyj, Bohdan; Tsizh, Maksym; Kulinich, Yurij

2017-02-01

We analyse the evolution of cosmological perturbations which leads to the formation of large isolated voids in the Universe. We assume that initial perturbations are spherical and all components of the Universe (radiation, matter and dark energy) are continuous media with ideal fluid energy-momentum tensors, which interact only gravitationally. Equations of the evolution of perturbations for every component in the comoving to cosmological background reference frame are obtained from equations of energy and momentum conservation and Einstein's ones and are integrated numerically. Initial conditions are set at the early stage of evolution in the radiation-dominated epoch, when the scale of perturbation is much larger than the particle horizon. Results show how the profiles of density and velocity of matter and dark energy are formed and how they depend on parameters of dark energy and initial conditions. In particular, it is shown that final matter density and velocity amplitudes change within range ˜4-7 per cent when the value of equation-of-state parameter of dark energy w vary in the range from -0.8 to -1.2, and change within ˜1 per cent only when the value of effective sound speed of dark energy vary over all allowable range of its values.

A mathematical model for evolution and SETI.

PubMed

Maccone, Claudio

2011-12-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f(l) in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f(l) is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

Modelling Evolution and SETI Mathematically

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2012-05-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor fl is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factor increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions constrained between the time axis and the exponential growth curve. Finally, since each lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

A Mathematical Model for Evolution and SETI

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2011-12-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor fl is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

Coupled electronic and atomic effects on defect evolution in silicon carbide under ion irradiation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Yanwen; Xue, Haizhou; Zarkadoula, Eva

Understanding energy dissipation processes in electronic/atomic subsystems and subsequent non-equilibrium defect evolution is a long-standing challenge in materials science. In the intermediate energy regime, energetic particles simultaneously deposit a significant amount of energy to both electronic and atomic subsystems of silicon carbide (SiC). Here we show that defect evolution in SiC closely depends on the electronic-to-nuclear energy loss ratio (S e/S n), nuclear stopping powers ( dE/dx nucl), electronic stopping powers ( dE/dx ele), and the temporal and spatial coupling of electronic and atomic subsystem for energy dissipation. The integrated experiments and simulations reveal that: (1) increasing S e/S nmore » slows damage accumulation; (2) the transient temperatures during the ionization-induced thermal spike increase with dE/dx ele, which causes efficient damage annealing along the ion trajectory; and (3) for more condensed displacement damage within the thermal spike, damage production is suppressed due to the coupled electronic and atomic dynamics. Ionization effects are expected to be more significant in materials with covalent/ionic bonding involving predominantly well-localized electrons. Here, insights into the complex electronic and atomic correlations may pave the way to better control and predict SiC response to extreme energy deposition« less

In-process, non-destructive multimodal dynamic testing of high-speed composite rotors

NASA Astrophysics Data System (ADS)

Kuschmierz, Robert; Filippatos, Angelos; Langkamp, Albert; Hufenbach, Werner; Czarske, Jürgern W.; Fischer, Andreas

2014-03-01

Fibre reinforced plastic (FRP) rotors are lightweight and offer great perspectives in high-speed applications such as turbo machinery. Currently, novel rotor structures and materials are investigated for the purpose of increasing machine efficiency, lifetime and loading limits. Due to complex rotor structures, high anisotropy and non-linear behavior of FRP under dynamic loads, an in-process measurement system is necessary to monitor and to investigate the evolution of damages under real operation conditions. A non-invasive, optical laser Doppler distance sensor measurement system is applied to determine the biaxial deformation of a bladed FRP rotor with micron uncertainty as well as the tangential blade vibrations at surface speeds above 300 m/s. The laser Doppler distance sensor is applicable under vacuum conditions. Measurements at varying loading conditions are used to determine elastic and plastic deformations. Furthermore they allow to determine hysteresis, fatigue, Eigenfrequency shifts and loading limits. The deformation measurements show a highly anisotropic and nonlinear behavior and offer a deeper understanding of the damage evolution in FRP rotors. The experimental results are used to validate and to calibrate a simulation model of the deformation. The simulation combines finite element analysis and a damage mechanics model. The combination of simulation and measurement system enables the monitoring and prediction of damage evolutions of FRP rotors in process.

Comparison of Tensile Damage Evolution in Ti6A14V Joints Between Laser Beam Welding and Gas Tungsten Arc Welding

NASA Astrophysics Data System (ADS)

Gao, Xiao-Long; Zhang, Lin-Jie; Liu, Jing; Zhang, Jian-Xun

2014-12-01

The present paper studied the evolution of tensile damage in joints welded using laser beam welding (LBW) and gas tungsten arc welding (TIG) under a uniaxial tensile load. The damage evolution in the LBW joints and TIG-welded joints was studied by using digital image correlation (DIC) technology and monitoring changes in Young's modulus during tensile testing. To study the mechanism of void nucleation and growth in the LBW joints and TIG-welded joints, test specimens with various amounts of plastic deformation were analyzed using a scanning electron microscope (SEM). Compared with TIG-welded joints, LBW-welded joints have a finer microstructure and higher microhardness in the fusion zone. The SEM analysis and DIC test results indicated that the critical strain of void nucleation was greater in the LBW-welded joints than in the TIG-welded joints, while the growth rate of voids was lower in the LBW-welded joints than in the TIG-welded joints. Thus, the damage ratio in the LBW joints was lower than that in the TIG-welded joints during tensile testing. This can be due to the coarser martensitic α' and the application of TC-1 welding rods in the TIG-welded joint.

Deformation analysis of polymers composites: rheological model involving time-based fractional derivative

NASA Astrophysics Data System (ADS)

Zhou, H. W.; Yi, H. Y.; Mishnaevsky, L.; Wang, R.; Duan, Z. Q.; Chen, Q.

2017-05-01

A modeling approach to time-dependent property of Glass Fiber Reinforced Polymers (GFRP) composites is of special interest for quantitative description of long-term behavior. An electronic creep machine is employed to investigate the time-dependent deformation of four specimens of dog-bond-shaped GFRP composites at various stress level. A negative exponent function based on structural changes is introduced to describe the damage evolution of material properties in the process of creep test. Accordingly, a new creep constitutive equation, referred to fractional derivative Maxwell model, is suggested to characterize the time-dependent behavior of GFRP composites by replacing Newtonian dashpot with the Abel dashpot in the classical Maxwell model. The analytic solution for the fractional derivative Maxwell model is given and the relative parameters are determined. The results estimated by the fractional derivative Maxwell model proposed in the paper are in a good agreement with the experimental data. It is shown that the new creep constitutive model proposed in the paper needs few parameters to represent various time-dependent behaviors.

Intraspecific competition facilitates the evolution of tolerance to insect damage in the perennial plant Solanum carolinense.

PubMed

McNutt, David W; Halpern, Stacey L; Barrows, Kahaili; Underwood, Nora

2012-12-01

Tolerance to herbivory (the degree to which plants maintain fitness after damage) is a key component of plant defense, so understanding how natural selection and evolutionary constraints act on tolerance traits is important to general theories of plant-herbivore interactions. These factors may be affected by plant competition, which often interacts with damage to influence trait expression and fitness. However, few studies have manipulated competitor density to examine the evolutionary effects of competition on tolerance. In this study, we tested whether intraspecific competition affects four aspects of the evolution of tolerance to herbivory in the perennial plant Solanum carolinense: phenotypic expression, expression of genetic variation, the adaptive value of tolerance, and costs of tolerance. We manipulated insect damage and intraspecific competition for clonal lines of S. carolinense in a greenhouse experiment, and measured tolerance in terms of sexual and asexual fitness components. Compared to plants growing at low density, plants growing at high density had greater expression of and genetic variation in tolerance, and experienced greater fitness benefits from tolerance when damaged. Tolerance was not costly for plants growing at either density, and only plants growing at low density benefited from tolerance when undamaged, perhaps due to greater intrinsic growth rates of more tolerant genotypes. These results suggest that competition is likely to facilitate the evolution of tolerance in S. carolinense, and perhaps in other plants that regularly experience competition, while spatio-temporal variation in density may maintain genetic variation in tolerance.

Long-term strength and damage accumulation in laminates

NASA Astrophysics Data System (ADS)

Dzenis, Yuris A.; Joshi, Shiv P.

1993-04-01

A modified version of the probabilistic model developed by authors for damage evolution analysis of laminates subjected to random loading is utilized to predict long-term strength of laminates. The model assumes that each ply in a laminate consists of a large number of mesovolumes. Probabilistic variation functions for mesovolumes stiffnesses as well as strengths are used in the analysis. Stochastic strains are calculated using the lamination theory and random function theory. Deterioration of ply stiffnesses is calculated on the basis of the probabilities of mesovolumes failures using the theory of excursions of random process beyond the limits. Long-term strength and damage accumulation in a Kevlar/epoxy laminate under tension and complex in-plane loading are investigated. Effects of the mean level and stochastic deviation of loading on damage evolution and time-to-failure of laminate are discussed. Long-term cumulative damage at the time of the final failure at low loading levels is more than at high loading levels. The effect of the deviation in loading is more pronounced at lower mean loading levels.

Roughness evolution of metallic implant surfaces under contact loading and nanometer-scale chemical etching.

PubMed

Ryu, J J; Letchuman, S; Shrotriya, P

2012-10-01

Surface damage of metallic implant surface at taper lock and clamped interfaces may take place through synergistic interactions between repeated contact loading and corrosion. In the present research, we investigated the influence of surface roughness and contact loading on the mechanical and chemical damage phenomena. Cobalt-chromium (CoCrMo) specimens with two different roughness configurations created by milling and grinding process were subjected to normal and inclined contact loading. During repeated contact loading, amplitude of surface roughness reached a steady value after decreasing during the first few cycles. During the second phase, the alternating experiment of rough surface contact and micro-etching was conducted to characterize surface evolution behavior. As a result, surface roughness amplitude continuously evolved-decreasing during contact loading due to plastic deformation of contacting asperities and increasing on exposure to corrosive environment by the preferential corrosion attack on stressed area. Two different instabilities could be identified in the surface roughness evolution during etching of contact loaded surfaces: increase in the amplitude of dominant wavenumber and increase in amplitude of a small group of roughness modes. A damage mechanism that incorporates contact-induced residual stress development and stress-assisted dissolution is proposed to elucidate the measured instabilities in surface roughness evolution. Copyright © 2012 Elsevier Ltd. All rights reserved.

Nonlinear evolutions of an ultra-intense ultra-short laser pulse in a rarefied plasma through a new quasi-static theory

NASA Astrophysics Data System (ADS)

Yazdanpanah, J.

2018-02-01

In this paper, we present a new description of self-consistent wake excitation by an intense short laser pulse, based on applying the quasi-static approximation (slow variations of the pulse-envelope) in the instantaneous Lorentz-boosted pulse co-moving frame (PCMF), and best verify our results through comparison with particle-in-cell simulations. According to this theory, the plasma motion can be treated perturbatively in the PCMF due to its high initial-velocity and produces a quasi-static wakefield in this frame. The pulse envelope, on the other hand, is governed by a form of the Schrödinger equation in the PCMF, in which the wakefield acts as an effective potential. In this context, pulse evolutions are characterized by local conservation laws resulted from this equation and subjected to Lorentz transformation into the laboratory frame. Using these conservation laws, precise formulas are obtained for spatiotemporal pulse evolutions and related wakefield variations at initial stages, and new equations are derived for instantaneous group velocity and carrier frequency. In addition, based on properties of the Schrödinger equation, spectral-evolutions of the pulse are described and the emergence of an anomalous dispersion branch with linear relation ω ≈ ck (c is the light speed) is predicted. Our results are carefully discussed versus previous publications and the significance of our approach is described by showing almost all suggestive definitions of group-velocity based on energy arguments fail to reproduce our formula and correctly describe the instantaneous pulse-velocity.

Signatures of extra dimensions in gravitational waves from black hole quasinormal modes

NASA Astrophysics Data System (ADS)

Chakraborty, Sumanta; Chakravarti, Kabir; Bose, Sukanta; SenGupta, Soumitra

2018-05-01

In this work, we have derived the evolution equation for gravitational perturbation in four-dimensional spacetime in the presence of a spatial extra dimension. The evolution equation is derived by perturbing the effective gravitational field equations on the four-dimensional spacetime, which inherits nontrivial higher-dimensional effects. Note that this is different from the perturbation of the five-dimensional gravitational field equations that exist in the literature and possess quantitatively new features. The gravitational perturbation has further been decomposed into a purely four-dimensional part and another piece that depends on extra dimensions. The four-dimensional gravitational perturbation now admits massive propagating degrees of freedom, owing to the existence of higher dimensions. We have also studied the influence of these massive propagating modes on the quasinormal mode frequencies, signaling the higher-dimensional nature of the spacetime, and have contrasted these massive modes with the massless modes in general relativity. Surprisingly, it turns out that the massive modes experience damping much smaller than that of the massless modes in general relativity and may even dominate over and above the general relativity contribution if one observes the ringdown phase of a black hole merger event at sufficiently late times. Furthermore, the whole analytical framework has been supplemented by the fully numerical Cauchy evolution problem, as well. In this context, we have shown that, except for minute details, the overall features of the gravitational perturbations are captured both in the Cauchy evolution as well as in the analysis of quasinormal modes. The implications on observations of black holes with LIGO and proposed space missions such as LISA are also discussed.

Soliton switching in a site-dependent ferromagnet

NASA Astrophysics Data System (ADS)

Senjudarvannan, R.; Sathishkumar, P.; Vijayalakshmi, S.

2017-02-01

Switching of soliton in a ferromagnetic medium offers the possibility of developing a new innovative approach for information storage technologies. The nonlinear spin dynamics of a site-dependent Heisenberg ferromagnetic spin chain with Gilbert damping under the influence of external magnetic field is expressed in the form of the Landau-Lifshitz-Gilbert equation in the classical continuum limit. The corresponding evolution equation is developed through stereographic projection technique by projecting the unit sphere of spin onto a complex plane. The exact soliton solutions are constructed by solving the associated evolution equation through the modified extended tanh-function method. The impact of damping and external magnetic field on the magnetic soliton under the invariant inhomogeneity is investigated and finally, the magnetization switching in the form of shape changing solitons are demonstrated.

Stochastic functional evolution equations with monotone nonlinearity: Existence and stability of the mild solutions

NASA Astrophysics Data System (ADS)

Jahanipur, Ruhollah

In this paper, we study a class of semilinear functional evolution equations in which the nonlinearity is demicontinuous and satisfies a semimonotone condition. We prove the existence, uniqueness and exponentially asymptotic stability of the mild solutions. Our approach is to apply a convenient version of Burkholder inequality for convolution integrals and an iteration method based on the existence and measurability results for the functional integral equations in Hilbert spaces. An Itô-type inequality is the main tool to study the uniqueness, p-th moment and almost sure sample path asymptotic stability of the mild solutions. We also give some examples to illustrate the applications of the theorems and meanwhile we compare the results obtained in this paper with some others appeared in the literature.

High-energy evolution to three loops

NASA Astrophysics Data System (ADS)

Caron-Huot, Simon; Herranen, Matti

2018-02-01

The Balitsky-Kovchegov equation describes the high-energy growth of gauge theory scattering amplitudes as well as nonlinear saturation effects which stop it. We obtain the three-loop corrections to the equation in planar N = 4 super Yang-Mills theory. Our method exploits a recently established equivalence with the physics of soft wide-angle radiation, so-called non-global logarithms, and thus yields at the same time the threeloop evolution equation for non-global logarithms. As a by-product of our analysis, we develop a Lorentz-covariant method to subtract infrared and collinear divergences in crosssection calculations in the planar limit. We compare our result in the linear regime with a recent prediction for the so-called Pomeron trajectory, and compare its collinear limit with predictions from the spectrum of twist-two operators.

2-Dimensional B-Spline Algorithms with Applications to Ray Tracing in Media of Spatially-Varying Refractive Index

DTIC Science & Technology

2007-08-01

In the approach, photon trajectories are computed using a solution of the Eikonal equation (ray-tracing methods) rather than linear trajectories. The...coupling the radiative transport solution into heat transfer and damage models. 15. SUBJECT TERMS: B-Splines, Ray-Tracing, Eikonal Equation...multi-layer biological tissue model. In the approach, photon trajectories are computed using a solution of the Eikonal equation (ray-tracing methods

A continuous damage model based on stepwise-stress creep rupture tests

NASA Technical Reports Server (NTRS)

Robinson, D. N.

1985-01-01

A creep damage accumulation model is presented that makes use of the Kachanov damage rate concept with a provision accounting for damage that results from a variable stress history. This is accomplished through the introduction of an additional term in the Kachanov rate equation that is linear in the stress rate. Specification of the material functions and parameters in the model requires two types of constituting a data base: (1) standard constant-stress creep rupture tests, and (2) a sequence of two-step creep rupture tests.

Surface phenomena and the evolution of radiating fluid spheres in general relativity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herrera, L.; Jimenez, J.; Esculpi, M.

1989-10-01

A method used to study the evolution of radiating spheres (Herrera, Jimenez, and Ruggeri) is extended to the case in which surface phenomena are taken into account. The equations have been integrated numerically for a model derived from the Schwarzschild interior solution, bringing out the effects of surface tension on the evolution of the spheres. 17 refs.

Thermoviscoelastoplastic Deformation of Compound Shells of Revolution Made of a Damageable Material

NASA Astrophysics Data System (ADS)

Shevchenko, Yu. N.; Galishin, A. Z.; Babeshko, M. E.

2015-11-01

A technique for numerical analysis of the thermoviscoelastoplastic deformation of thin compound shells made of a damageable material in which a fracture front propagates is described. A procedure for automatic variation in the step of integration of the kinetic damage equation is developed. A two-layer cylindrical shell cooling by convection and subjected to internal pressure and tensile force is analyzed as an example. The numerical data are presented and analyzed

Non-linear instability analysis of the two-dimensional Navier-Stokes equation: The Taylor-Green vortex problem

NASA Astrophysics Data System (ADS)

Sengupta, Tapan K.; Sharma, Nidhi; Sengupta, Aditi

2018-05-01

An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physical instability is triggered by the growth of disturbances and is explained by the evolution of disturbance mechanical energy and enstrophy. The disturbance evolution equations have been traced by looking at (a) disturbance mechanical energy of the Navier-Stokes equation, as described in the work of Sengupta et al., "Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003), and (b) the creation of rotationality via the enstrophy transport equation in the work of Sengupta et al., "Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow," Comput. Fluids 88, 440-451 (2013).

Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Middleton, Chad A.; Stanley, Ethan

2011-10-15

We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates. By adopting equations of state relating the 3D and higher-dimensional pressures to the density, we obtain an exact expression relating the higher-dimensional scale factor to a function of the 3D scale factor. This relation allows us to write the Friedmann-Robertson-Walker field equations exclusively in terms of the 3D scale factor, thus yielding a set of 4D effective Friedmann-Robertson-Walker field equations. We examine the effective field equations inmore » the general case and obtain an exact expression relating a function of the 3D scale factor to the time. This expression involves a hypergeometric function and cannot, in general, be inverted to yield an analytical expression for the 3D scale factor as a function of time. When the hypergeometric function is expanded for small and large arguments, we obtain a generalized treatment of the dynamical compactification scenario of Mohammedi [Phys. Rev. D 65, 104018 (2002)] and the 5D vacuum solution of Chodos and Detweiler [Phys. Rev. D 21, 2167 (1980)], respectively. By expanding the hypergeometric function near a branch point, we obtain the perturbative solution for the 3D scale factor in the small time regime. This solution exhibits accelerated expansion, which, remarkably, is independent of the value of the 4D equation of state parameter w. This early-time epoch of accelerated expansion arises naturally out of the anisotropic evolution of 5D spacetime when the pressure in the extra dimension is negative and offers a possible alternative to scalar field inflationary theory.« less

Evolution of a proto-neutron star with a nuclear many-body equation of state: Neutrino luminosity and gravitational wave frequencies

DOE PAGES

Camelio, Giovanni; Lovato, Alessandro; Gualtieri, Leonardo; ...

2017-08-30

In a core-collapse supernova, a huge amount of energy is released in the Kelvin-Helmholtz phase subsequent to the explosion, when the proto-neutron star cools and deleptonizes as it loses neutrinos. Most of this energy is emitted through neutrinos, but a fraction of it can be released through gravitational waves. We model the evolution of a proto-neutron star in the Kelvin-Helmholtz phase using a general relativistic numerical code, and a recently proposed finite temperature, many-body equation of state; from this we consistently compute the diffusion coefficients driving the evolution. To include the many-body equation of state, we develop a new fittingmore » formula for the high density baryon free energy at finite temperature and intermediate proton fraction. Here, we estimate the emitted neutrino signal, assessing its detectability by present terrestrial detectors, and we determine the frequencies and damping times of the quasinormal modes which would characterize the gravitational wave signal emitted in this stage.« less

Evolution of a proto-neutron star with a nuclear many-body equation of state: Neutrino luminosity and gravitational wave frequencies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Camelio, Giovanni; Lovato, Alessandro; Gualtieri, Leonardo

In a core-collapse supernova, a huge amount of energy is released in the Kelvin-Helmholtz phase subsequent to the explosion, when the proto-neutron star cools and deleptonizes as it loses neutrinos. Most of this energy is emitted through neutrinos, but a fraction of it can be released through gravitational waves. We model the evolution of a proto-neutron star in the Kelvin-Helmholtz phase using a general relativistic numerical code, and a recently proposed finite temperature, many-body equation of state; from this we consistently compute the diffusion coefficients driving the evolution. To include the many-body equation of state, we develop a new fittingmore » formula for the high density baryon free energy at finite temperature and intermediate proton fraction. Here, we estimate the emitted neutrino signal, assessing its detectability by present terrestrial detectors, and we determine the frequencies and damping times of the quasinormal modes which would characterize the gravitational wave signal emitted in this stage.« less

Structural health monitoring and damage evaluation for steel confined reinforced concrete column using the acoustic emission technique

NASA Astrophysics Data System (ADS)

Du, Fangzhu; Li, Dongsheng

2018-03-01

As a new kind of composite structures, the using of steel confined reinforced concrete column attract increasing attention in civil engineer. During the damage process, this new structure offers highly complex and invisible failure mechanism due to the combination effects of steel tubes, concrete, and steel rebar. Acoustic emission (AE) technique has been extensively studied in nondestructive testing (NDT) and is currently applied in civil engineering for structural health monitoring (SHM) and damage evaluation. In the present study, damage property and failure evolution of steel confined and unconfined reinforced concrete (RC) columns are investigated under quasi-static loading through (AE) signal. Significantly improved loading capacity and excellent energy dissipation characteristic demonstrated the practicality of that proposed structure. AE monitoring results indicated that the progressive deformation of the test specimens occur in three stages representing different damage conditions. Sentry function compares the logarithm ratio between the stored strain energy (Es) and the released acoustic energy (Ea); explicitly disclose the damage growth and failure mechanism of the test specimens. Other extended AE features including index of damage (ID), and relax ratio are calculated to quantitatively evaluate the damage severity and critical point. Complicated temporal evolution of different AE features confirms the potential importance of integrated analysis of two or more parameters. The proposed multi-indicators analysis is capable of revealing the damage growth and failure mechanism for steel confined RC columns, and providing critical warning information for structure failure.

Decoupling the NLO-coupled QED⊗QCD, DGLAP evolution equations, using Laplace transform method

NASA Astrophysics Data System (ADS)

Mottaghizadeh, Marzieh; Eslami, Parvin; Taghavi-Shahri, Fatemeh

2017-05-01

We analytically solved the QED⊗QCD-coupled DGLAP evolution equations at leading order (LO) quantum electrodynamics (QED) and next-to-leading order (NLO) quantum chromodynamics (QCD) approximations, using the Laplace transform method and then computed the proton structure function in terms of the unpolarized parton distribution functions. Our analytical solutions for parton densities are in good agreement with those from CT14QED (1.2952 < Q2 < 1010) (Ref. 6) global parametrizations and APFEL (A PDF Evolution Library) (2 < Q2 < 108) (Ref. 4). We also compared the proton structure function, F2p(x,Q2), with the experimental data released by the ZEUS and H1 collaborations at HERA. There is a nice agreement between them in the range of low and high x and Q2.

Black hole evolution by spectral methods

NASA Astrophysics Data System (ADS)

Kidder, Lawrence E.; Scheel, Mark A.; Teukolsky, Saul A.; Carlson, Eric D.; Cook, Gregory B.

2000-10-01

Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast with finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.

Solvable Hydrodynamics of Quantum Integrable Systems

NASA Astrophysics Data System (ADS)

Bulchandani, Vir B.; Vasseur, Romain; Karrasch, Christoph; Moore, Joel E.

2017-12-01

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudomomenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudomomentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.

Research on Buckling State of Prestressed Fiber-Strengthened Steel Pipes

NASA Astrophysics Data System (ADS)

Wang, Ruheng; Lan, Kunchang

2018-01-01

The main restorative methods of damaged oil and gas pipelines include welding reinforcement, fixture reinforcement and fiber material reinforcement. Owing to the severe corrosion problems of pipes in practical use, the research on renovation and consolidation techniques of damaged pipes gains extensive attention by experts and scholars both at home and abroad. The analysis of mechanical behaviors of reinforced pressure pipelines and further studies focusing on “the critical buckling” and intensity of pressure pipeline failure are conducted in this paper, providing theoretical basis to restressed fiber-strengthened steel pipes. Deformation coordination equations and buckling control equations of steel pipes under the effect of prestress is deduced by using Rayleigh Ritz method, which is an approximation method based on potential energy stationary value theory and minimum potential energy principle. According to the deformation of prestressed steel pipes, the deflection differential equation of prestressed steel pipes is established, and the critical value of buckling under prestress is obtained.

Fatigue behavior of type 316 stainless steel following neutron irradiation inducing helium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grossbeck, M.L.; Liu, K.C.

1980-01-01

Since a tokamak fusion reactor operates in a cyclic mode, thermal stresses will result in fatigue in structural components, especially the first wall and blanket. Type 316 stainless steel in the 20% cold-worked condition has been irradiated in the HFIR in order to introduce helium as well as displacement damage. A miniature hourglass specimen was developed for the reactor irradiations and subsequent fully reversed low cycle fatigue testing. For material irradiated and tested at 430/sup 0/C in vacuum to a damage level of 7 to 15 dpa and containing 200 to 1000 appm He, a reduction in life by amore » factor of 3 to 10 was observed. An attempt was made to predict irradiated fatigue life by fitting data from irradiated material to a power law equation similar to the universal slopes equation and using ductility ratios from tensile tests to modify the equation for irradiated material.« less

A theoretical derivation of the dilatancy equation for brittle rocks based on Maxwell model

NASA Astrophysics Data System (ADS)

Li, Jie; Huang, Houxu; Wang, Mingyang

2017-03-01

In this paper, the micro-cracks in the brittle rocks are assumed to be penny shaped and evenly distributed; the damage and dilatancy of the brittle rocks is attributed to the growth and expansion of numerous micro-cracks under the local tensile stress. A single crack's behaviour under the local tensile stress is generalized to all cracks based on the distributed damage mechanics. The relationship between the local tensile stress and the external loading is derived based on the Maxwell model. The damage factor corresponding to the external loading is represented using the p-alpha ( p- α) model. A dilatancy equation that can build up a link between the external loading and the rock dilatancy is established. A test of dilatancy of a brittle rock under triaxial compression is conducted; the comparison between experimental results and our theoretical results shows good consistency.

The hair-trigger effect for a class of nonlocal nonlinear equations

NASA Astrophysics Data System (ADS)

Finkelshtein, Dmitri; Tkachov, Pasha

2018-06-01

We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on which have only two constant stationary solutions, 0 and . The effect consists in that the solution with an initial condition non identical to zero converges (when time goes to ) to θ locally uniformly in . We also find sufficient conditions for existence, uniqueness and comparison principle in the considered equations.

Computing generalized Langevin equations and generalized Fokker-Planck equations.

PubMed

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-07-07

The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

Soliton and quasi-periodic wave solutions for b-type Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Singh, Manjit; Gupta, R. K.

2017-11-01

In this paper, truncated Laurent expansion is used to obtain the bilinear equation of a nonlinear evolution equation. As an application of Hirota's method, multisoliton solutions are constructed from the bilinear equation. Extending the application of Hirota's method and employing multidimensional Riemann theta function, one and two-periodic wave solutions are also obtained in a straightforward manner. The asymptotic behavior of one and two-periodic wave solutions under small amplitude limits is presented, and their relations with soliton solutions are also demonstrated.

Time-delayed reaction-diffusion fronts

NASA Astrophysics Data System (ADS)

Isern, Neus; Fort, Joaquim

2009-11-01

A time-delayed second-order approximation for the front speed in reaction-dispersion systems was obtained by Fort and Méndez [Phys. Rev. Lett. 82, 867 (1999)]. Here we show that taking proper care of the effect of the time delay on the reactive process yields a different evolution equation and, therefore, an alternate equation for the front speed. We apply the new equation to the Neolithic transition. For this application the new equation yields speeds about 10% slower than the previous one.

Some More Solutions of Burgers' Equation

NASA Astrophysics Data System (ADS)

Kumar, Mukesh; Kumar, Raj

2015-01-01

In this work, similarity solutions of viscous one-dimensional Burgers' equation are attained by using Lie group theory. The symmetry generators are used for constructing Lie symmetries with commuting infinitesimal operators which lead the governing partial differential equation (PDE) to ordinary differential equation (ODE). Most of the constructed solutions are found in terms of Bessel functions which are new as far as authors are aware. Effect of various parameters in the evolutional profile of the solutions are shown graphically and discussed them physically.

Ion irradiation induced defect evolution in Ni and Ni-based FCC equiatomic binary alloys

DOE PAGES

Jin, Ke; Zhang, Yanwen; Bei, Hongbin

2015-09-09

In order to explore the chemical effects on radiation response of alloys with multi-principal elements, defect evolution under Au ion irradiation was investigated in the elemental Ni, equiatomic NiCo and NiFe alloys. Single crystals were successfully grown in an optical floating zone furnace and their (100) surfaces were irradiated with 3 MeV Au ions at fluences ranging from 1 × 10 13 to 5 × 10 15 ions cm –2 at room temperature. The irradiation-induced defect evolution was analyzed by using ion channeling technique. Experiment shows that NiFe is more irradiation-resistant than NiCo and pure Ni at low fluences. Withmore » continuously increasing the ion fluences, damage level is eventually saturated for all materials but at different dose levels. The saturation level in pure Ni appears at relatively lower irradiation fluence than the alloys, suggesting that damage accumulation slows down in the alloys. Here, under high-fluence irradiations, pure Ni has wider damage ranges than the alloys, indicating that defects in pure Ni have high mobility.« less

Lifetimes and spatio-temporal response of protein crystals in intense X-ray microbeams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warkentin, Matthew A.; Atakisi, Hakan; Hopkins, Jesse B.

Serial synchrotron-based crystallography using intense microfocused X-ray beams, fast-framing detectors and protein microcrystals held at 300 K promises to expand the range of accessible structural targets and to increase overall structure-pipeline throughputs. To explore the nature and consequences of X-ray radiation damage under microbeam illumination, the time-, dose- and temperature-dependent evolution of crystal diffraction have been measured with maximum dose rates of 50 MGy s −1 . At all temperatures and dose rates, the integrated diffraction intensity for a fixed crystal orientation shows non-exponential decays with dose. Non-exponential decays are a consequence of non-uniform illumination and the resulting spatial evolution of diffracted intensitymore » within the illuminated crystal volume. To quantify radiation-damage lifetimes and the damage state of diffracting crystal regions, a revised diffraction-weighted dose (DWD) is defined and it is shown that for Gaussian beams the DWD becomes nearly independent of actual dose at large doses. An apparent delayed onset of radiation damage seen in some intensity–dose curves is in fact a consequence of damage. Intensity fluctuations at high dose rates may arise from the impulsive release of gaseous damage products. Accounting for these effects, data collection at the highest dose rates increases crystal radiation lifetimes near 300 K (but not at 100 K) by a factor of ∼1.5–2 compared with those observed at conventional dose rates. Improved quantification and modeling of the complex spatio-temporal evolution of protein microcrystal diffraction in intense microbeams will enable more efficient data collection, and will be essential in improving the accuracy of structure factors and structural models.« less

Lifetimes and spatio-temporal response of protein crystals in intense X-ray microbeams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warkentin, Matthew A.; Atakisi, Hakan; Hopkins, Jesse B.

Serial synchrotron-based crystallography using intense microfocused X-ray beams, fast-framing detectors and protein microcrystals held at 300 K promises to expand the range of accessible structural targets and to increase overall structure-pipeline throughputs. To explore the nature and consequences of X-ray radiation damage under microbeam illumination, the time-, dose- and temperature-dependent evolution of crystal diffraction have been measured with maximum dose rates of 50 MGy s –1. At all temperatures and dose rates, the integrated diffraction intensity for a fixed crystal orientation shows non-exponential decays with dose. Non-exponential decays are a consequence of non-uniform illumination and the resulting spatial evolution ofmore » diffracted intensity within the illuminated crystal volume. To quantify radiation-damage lifetimes and the damage state of diffracting crystal regions, a revised diffraction-weighted dose (DWD) is defined and it is shown that for Gaussian beams the DWD becomes nearly independent of actual dose at large doses. An apparent delayed onset of radiation damage seen in some intensity–dose curves is in fact a consequence of damage. Intensity fluctuations at high dose rates may arise from the impulsive release of gaseous damage products. Accounting for these effects, data collection at the highest dose rates increases crystal radiation lifetimes near 300 K (but not at 100 K) by a factor of ~1.5–2 compared with those observed at conventional dose rates. As a result, improved quantification and modeling of the complex spatio-temporal evolution of protein microcrystal diffraction in intense microbeams will enable more efficient data collection, and will be essential in improving the accuracy of structure factors and structural models.« less

Response and representation of ductile damage under varying shock loading conditions in tantalum

DOE PAGES

Bronkhorst, C. A.; Gray, III, G. T.; Addessio, F. L.; ...

2016-02-25

The response of polycrystalline metals, which possess adequate mechanisms for plastic deformation under extreme loading conditions, is often accompanied by the formation of pores within the structure of the material. This large deformation process is broadly identified as progressive with nucleation, growth, coalescence, and failure the physical path taken over very short periods of time. These are well known to be complex processes strongly influenced by microstructure, loading path, and the loading profile, which remains a significant challenge to represent and predict numerically. In the current study, the influence of loading path on the damage evolution in high-purity tantalum ismore » presented. Tantalum samples were shock loaded to three different peak shock stresses using both symmetric impact, and two different composite flyer plate configurations such that upon unloading the three samples displayed nearly identical “pull-back” signals as measured via rear-surface velocimetry. While the “pull-back” signals observed were found to be similar in magnitude, the sample loaded to the highest peak stress nucleated a connected field of ductile fracture which resulted in complete separation, while the two lower peak stresses resulted in incipient damage. The damage evolution in the “soft” recovered tantalum samples was quantified using optical metallography, electron-back-scatter diffraction, and tomography. These experiments are examined numerically through the use of a model for shock-induced porosity evolution during damage. The model is shown to describe the response of the tantalum reasonably well under strongly loaded conditions but less well in the nucleation dominated regime. As a result, numerical results are also presented as a function of computational mesh density and discussed in the context of improved representation of the influence of material structure upon macro-scale models of ductile damage.« less

Lifetimes and spatio-temporal response of protein crystals in intense X-ray microbeams

DOE PAGES

Warkentin, Matthew A.; Atakisi, Hakan; Hopkins, Jesse B.; ...

2017-10-13

Serial synchrotron-based crystallography using intense microfocused X-ray beams, fast-framing detectors and protein microcrystals held at 300 K promises to expand the range of accessible structural targets and to increase overall structure-pipeline throughputs. To explore the nature and consequences of X-ray radiation damage under microbeam illumination, the time-, dose- and temperature-dependent evolution of crystal diffraction have been measured with maximum dose rates of 50 MGy s –1. At all temperatures and dose rates, the integrated diffraction intensity for a fixed crystal orientation shows non-exponential decays with dose. Non-exponential decays are a consequence of non-uniform illumination and the resulting spatial evolution ofmore » diffracted intensity within the illuminated crystal volume. To quantify radiation-damage lifetimes and the damage state of diffracting crystal regions, a revised diffraction-weighted dose (DWD) is defined and it is shown that for Gaussian beams the DWD becomes nearly independent of actual dose at large doses. An apparent delayed onset of radiation damage seen in some intensity–dose curves is in fact a consequence of damage. Intensity fluctuations at high dose rates may arise from the impulsive release of gaseous damage products. Accounting for these effects, data collection at the highest dose rates increases crystal radiation lifetimes near 300 K (but not at 100 K) by a factor of ~1.5–2 compared with those observed at conventional dose rates. As a result, improved quantification and modeling of the complex spatio-temporal evolution of protein microcrystal diffraction in intense microbeams will enable more efficient data collection, and will be essential in improving the accuracy of structure factors and structural models.« less

Lifetimes and spatio-temporal response of protein crystals in intense X-ray microbeams

DOE PAGES

Warkentin, Matthew A.; Atakisi, Hakan; Hopkins, Jesse B.; ...

2017-10-13

Serial synchrotron-based crystallography using intense microfocused X-ray beams, fast-framing detectors and protein microcrystals held at 300 K promises to expand the range of accessible structural targets and to increase overall structure-pipeline throughputs. To explore the nature and consequences of X-ray radiation damage under microbeam illumination, the time-, dose- and temperature-dependent evolution of crystal diffraction have been measured with maximum dose rates of 50 MGy s −1 . At all temperatures and dose rates, the integrated diffraction intensity for a fixed crystal orientation shows non-exponential decays with dose. Non-exponential decays are a consequence of non-uniform illumination and the resulting spatial evolution of diffracted intensitymore » within the illuminated crystal volume. To quantify radiation-damage lifetimes and the damage state of diffracting crystal regions, a revised diffraction-weighted dose (DWD) is defined and it is shown that for Gaussian beams the DWD becomes nearly independent of actual dose at large doses. An apparent delayed onset of radiation damage seen in some intensity–dose curves is in fact a consequence of damage. Intensity fluctuations at high dose rates may arise from the impulsive release of gaseous damage products. Accounting for these effects, data collection at the highest dose rates increases crystal radiation lifetimes near 300 K (but not at 100 K) by a factor of ∼1.5–2 compared with those observed at conventional dose rates. Improved quantification and modeling of the complex spatio-temporal evolution of protein microcrystal diffraction in intense microbeams will enable more efficient data collection, and will be essential in improving the accuracy of structure factors and structural models.« less

Study on mechanical properties and damage behaviors of Kevlar fiber reinforced epoxy composites by digital image correlation technique under optical microscope

NASA Astrophysics Data System (ADS)

Gao, Xiang; Shao, Wenquan; Ji, Hongwei

2010-10-01

Kevlar fiber-reinforced epoxy (KFRE) composites are widely used in the fields of aerospace, weapon, shipping, and civil industry, due to their outstanding capabilities. In this paper, mechanical properties and damage behaviors of KFRE laminate (02/902) were tested and studied under tension condition. To precisely measure the tensile mechanical properties of the material and investigate its micro-scale damage evolution, a micro-image measuring system with in-situ tensile device was designed. The measuring system, by which the in-situ tensile test can be carried out and surface morphology evolution of the tensile specimen can be visually monitored and recorded during the process of loading, includes an ultra-long working distance zoom microscope and a in-situ tensile loading device. In this study, a digital image correlation method (DICM) was used to calculate the deformation of the tensile specimen under different load levels according to the temporal series images captured by an optical microscope and CCD camera. Then, the elastic modulus and Poisson's ratio of the KFRE was obtained accordingly. The damage progresses of the KFRE laminates were analyzed. Experimental results indicated that: (1) the KFRE laminate (02/902) is almost elastic, its failure mode is brittle tensile fracture.(2) Mechanical properties parameters of the material are as follows: elastic modulus is 14- 16GPa, and tensile ultimate stress is 450-480 Mpa respectively. (3) The damage evolution of the material is that cracks appear in epoxy matrix firstly, then, with the increasing of the tensile loading, matrix cracks add up and extend along a 45° angle direction with tensile load. Furthermore, decohesion between matrix and fibers as well as delamination occurs. Eventually, fibers break and the material is damaged.

2-D hydro-viscoelastic model for convective drying of deformable and unsaturated porous material

NASA Astrophysics Data System (ADS)

Hassini, Lamine; Raja, Lamloumi; Lecompte-Nana, Gisèle Laure; Elcafsi, Mohamed Afif

2017-04-01

The aim of this work was to simulate in two dimensions the spatio-temporal evolution of the moisture content, the temperature, the solid (dry matter) concentration, the dry product total porosity, the gas porosity, and the mechanical stress within a deformable and unsaturated product during convective drying. The material under study was an elongated cellulose-clay composite sample with a square section placed in hot air flow. Currently, this innovative composite is used in the processing of boxes devoted to the preservation of heritage and precious objects against fire damage and other degradation (moisture, insects, etc.). A comprehensive and rigorous hydrothermal model had been merged with a dynamic linear viscoelasticity model based on Bishop's effective stress theory, assuming that the stress tensor is the sum of solid, liquid, and gas stresses. The material viscoelastic properties were measured by means of stress relaxation tests for different water contents. The viscoelastic behaviour was described by a generalized Maxwell model whose parameters were correlated to the water content. The equations of our model were solved by means of the 'COMSOL Multiphysics' software. The hydrothermal part of the model was validated by comparison with experimental drying curves obtained in a laboratory hot-air dryer. The simulations of the spatio-temporal distributions of mechanical stress were performed and interpreted in terms of material potential damage. The sample shape was also predicted all over the drying process.

Effective properties of dispersed phase reinforced composite materials with perfect and imperfect interfaces

NASA Astrophysics Data System (ADS)

Han, Ru

This thesis focuses on the analysis of dispersed phase reinforced composite materials with perfect as well as imperfect interfaces using the Boundary Element Method (BEM). Two problems of interest are considered, namely, to determine the limitations in the use of effective properties and the analysis of failure progression at the inclusion-matrix interface. The effective moduli (effective Young's modulus, effective Poisson's ratio, effective shear modulus, and effective bulk modulus) of composite materials can be determined at the mesoscopic level using three-dimensional parallel BEM simulations. By comparing the mesoscopic BEM results and the macroscopic results based on effective properties, limitations in the effective property approach can be determined. Decohesion is an important failure mode associated with fiber-reinforced composite materials. Analysis of failure progression at the fiber-matrix interface in fiber-reinforced composite materials is considered using a softening decohesion model consistent with thermodynamic concepts. In this model, the initiation of failure is given directly by a failure criterion. Damage is interpreted by the development of a discontinuity of displacement. The formulation describing the potential development of damage is governed by a discrete decohesive constitutive equation. Numerical simulations are performed using the direct boundary element method. Incremental decohesion simulations illustrate the progressive evolution of debonding zones and the propagation of cracks along the interfaces. The effect of decohesion on the macroscopic response of composite materials is also investigated.

Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adcock, T. A. A.; Taylor, P. H.

2016-01-15

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest whichmore » leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.« less

Bound states of moving potential wells in discrete wave mechanics

NASA Astrophysics Data System (ADS)

Longhi, S.

2017-10-01

Discrete wave mechanics describes the evolution of classical or matter waves on a lattice, which is governed by a discretized version of the Schrödinger equation. While for a vanishing lattice spacing wave evolution of the continuous Schrödinger equation is retrieved, spatial discretization and lattice effects can deeply modify wave dynamics. Here we discuss implications of breakdown of exact Galilean invariance of the discrete Schrödinger equation on the bound states sustained by a smooth potential well which is uniformly moving on the lattice with a drift velocity v. While in the continuous limit the number of bound states does not depend on the drift velocity v, as one expects from the covariance of ordinary Schrödinger equation for a Galilean boost, lattice effects can lead to a larger number of bound states for the moving potential well as compared to the potential well at rest. Moreover, for a moving potential bound states on a lattice become rather generally quasi-bound (resonance) states.

Snow Micro-Structure Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Micah Johnson, Andrew Slaughter

PIKA is a MOOSE-based application for modeling micro-structure evolution of seasonal snow. The model will be useful for environmental, atmospheric, and climate scientists. Possible applications include application to energy balance models, ice sheet modeling, and avalanche forecasting. The model implements physics from published, peer-reviewed articles. The main purpose is to foster university and laboratory collaboration to build a larger multi-scale snow model using MOOSE. The main feature of the code is that it is implemented using the MOOSE framework, thus making features such as multiphysics coupling, adaptive mesh refinement, and parallel scalability native to the application. PIKA implements three equations:more » the phase-field equation for tracking the evolution of the ice-air interface within seasonal snow at the grain-scale; the heat equation for computing the temperature of both the ice and air within the snow; and the mass transport equation for monitoring the diffusion of water vapor in the pore space of the snow.« less

4-wave dynamics in kinetic wave turbulence

NASA Astrophysics Data System (ADS)

Chibbaro, Sergio; Dematteis, Giovanni; Rondoni, Lamberto

2018-01-01

A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function Z is obtained within an ;interaction representation; and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman-Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for Z. A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the N-mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency. Some of the main results which are developed here in detail have been tested numerically in a recent work.

Evolution with Stochastic Fitness and Stochastic Migration

PubMed Central

Rice, Sean H.; Papadopoulos, Anthony

2009-01-01

Background Migration between local populations plays an important role in evolution - influencing local adaptation, speciation, extinction, and the maintenance of genetic variation. Like other evolutionary mechanisms, migration is a stochastic process, involving both random and deterministic elements. Many models of evolution have incorporated migration, but these have all been based on simplifying assumptions, such as low migration rate, weak selection, or large population size. We thus have no truly general and exact mathematical description of evolution that incorporates migration. Methodology/Principal Findings We derive an exact equation for directional evolution, essentially a stochastic Price equation with migration, that encompasses all processes, both deterministic and stochastic, contributing to directional change in an open population. Using this result, we show that increasing the variance in migration rates reduces the impact of migration relative to selection. This means that models that treat migration as a single parameter tend to be biassed - overestimating the relative impact of immigration. We further show that selection and migration interact in complex ways, one result being that a strategy for which fitness is negatively correlated with migration rates (high fitness when migration is low) will tend to increase in frequency, even if it has lower mean fitness than do other strategies. Finally, we derive an equation for the effective migration rate, which allows some of the complex stochastic processes that we identify to be incorporated into models with a single migration parameter. Conclusions/Significance As has previously been shown with selection, the role of migration in evolution is determined by the entire distributions of immigration and emigration rates, not just by the mean values. The interactions of stochastic migration with stochastic selection produce evolutionary processes that are invisible to deterministic evolutionary theory. PMID:19816580

Quasi-static evolution of coronal magnetic fields

NASA Technical Reports Server (NTRS)

Longcope, D. W.; Sudan, R. N.

1992-01-01

A formalism is developed to describe the purely quasi-static part of the evolution of a coronal loop driven by its footpoints. This is accomplished under assumptions of a long, thin loop. The quasi-static equations reveal the possibility for sudden 'loss of equilibrium' at which time the system evolves dynamically rather than quasi-statically. Such quasi-static crises produce high-frequency Alfven waves and, in conjunction with Alfven wave dissipation models, form a viable coronal heating mechanism. Furthermore, an approximate solution to the quasi-static equations by perturbation method verifies the development of small-scale spatial current structure.

Synergistic Effects of Temperature, Oxidation and Stress Level on Fatigue Damage Evolution and Lifetime Prediction of Cross-Ply SiC/CAS Ceramic-Matrix Composites Through Hysteresis-Based Parameters

NASA Astrophysics Data System (ADS)

Li, Longbiao

2017-12-01

The damage development and cyclic fatigue lifetime of cross-ply SiC/CAS ceramic-matrix composites have been investigated at different testing temperatures in air atmosphere. The relationships between the fatigue hysteresis-based damage parameters, i.e., fatigue hysteresis dissipated energy, fatigue hysteresis modulus and fatigue peak strain and the damage mechanisms of matrix multicracking, fiber/matrix interface debonding, interface sliding and fibers failure, have been established. With the increase in the cycle number, the evolution of the fatigue hysteresis modulus, fatigue peak strain and fatigue hysteresis dissipated energy depends upon the fatigue peak stress levels, interface and fibers oxidation and testing temperature. The fatigue life S-N curves of cross-ply SiC/CAS composite at room and elevated temperatures have been predicted, and the fatigue limit stresses at room temperature, 750 and 850 °C, are 50, 36 and 30% of the tensile strength, respectively.

Microstructural evolution in fast-neutron-irradiated austenitic stainless steels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stoller, R.E.

1987-12-01

The present work has focused on the specific problem of fast-neutron-induced radiation damage to austenitic stainless steels. These steels are used as structural materials in current fast fission reactors and are proposed for use in future fusion reactors. Two primary components of the radiation damage are atomic displacements (in units of displacements per atom, or dpa) and the generation of helium by nuclear transmutation reactions. The radiation environment can be characterized by the ratio of helium to displacement production, the so-called He/dpa ratio. Radiation damage is evidenced microscopically by a complex microstructural evolution and macroscopically by density changes and alteredmore » mechanical properties. The purpose of this work was to provide additional understanding about mechanisms that determine microstructural evolution in current fast reactor environments and to identify the sensitivity of this evolution to changes in the He/dpa ratio. This latter sensitivity is of interest because the He/dpa ratio in a fusion reactor first wall will be about 30 times that in fast reactor fuel cladding. The approach followed in the present work was to use a combination of theoretical and experimental analysis. The experimental component of the work primarily involved the examination by transmission electron microscopy of specimens of a model austenitic alloy that had been irradiated in the Oak Ridge Research Reactor. A major aspect of the theoretical work was the development of a comprehensive model of microstructural evolution. This included explicit models for the evolution of the major extended defects observed in neutron irradiated steels: cavities, Frank faulted loops and the dislocation network. 340 refs., 95 figs., 18 tabs.« less

On the coupled evolution of oceanic internal waves and quasi-geostrophic flow

NASA Astrophysics Data System (ADS)

Wagner, Gregory LeClaire

Oceanic motion outside thin boundary layers is primarily a mixture of quasi-geostrophic flow and internal waves with either near-inertial frequencies or the frequency of the semidiurnal lunar tide. This dissertation seeks a deeper understanding of waves and flow through reduced models that isolate their nonlinear and coupled evolution from the Boussinesq equations. Three physical-space models are developed: an equation that describes quasi-geostrophic evolution in an arbitrary and prescribed field of hydrostatic internal waves; a three-component model that couples quasi-geostrophic flow to both near-inertial waves and the near-inertial second harmonic; and a model for the slow evolution of hydrostatic internal tides in quasi-geostrophic flow of near-arbitrary scale. This slow internal tide equation opens the path to a coupled model for the energetic interaction of quasi-geostrophic flow and oceanic internal tides. Four results emerge. First, the wave-averaged quasi-geostrophic equation reveals that finite-amplitude waves give rise to a mean flow that advects quasi-geostrophic potential vorticity. Second is the definition of a new material invariant: Available Potential Vorticity, or APV. APV isolates the part of Ertel potential vorticity available for balanced-flow evolution in Eulerian frames and proves necessary in the separating waves and quasi-geostrophic flow. The third result, hashed out for near-inertial waves and quasi-geostrophic flow, is that wave-flow interaction leads to energy exchange even under conditions of weak nonlinearity. For storm-forced oceanic near-inertial waves the interaction often energizes waves at the expense of flow. We call this extraction of balanced quasi-geostrophic energy 'stimulated generation' since it requires externally-forced rather than spontaneously-generated waves. The fourth result is that quasi-geostrophic flow can encourage or 'catalyze' a nonlinear interaction between a near-inertial wave field and its second harmonic that transfers energy to the small near-inertial vertical scales of wave breaking and mixing.

3D Microstructures for Materials and Damage Models

DOE PAGES

Livescu, Veronica; Bronkhorst, Curt Allan; Vander Wiel, Scott Alan

2017-02-01

Many challenges exist with regard to understanding and representing complex physical processes involved with ductile damage and failure in polycrystalline metallic materials. Currently, the ability to accurately predict the macroscale ductile damage and failure response of metallic materials is lacking. Research at Los Alamos National Laboratory (LANL) is aimed at building a coupled experimental and computational methodology that supports the development of predictive damage capabilities by: capturing real distributions of microstructural features from real material and implementing them as digitally generated microstructures in damage model development; and, distilling structure-property information to link microstructural details to damage evolution under a multitudemore » of loading states.« less

Modeling the effect of orientation on the shock response of a damageable composite material

NASA Astrophysics Data System (ADS)

Lukyanov, Alexander A.

2012-10-01

A carbon fiber-epoxy composite (CFEC) shock response in the through thickness orientation and in one of the fiber directions is significantly different. The hydrostatic pressure inside anisotropic materials depends on deviatoric strain components as well as volumetric strain. Non-linear effects, such as shock effects, can be incorporated through the volumetric straining in the material. Thus, a new basis is required to couple the anisotropic material stiffness and strength with anisotropic shock effects, associated energy dependence, and damage softening process. This article presents these constitutive equations for shock wave modeling of a damageable carbon fiber-epoxy composite. Modeling the effect of fiber orientation on the shock response of a CFEC has been performed using a generalized decomposition of the stress tensor [A. A. Lukyanov, Int. J. Plast. 24, 140 (2008)] and Mie-Grüneisen's extrapolation of high-pressure shock Hugoniot states to other thermodynamics states for shocked CFEC materials. The three-wave structure (non-linear anisotropic, fracture, and isotropic elastic waves) that accompanies damage softening process is also proposed in this work for describing CFEC behavior under shock loading which allows to remove any discontinuities observed in the linear case for relation between shock velocities and particle velocities [A. A. Lukyanov, Eur. Phys. J. B 74, 35 (2010)]. Different Hugoniot stress levels are obtained when the material is impacted in different directions; their good agreement with the experiment demonstrates that the anisotropic equation of state, strength, and damage model are adequate for the simulation of shock wave propagation within damageable CFEC material. Remarkably, in the through thickness orientation, the material behaves similar to a simple polymer whereas in the fiber direction, the proposed in this paper model explains an initial ramp, before at sufficiently high stresses, and a much faster rising shock above it. The numerical results for shock wave modeling using proposed constitutive equations are presented, discussed, and future studies are outlined.

Time evolution of Rényi entropy under the Lindblad equation.

PubMed

Abe, Sumiyoshi

2016-08-01

In recent years, the Rényi entropy has repeatedly been discussed for characterization of quantum critical states and entanglement. Here, time evolution of the Rényi entropy is studied. A compact general formula is presented for the lower bound on the entropy rate.

A Watched Ocean World Never Boils: Inspecting the Geochemical Impact on Ocean Worlds from Their Thermal Evolution

NASA Astrophysics Data System (ADS)

Spiers, E. M.; Schmidt, B. E.

2018-05-01

I aim to acquire better understanding of coupled thermal evolution and geochemical fluxes of an ocean world through a box model. A box model divides the system into plainer elements with realistically-solvable, dynamic equations.

Reduction of Large Dynamical Systems by Minimization of Evolution Rate

NASA Technical Reports Server (NTRS)

Girimaji, Sharath S.

1999-01-01

Reduction of a large system of equations to a lower-dimensional system of similar dynamics is investigated. For dynamical systems with disparate timescales, a criterion for determining redundant dimensions and a general reduction method based on the minimization of evolution rate are proposed.

Variety of (d + 1) dimensional cosmological evolutions with and without bounce in a class of LQC-inspired models

NASA Astrophysics Data System (ADS)

Rama, S. Kalyana

2017-08-01

The bouncing evolution of an universe in Loop Quantum Cosmology can be described very well by a set of effective equations, involving a function sin x. Recently, we have generalised these effective equations to (d + 1) dimensions and to any function f( x). Depending on f( x) in these models inspired by Loop Quantum Cosmology, a variety of cosmological evolutions are possible, singular as well as non singular. In this paper, we study them in detail. Among other things, we find that the scale factor a(t) ∝ t^{ 2 q/(2 q - 1) (1 + w) d} for f(x) = x^q, and find explicit Kasner-type solutions if w = 2 q - 1 also. A result which we find particularly fascinating is that, for f(x) = √{x}, the evolution is non singular and the scale factor a( t) grows exponentially at a rate set, not by a constant density, but by a quantum parameter related to the area quantum.

Equivalence of equations describing trace element distribution during equilibrium partial melting

NASA Technical Reports Server (NTRS)

Consolmagno, G. J.; Drake, M. J.

1976-01-01

It is shown that four equations used for calculating the evolution of trace-element abundances during equilibrium partial melting are mathematically equivalent. The equations include those of Hertogen and Gijbels (1976), Shaw (1970), Schilling (1971), and O'Nions and Clarke (1972). The general form to which all these equations reduce is presented, and an analysis is performed to demonstrate their mathematical equivalence. It is noted that the utility of the general equation flows from the nature of equilibrium (i.e., the final state is independent of the path by which that state is attained).

Simple derivation of the Lindblad equation

NASA Astrophysics Data System (ADS)

Pearle, Philip

2012-07-01

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is ‘simple’ in that all it uses is the expression of a Hermitian matrix in terms of its orthonormal eigenvectors and real eigenvalues. Thus, it is appropriate for students who have learned the algebra of quantum theory. Where helpful, arguments are first given in a two-dimensional Hilbert space.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Doualle, T.; Gallais, L., E-mail: laurent.gallais@fresnel.fr; Cormont, P.

We investigate the effect of different heat treatments on the laser-induced damage probabilities of fused silica samples. Isothermal annealing in a furnace is applied, with different temperatures in the range 700–1100 °C and 12 h annealing time, to super-polished fused silica samples. The surface flatness and laser damage probabilities at 3 ns, 351 nm are measured before and after the different annealing procedures. We have found a significant improvement of the initial laser damage probabilities of the silica surface after annealing at 1050 °C for 12 h. A similar study has been conducted on CO{sub 2} laser-processed sites on the surface of the samples. Before andmore » after annealing, we have studied the morphology of the sites, the evolution of residual stress, and the laser-induced damage threshold measured at 351 nm, 3 ns. In this case, we observe that the laser damage resistance of the laser created craters can reach the damage level of the bare fused silica surface after the annealing process, with a complete stress relieve. The obtained results are then compared to the case of local annealing process by CO{sub 2} laser irradiation during 1 s, and we found similar improvements in both cases. The different results obtained in the study are compared to numerical simulations made with a thermo-mechanical model based on finite-element method that allows the simulation of the isothermal or the local annealing process, the evolution of stress and fictive temperature. The simulation results were found to be very consistent with experimental observations for the stresses evolution after annealing and estimation of the heat affected area during laser-processing based on the density dependence with fictive temperature. Following this work, the temperature for local annealing should reach 1330–1470 °C for an optimized reduction of damage probability and be below the threshold for material removal, whereas furnace annealing should be kept below the annealing point to avoid sample deformation.« less

Remarks on the chemical Fokker-Planck and Langevin equations: Nonphysical currents at equilibrium.

PubMed

Ceccato, Alessandro; Frezzato, Diego

2018-02-14

The chemical Langevin equation and the associated chemical Fokker-Planck equation are well-known continuous approximations of the discrete stochastic evolution of reaction networks. In this work, we show that these approximations suffer from a physical inconsistency, namely, the presence of nonphysical probability currents at the thermal equilibrium even for closed and fully detailed-balanced kinetic schemes. An illustration is given for a model case.

Evolution equation in the field theory of strings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marui, M.; Sugamoto, A.; Oda, I.

This paper reports on a stringy version of the Altarelli-Parisi equation given within the field theory of bosonic strings formulated in the light-cone gauge. Using this equation, the authors study the behavior of the decay function of strings under the change of reference scale, especially imposing an assumption of large transverse momentum. In some cases the n-th moment of the decay function behaves very differently from QCD.

Adaptive focusing of laser radiation onto a rough reflecting surface through the turbulent and nonlinear atmosphere

NASA Astrophysics Data System (ADS)

Vorontsov, Mikhail A.; Kolosov, Valeriy V.

2004-12-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related with maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing outgoing wave propagation, and the equation describing evolution of the mutual coherence function (MCF) for the backscattered (returned) wave. The resulting evolution equation for the MCF is further simplified by the use of the smooth refractive index approximation. This approximation enables derivation of the transport equation for the returned wave brightness function, analyzed here using method characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wavefront sensors that perform sensing of speckle-averaged characteristics of the wavefront phase (TIL sensors). Analysis of the wavefront phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric turbulence-related phase aberrations. We also show that wavefront sensing results depend on the extended target shape, surface roughness, and the outgoing beam intensity distribution on the target surface.

Analysis of wave propagation and wavefront sensing in target-in-the-loop beam control systems

NASA Astrophysics Data System (ADS)

Vorontsov, Mikhail A.; Kolosov, Valeri V.

2004-10-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related with maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing outgoing wave propagation, and the equation describing evolution of the mutual intensity function (MIF) for the backscattered (returned) wave. The resulting evolution equation for the MIF is further simplified by the use of the smooth refractive index approximation. This approximation enables derivation of the transport equation for the returned wave brightness function, analyzed here using method characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wavefront sensors that perform sensing of speckle-averaged characteristics of the wavefront phase (TIL sensors). Analysis of the wavefront phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric turbulence-related phase aberrations. We also show that wavefront sensing results depend on the extended target shape, surface roughness, and the outgoing beam intensity distribution on the target surface.

Canonical form of master equations and characterization of non-Markovianity

NASA Astrophysics Data System (ADS)

Hall, Michael J. W.; Cresser, James D.; Li, Li; Andersson, Erika

2014-04-01

Master equations govern the time evolution of a quantum system interacting with an environment, and may be written in a variety of forms. Time-independent or memoryless master equations, in particular, can be cast in the well-known Lindblad form. Any time-local master equation, Markovian or non-Markovian, may in fact also be written in a Lindblad-like form. A diagonalization procedure results in a unique, and in this sense canonical, representation of the equation, which may be used to fully characterize the non-Markovianity of the time evolution. Recently, several different measures of non-Markovianity have been presented which reflect, to varying degrees, the appearance of negative decoherence rates in the Lindblad-like form of the master equation. We therefore propose using the negative decoherence rates themselves, as they appear in the canonical form of the master equation, to completely characterize non-Markovianity. The advantages of this are especially apparent when more than one decoherence channel is present. We show that a measure proposed by Rivas et al. [Phys. Rev. Lett. 105, 050403 (2010), 10.1103/PhysRevLett.105.050403] is a surprisingly simple function of the canonical decoherence rates, and give an example of a master equation that is non-Markovian for all times t >0, but to which nearly all proposed measures are blind. We also give necessary and sufficient conditions for trace distance and volume measures to witness non-Markovianity, in terms of the Bloch damping matrix.

The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Neill, Duff

Here, we develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. Furthermore, this equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We also compute the decay width analytically, giving a closed form expression, and find it to be jet geometrymore » independent, up to the number of legs of the dipole in the active jet. By enabling the asymptotic expansion we find that the perturbative seed is correct; we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.« less

The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts

DOE PAGES

Neill, Duff

2017-01-25

Here, we develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. Furthermore, this equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We also compute the decay width analytically, giving a closed form expression, and find it to be jet geometrymore » independent, up to the number of legs of the dipole in the active jet. By enabling the asymptotic expansion we find that the perturbative seed is correct; we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.« less

Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements

NASA Astrophysics Data System (ADS)

Zander, C.; Plastino, A. R.; Díaz-Alonso, J.

2015-11-01

We investigate time-dependent solutions for a non-linear Schrödinger equation recently proposed by Nassar and Miret-Artés (NM) to describe the continuous measurement of the position of a quantum particle (Nassar, 2013; Nassar and Miret-Artés, 2013). Here we extend these previous studies in two different directions. On the one hand, we incorporate a potential energy term in the NM equation and explore the corresponding wave packet dynamics, while in the previous works the analysis was restricted to the free-particle case. On the other hand, we investigate time-dependent solutions while previous studies focused on a stationary one. We obtain exact wave packet solutions for linear and quadratic potentials, and approximate solutions for the Morse potential. The free-particle case is also revisited from a time-dependent point of view. Our analysis of time-dependent solutions allows us to determine the stability properties of the stationary solution considered in Nassar (2013), Nassar and Miret-Artés (2013). On the basis of these results we reconsider the Bohmian approach to the NM equation, taking into account the fact that the evolution equation for the probability density ρ =| ψ | 2 is not a continuity equation. We show that the effect of the source term appearing in the evolution equation for ρ has to be explicitly taken into account when interpreting the NM equation from a Bohmian point of view.

Evolution and End Point of the Black String Instability: Large D Solution.

PubMed

Emparan, Roberto; Suzuki, Ryotaku; Tanabe, Kentaro

2015-08-28

We derive a simple set of nonlinear, (1+1)-dimensional partial differential equations that describe the dynamical evolution of black strings and branes to leading order in the expansion in the inverse of the number of dimensions D. These equations are easily solved numerically. Their solution shows that thin enough black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to stable nonuniform black strings. This proves an earlier conjecture about the end point of the instability of black strings in a large enough number of dimensions. If the initial black string is very thin, the final configuration is highly nonuniform and resembles a periodic array of localized black holes joined by short necks. We also present the equations that describe the nonlinear dynamics of anti-de Sitter black branes at large D.

Numerical solutions of the complete Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Hassan, H. A.

1993-01-01

The objective of this study is to compare the use of assumed pdf (probability density function) approaches for modeling supersonic turbulent reacting flowfields with the more elaborate approach where the pdf evolution equation is solved. Assumed pdf approaches for averaging the chemical source terms require modest increases in CPU time typically of the order of 20 percent above treating the source terms as 'laminar.' However, it is difficult to assume a form for these pdf's a priori that correctly mimics the behavior of the actual pdf governing the flow. Solving the evolution equation for the pdf is a theoretically sound approach, but because of the large dimensionality of this function, its solution requires a Monte Carlo method which is computationally expensive and slow to coverage. Preliminary results show both pdf approaches to yield similar solutions for the mean flow variables.

Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion

NASA Astrophysics Data System (ADS)

Congy, T.; Ivanov, S. K.; Kamchatnov, A. M.; Pavloff, N.

2017-08-01

We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks, which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations.

Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion.

PubMed

Congy, T; Ivanov, S K; Kamchatnov, A M; Pavloff, N

2017-08-01

We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks, which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations.

An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations

PubMed Central

Mirzaev, Inom; Byrne, Erin C.; Bortz, David M.

2016-01-01

We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach. PMID:28316360

A note on a nonlinear equation arising in discussions of the steady fall of a resistive, viscous, isothermal fluid across a magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tautz, R. C., E-mail: robert.c.tautz@gmail.com; Lerche, I., E-mail: lercheian@yahoo.com

2015-11-15

This note considers the evolution of steady isothermal flow across a uniform magnetic field from an analytic standpoint. This problem is of concern in developments of magnetic fields in the solar corona and for prominence dynamics. Limiting behaviors are obtained to the nonlinear equation describing the flow depending on the value of a single parameter. For the situation where the viscous drag is a small correction to the inviscid flow limiting structures are also outlined. The purpose of the note is to show how one can evaluate some of the analytic properties of the highly nonlinear equation that are ofmore » use in considering the numerical evolution as done in Low and Egan [Phys. Plasmas 21, 062105 (2014)].« less

Asymptotically Almost Periodic Solutions of Evolution Equations in Banach Spaces

NASA Astrophysics Data System (ADS)

Ruess, W. M.; Phong, V. Q.

Tile linear abstract evolution equation (∗) u'( t) = Au( t) + ƒ( t), t ∈ R, is considered, where A: D( A) ⊂ E → E is the generator of a strongly continuous semigroup of operators in the Banach space E. Starting from analogs of Kadets' and Loomis' Theorems for vector valued almost periodic Functions, we show that if σ( A) ∩ iR is countable and ƒ: R → E is [asymptotically] almost periodic, then every bounded and uniformly continuous solution u to (∗) is [asymptotically] almost periodic, provided e-λ tu( t) has uniformly convergent means for all λ ∈ σ( A) ∩ iR. Related results on Eberlein-weakly asymptotically almost periodic, periodic, asymptotically periodic and C 0-solutions of (∗), as well as on the discrete case of solutions of difference equations are included.

Ring Current Ion Coupling with Electromagnetic Ion Cyclotron Waves

NASA Technical Reports Server (NTRS)

Khazanov, George V.

2002-01-01

A new ring current global model has been developed for the first time that couples the system of two kinetic equations: one equation describes the ring current (RC) ion dynamic, and another equation describes wave evolution of electromagnetic ion cyclotron waves (EMIC). The coupled model is able to simulate, for the first time self-consistently calculated RC ion kinetic and evolution of EMIC waves that propagate along geomagnetic field lines and reflect from the ionosphere. Ionospheric properties affect the reflection index through the integral Pedersen and Hall coductivities. The structure and dynamics of the ring current proton precipitating flux regions, intensities of EMIC, global RC energy balance, and some other parameters will be studied in detail for the selected geomagnetic storms. The space whether aspects of RC modelling and comparison with the data will also be discussed.

Modeling collective behavior of dislocations in crystalline materials

NASA Astrophysics Data System (ADS)

Varadhan, Satya N.

Elastic interaction of dislocations leads to collective behavior and determines plastic response at the mesoscale. Notable characteristics of mesoscale plasticity include the formation of dislocation patterns, propagative instability phenomena due to strain aging such as the Luders and Portevin-Le Chatelier effects, and size-dependence of low stress. This work presents a unified approach to modeling collective behavior based on mesoscale field dislocation mechanics and crystal plasticity, using constitutive models with physical basis. Successful application is made to: compression of a bicrystal, where "smaller is stronger"---the flow stress increases as the specimen size is reduced; torsional creep of ice single crystals, where the plastic strain rate increases with time under constant applied torque; strain aging in a single crystal alloy, where the transition from homogeneous deformation to intermittent bands to continuous band is captured as the applied deformation rate is increased. A part of this work deals with the kinematics of dislocation density evolution. An explicit Galerkin/least-squares formulation is introduced for the quasilinear evolution equation, which leads to a symmetric and well-conditioned system of equations with constant coefficients, making it attractive for large-scale problems. It is shown that the evolution equation simplifies to the Hamilton-Jacobi equations governing geometric optics and level set methods in the following physical contexts: annihilation of dislocations, expansion of a polygonal dislocation loop and operation of a Frank-Read source. The weak solutions to these equations are not unique, and the numerical method is able to capture solutions corresponding to shock as well as expansion fans.

Hybrid discrete-time neural networks.

PubMed

Cao, Hongjun; Ibarz, Borja

2010-11-13

Hybrid dynamical systems combine evolution equations with state transitions. When the evolution equations are discrete-time (also called map-based), the result is a hybrid discrete-time system. A class of biological neural network models that has recently received some attention falls within this category: map-based neuron models connected by means of fast threshold modulation (FTM). FTM is a connection scheme that aims to mimic the switching dynamics of a neuron subject to synaptic inputs. The dynamic equations of the neuron adopt different forms according to the state (either firing or not firing) and type (excitatory or inhibitory) of their presynaptic neighbours. Therefore, the mathematical model of one such network is a combination of discrete-time evolution equations with transitions between states, constituting a hybrid discrete-time (map-based) neural network. In this paper, we review previous work within the context of these models, exemplifying useful techniques to analyse them. Typical map-based neuron models are low-dimensional and amenable to phase-plane analysis. In bursting models, fast-slow decomposition can be used to reduce dimensionality further, so that the dynamics of a pair of connected neurons can be easily understood. We also discuss a model that includes electrical synapses in addition to chemical synapses with FTM. Furthermore, we describe how master stability functions can predict the stability of synchronized states in these networks. The main results are extended to larger map-based neural networks.

The evolution of hyperboloidal data with the dual foliation formalism: mathematical analysis and wave equation tests

NASA Astrophysics Data System (ADS)

Hilditch, David; Harms, Enno; Bugner, Marcus; Rüter, Hannes; Brügmann, Bernd

2018-03-01

A long-standing problem in numerical relativity is the satisfactory treatment of future null-infinity. We propose an approach for the evolution of hyperboloidal initial data in which the outer boundary of the computational domain is placed at infinity. The main idea is to apply the ‘dual foliation’ formalism in combination with hyperboloidal coordinates and the generalized harmonic gauge formulation. The strength of the present approach is that, following the ideas of Zenginoğlu, a hyperboloidal layer can be naturally attached to a central region using standard coordinates of numerical relativity applications. Employing a generalization of the standard hyperboloidal slices, developed by Calabrese et al, we find that all formally singular terms take a trivial limit as we head to null-infinity. A byproduct is a numerical approach for hyperboloidal evolution of nonlinear wave equations violating the null-condition. The height-function method, used often for fixed background spacetimes, is generalized in such a way that the slices can be dynamically ‘waggled’ to maintain the desired outgoing coordinate lightspeed precisely. This is achieved by dynamically solving the eikonal equation. As a first numerical test of the new approach we solve the 3D flat space scalar wave equation. The simulations, performed with the pseudospectral bamps code, show that outgoing waves are cleanly absorbed at null-infinity and that errors converge away rapidly as resolution is increased.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Livescu, Veronica; Bronkhorst, Curt Allan; Vander Wiel, Scott Alan

Many challenges exist with regard to understanding and representing complex physical processes involved with ductile damage and failure in polycrystalline metallic materials. Currently, the ability to accurately predict the macroscale ductile damage and failure response of metallic materials is lacking. Research at Los Alamos National Laboratory (LANL) is aimed at building a coupled experimental and computational methodology that supports the development of predictive damage capabilities by: capturing real distributions of microstructural features from real material and implementing them as digitally generated microstructures in damage model development; and, distilling structure-property information to link microstructural details to damage evolution under a multitudemore » of loading states.« less

Transverse momentum dependent parton distributions at small- x

DOE PAGES

Xiao, Bo-Wen; Yuan, Feng; Zhou, Jian

2017-05-23

We study the transverse momentum dependent (TMD) parton distributions at small-x in a consistent framework that takes into account the TMD evolution and small-x evolution simultaneously. The small-x evolution effects are included by computing the TMDs at appropriate scales in terms of the dipole scattering amplitudes, which obey the relevant Balitsky–Kovchegov equation. Meanwhile, the TMD evolution is obtained by resumming the Collins–Soper type large logarithms emerged from the calculations in small-x formalism into Sudakov factors.

Transverse momentum dependent parton distributions at small-x

NASA Astrophysics Data System (ADS)

Xiao, Bo-Wen; Yuan, Feng; Zhou, Jian

2017-08-01

We study the transverse momentum dependent (TMD) parton distributions at small-x in a consistent framework that takes into account the TMD evolution and small-x evolution simultaneously. The small-x evolution effects are included by computing the TMDs at appropriate scales in terms of the dipole scattering amplitudes, which obey the relevant Balitsky-Kovchegov equation. Meanwhile, the TMD evolution is obtained by resumming the Collins-Soper type large logarithms emerged from the calculations in small-x formalism into Sudakov factors.

Transverse momentum dependent parton distributions at small- x

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xiao, Bo-Wen; Yuan, Feng; Zhou, Jian

We study the transverse momentum dependent (TMD) parton distributions at small-x in a consistent framework that takes into account the TMD evolution and small-x evolution simultaneously. The small-x evolution effects are included by computing the TMDs at appropriate scales in terms of the dipole scattering amplitudes, which obey the relevant Balitsky–Kovchegov equation. Meanwhile, the TMD evolution is obtained by resumming the Collins–Soper type large logarithms emerged from the calculations in small-x formalism into Sudakov factors.

Characterizing single isolated radiation-damage events from molecular dynamics via virtual diffraction methods

DOE PAGES

Stewart, James A.; Brookman, G.; Price, Patrick Michael; ...

2018-04-25

In this study, the evolution and characterization of single-isolated-ion-strikes are investigated by combining atomistic simulations with selected-area electron diffraction (SAED) patterns generated from these simulations. Five molecular dynamics simulations are performed for a single 20 keV primary knock-on atom in bulk crystalline Si. The resulting cascade damage is characterized in two complementary ways. First, the individual cascade events are conventionally quantified through the evolution of the number of defects and the atomic (volumetric) strain associated with these defect structures. These results show that (i) the radiation damage produced is consistent with the Norgett, Robinson, and Torrens model of damage productionmore » and (ii) there is a net positive volumetric strain associated with the cascade structures. Second, virtual SAED patterns are generated for the resulting cascade-damaged structures along several zone axes. The analysis of the corresponding diffraction patterns shows the SAED spots approximately doubling in size, on average, due to broadening induced by the defect structures. Furthermore, the SAED spots are observed to exhibit an average radial outward shift between 0.33% and 0.87% depending on the zone axis. Finally, this characterization approach, as utilized here, is a preliminary investigation in developing methodologies and opportunities to link experimental observations with atomistic simulations to elucidate microstructural damage states.« less

Fault Wear by Damage Evolution During Steady-State Slip

NASA Astrophysics Data System (ADS)

Lyakhovsky, Vladimir; Sagy, Amir; Boneh, Yuval; Reches, Ze'ev

2014-11-01

Slip along faults generates wear products such as gouge layers and cataclasite zones that range in thickness from sub-millimeter to tens of meters. The properties of these zones apparently control fault strength and slip stability. Here we present a new model of wear in a three-body configuration that utilizes the damage rheology approach and considers the process as a microfracturing or damage front propagating from the gouge zone into the solid rock. The derivations for steady-state conditions lead to a scaling relation for the damage front velocity considered as the wear-rate. The model predicts that the wear-rate is a function of the shear-stress and may vanish when the shear-stress drops below the microfracturing strength of the fault host rock. The simulated results successfully fit the measured friction and wear during shear experiments along faults made of carbonate and tonalite. The model is also valid for relatively large confining pressures, small damage-induced change of the bulk modulus and significant degradation of the shear modulus, which are assumed for seismogenic zones of earthquake faults. The presented formulation indicates that wear dynamics in brittle materials in general and in natural faults in particular can be understood by the concept of a "propagating damage front" and the evolution of a third-body layer.

Characterizing single isolated radiation-damage events from molecular dynamics via virtual diffraction methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stewart, James A.; Brookman, G.; Price, Patrick Michael

In this study, the evolution and characterization of single-isolated-ion-strikes are investigated by combining atomistic simulations with selected-area electron diffraction (SAED) patterns generated from these simulations. Five molecular dynamics simulations are performed for a single 20 keV primary knock-on atom in bulk crystalline Si. The resulting cascade damage is characterized in two complementary ways. First, the individual cascade events are conventionally quantified through the evolution of the number of defects and the atomic (volumetric) strain associated with these defect structures. These results show that (i) the radiation damage produced is consistent with the Norgett, Robinson, and Torrens model of damage productionmore » and (ii) there is a net positive volumetric strain associated with the cascade structures. Second, virtual SAED patterns are generated for the resulting cascade-damaged structures along several zone axes. The analysis of the corresponding diffraction patterns shows the SAED spots approximately doubling in size, on average, due to broadening induced by the defect structures. Furthermore, the SAED spots are observed to exhibit an average radial outward shift between 0.33% and 0.87% depending on the zone axis. Finally, this characterization approach, as utilized here, is a preliminary investigation in developing methodologies and opportunities to link experimental observations with atomistic simulations to elucidate microstructural damage states.« less

Characterizing single isolated radiation-damage events from molecular dynamics via virtual diffraction methods

NASA Astrophysics Data System (ADS)

Stewart, J. A.; Brookman, G.; Price, P.; Franco, M.; Ji, W.; Hattar, K.; Dingreville, R.

2018-04-01

The evolution and characterization of single-isolated-ion-strikes are investigated by combining atomistic simulations with selected-area electron diffraction (SAED) patterns generated from these simulations. Five molecular dynamics simulations are performed for a single 20 keV primary knock-on atom in bulk crystalline Si. The resulting cascade damage is characterized in two complementary ways. First, the individual cascade events are conventionally quantified through the evolution of the number of defects and the atomic (volumetric) strain associated with these defect structures. These results show that (i) the radiation damage produced is consistent with the Norgett, Robinson, and Torrens model of damage production and (ii) there is a net positive volumetric strain associated with the cascade structures. Second, virtual SAED patterns are generated for the resulting cascade-damaged structures along several zone axes. The analysis of the corresponding diffraction patterns shows the SAED spots approximately doubling in size, on average, due to broadening induced by the defect structures. Furthermore, the SAED spots are observed to exhibit an average radial outward shift between 0.33% and 0.87% depending on the zone axis. This characterization approach, as utilized here, is a preliminary investigation in developing methodologies and opportunities to link experimental observations with atomistic simulations to elucidate microstructural damage states.

In-process deformation measurements of translucent high speed fibre-reinforced disc rotors

NASA Astrophysics Data System (ADS)

Philipp, Katrin; Filippatos, Angelos; Koukourakis, Nektarios; Kuschmierz, Robert; Leithold, Christoph; Langkamp, Albert; Fischer, Andreas; Czarske, Jürgen

2015-07-01

The high stiffness to weight ratio of glass fibre-reinforced polymers (GFRP) makes them an attractive material for rotors e.g. in the aerospace industry. We report on recent developments towards non-contact, in-situ deformation measurements with temporal resolution up to 200 µs and micron measurement uncertainty. We determine the starting point of damage evolution inside the rotor material through radial expansion measurements. This leads to a better understanding of dynamic material behaviour regarding damage evolution and the prediction of damage initiation and propagation. The measurements are conducted using a novel multi-sensor system consisting of four laser Doppler distance (LDD) sensors. The LDD sensor, a two-wavelength Mach-Zehnder interferometer was already successfully applied for dynamic deformation measurements at metallic rotors. While translucency of the GFRP rotor material limits the applicability of most optical measurement techniques due to speckles from both surface and volume of the rotor, the LDD profits from speckles and is not disturbed by backscattered laser light from the rotor volume. The LDD sensor evaluates only signals from the rotor surface. The anisotropic glass fibre-reinforcement results in a rotationally asymmetric dynamic deformation. A novel signal processing algorithm is applied for the combination of the single sensor signals to obtain the shape of the investigated rotors. In conclusion, the applied multi-sensor system allows high temporal resolution dynamic deformation measurements. First investigations regarding damage evolution inside GFRP are presented as an important step towards a fundamental understanding of the material behaviour and the prediction of damage initiation and propagation.

Scale covariant gravitation. V - Kinetic theory. VI - Stellar structure and evolution

NASA Technical Reports Server (NTRS)

Hsieh, S.-H.; Canuto, V. M.

1981-01-01

A scale covariant kinetic theory for particles and photons is developed. The mathematical framework of the theory is given by the tangent bundle of a Weyl manifold. The Liouville equation is derived, and solutions to corresponding equilibrium distributions are presented and shown to yield thermodynamic results identical to the ones obtained previously. The scale covariant theory is then used to derive results of interest to stellar structure and evolution. A radiative transfer equation is derived that can be used to study stellar evolution with a variable gravitational constant. In addition, it is shown that the sun's absolute luminosity scales as L approximately equal to GM/kappa, where kappa is the stellar opacity. Finally, a formula is derived for the age of globular clusters as a function of the gravitational constant using a previously derived expression for the absolute luminosity.

Estimating the time evolution of NMR systems via a quantum-speed-limit-like expression

NASA Astrophysics Data System (ADS)

Villamizar, D. V.; Duzzioni, E. I.; Leal, A. C. S.; Auccaise, R.

2018-05-01

Finding the solutions of the equations that describe the dynamics of a given physical system is crucial in order to obtain important information about its evolution. However, by using estimation theory, it is possible to obtain, under certain limitations, some information on its dynamics. The quantum-speed-limit (QSL) theory was originally used to estimate the shortest time in which a Hamiltonian drives an initial state to a final one for a given fidelity. Using the QSL theory in a slightly different way, we are able to estimate the running time of a given quantum process. For that purpose, we impose the saturation of the Anandan-Aharonov bound in a rotating frame of reference where the state of the system travels slower than in the original frame (laboratory frame). Through this procedure it is possible to estimate the actual evolution time in the laboratory frame of reference with good accuracy when compared to previous methods. Our method is tested successfully to predict the time spent in the evolution of nuclear spins 1/2 and 3/2 in NMR systems. We find that the estimated time according to our method is better than previous approaches by up to four orders of magnitude. One disadvantage of our method is that we need to solve a number of transcendental equations, which increases with the system dimension and parameter discretization used to solve such equations numerically.

Oxidative stress and the evolution of sex differences in life span and ageing in the decorated cricket, Gryllodes sigillatus.

PubMed

Archer, Catharine R; Sakaluk, Scott K; Selman, Colin; Royle, Nick J; Hunt, John

2013-03-01

The Free Radical Theory of Ageing (FRTA) predicts that oxidative stress, induced when levels of reactive oxygen species exceed the capacity of antioxidant defenses, causes ageing. Recently, it has also been argued that oxidative damage may mediate important life-history trade-offs. Here, we use inbred lines of the decorated cricket, Gryllodes sigillatus, to estimate the genetic (co)variance between age-dependent reproductive effort, life span, ageing, oxidative damage, and total antioxidant capacity within and between the sexes. The FRTA predicts that oxidative damage should accumulate with age and negatively correlate with life span. We find that protein oxidation is greater in the shorter lived sex (females) and negatively genetically correlated with life span in both sexes. However, oxidative damage did not accumulate with age in either sex. Previously we have shown antagonistic pleiotropy between the genes for early-life reproductive effort and ageing rate in both sexes, although this was stronger in females. In females, we find that elevated fecundity early in life is associated with greater protein oxidation later in life, which is in turn positively correlated with the rate of ageing. Our results provide mixed support for the FRTA but suggest that oxidative stress may mediate sex-specific life-history strategies in G. sigillatus. © 2012 The Author(s). Evolution© 2012 The Society for the Study of Evolution.

Numerical study of a Vlasov equation for systems with interacting particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herrera, Dianela; Curilef, Sergio

2015-03-10

We solve numerically the Vlasov equation for the self-gravitating sheet model. We used the method introduced by Cheng and Knorr [Comput Phys 22, 330-351 (1976)]. We discuss the quasi-stationary state for some thermodynamical observables, specifically the kinetic energy, whose trend is depicted for early evolution.

Unstable solitary-wave solutions of the generalized Benjamin-Bona-Mahony equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

McKinney, W.R.; Restrepo, J.M.; Bona, J.L.

1994-06-01

The evolution of solitary waves of the gBBM equation is investigated computationally. The experiments confirm previously derived theoretical stability estimates and, more importantly, yield insights into their behavior. For example, highly energetic unstable solitary waves when perturbed are shown to evolve into several stable solitary waves.

Yang-Baxter maps, discrete integrable equations and quantum groups

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Sergeev, Sergey M.

2018-01-01

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. The commuting Integrals of Motion are defined in the standard way via the Quantum Inverse Problem Method, utilizing Baxter's famous commuting transfer matrix approach. All elements of the above construction have a meaningful quasi-classical limit. As a result one obtains an integrable discrete Hamiltonian evolution system, where the local equation of motion are determined by a classical Yang-Baxter map and the action functional is determined by the quasi-classical asymptotics of the universal R-matrix of the underlying quantum algebra. In this paper we present detailed considerations of the above scheme on the example of the algebra Uq (sl (2)) leading to discrete Liouville equations, however the approach is rather general and can be applied to any quantized Lie algebra.

Cosmological applications of singular hypersurfaces in general relativity

NASA Astrophysics Data System (ADS)

Laguna-Castillo, Pablo

Three applications to cosmology of surface layers, based on Israel's formalism of singular hypersurfaces and thin shells in general relativity, are presented. Einstein's field equations are analyzed in the presence of a bubble nucleated in vacuum phase transitions within the context of the old inflationary universe scenario. The evolution of a bubble with vanishing surface energy density is studied. It is found that such bubbles lead to a worm-hole matching. Next, the observable four-dimensional universe is considered as a singular hypersurface of discontinuity embedded in a five-dimensional Kaluza-Klein cosmology. It is possible to rewrite the projected five-dimensional Einstein equations on the surface layer in a similar way to the four-dimensional Robertson-Walker cosmology equations. Next, a model is described for an infinite-length, straight U(1) cosmic string as a cylindrical, singular shell enclosing a region of false vacuum. A set of equations is introduced which are required to develop a three-dimensional computer code whose purpose is to study the process of intercommuting cosmic strings with the inclusion of gravitational effects. The outcome is evolution and constraint equations for the gravitational, scalar and gauge field of two initially separated, perpendicular, cosmic strings.

Kinematic validation of a quasi-geostrophic model for the fast dynamics in the Earth's outer core

NASA Astrophysics Data System (ADS)

Maffei, S.; Jackson, A.

2017-09-01

We derive a quasi-geostrophic (QG) system of equations suitable for the description of the Earth's core dynamics on interannual to decadal timescales. Over these timescales, rotation is assumed to be the dominant force and fluid motions are strongly invariant along the direction parallel to the rotation axis. The diffusion-free, QG system derived here is similar to the one derived in Canet et al. but the projection of the governing equations on the equatorial disc is handled via vertical integration and mass conservation is applied to the velocity field. Here we carefully analyse the properties of the resulting equations and we validate them neglecting the action of the Lorentz force in the momentum equation. We derive a novel analytical solution describing the evolution of the magnetic field under these assumptions in the presence of a purely azimuthal flow and an alternative formulation that allows us to numerically solve the evolution equations with a finite element method. The excellent agreement we found with the analytical solution proves that numerical integration of the QG system is possible and that it preserves important physical properties of the magnetic field. Implementation of magnetic diffusion is also briefly considered.

Coda Wave Interferometry Method Applied in Structural Monitoring to Assess Damage Evolution in Masonry and Concrete Structures

NASA Astrophysics Data System (ADS)

Masera, D.; Bocca, P.; Grazzini, A.

2011-07-01

In this experimental program the main goal is to monitor the damage evolution in masonry and concrete structures by Acoustic Emission (AE) signal analysis applying a well-know seismic method. For this reason the concept of the coda wave interferometry is applied to AE signal recorded during the tests. Acoustic Emission (AE) are very effective non-destructive techniques applied to identify micro and macro-defects and their temporal evolution in several materials. This technique permits to estimate the velocity of ultrasound waves propagation and the amount of energy released during fracture propagation to obtain information on the criticality of the ongoing process. By means of AE monitoring, an experimental analysis on a set of reinforced masonry walls under variable amplitude loading and strengthening reinforced concrete (RC) beams under monotonic static load has been carried out. In the reinforced masonry wall, cyclic fatigue stress has been applied to accelerate the static creep and to forecast the corresponding creep behaviour of masonry under static long-time loading. During the tests, the evaluation of fracture growth is monitored by coda wave interferometry which represents a novel approach in structural monitoring based on AE relative change velocity of coda signal. In general, the sensitivity of coda waves has been used to estimate velocity changes in fault zones, in volcanoes, in a mining environment, and in ultrasound experiments. This method uses multiple scattered waves, which travelled through the material along numerous paths, to infer tiny temporal changes in the wave velocity. The applied method has the potential to be used as a "damage-gauge" for monitoring velocity changes as a sign of damage evolution into masonry and concrete structures.

Implementation of a Mechanochemical Model for Dynamic Brittle Fracture in SIERRA

DTIC Science & Technology

2014-08-01

equations of state could be used in the future.† The energy associated with the deviatoric deformation is taken to be eiso(L ∗) = µ tr [ (L∗)2 ] (33...internal state variable can also be found in the book by Holzapfel.9 In the types of damage models considered by Kachanov, the energy density equation is...13b) The dimensions of K are: [K] = 1 [Time][ Stress ] . (14) The specific choice of equations 13 contain two physically questionable features,

In-situ X-ray CT results of damage evolution in L6 ordinary chondrite meteorites

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cuadra, Jefferson A.; Hazeli, Kavan; Ramesh, K. T.

2016-06-17

These are slides about in-situ X-ray CT results of damage evolution in L6 ordinary chondrite meteorites. The following topics are covered: mechanical and thermal damage characterization, list of Grosvenor Mountain (GRO) meteorite samples, in-situ x-ray compression test setup, GRO-chipped reference at 0 N - existing cracks, GRO-chipped loaded at 1580 N, in-situ x-ray thermal fatigue test setup, GRO-B14 room temperature reference, GRO-B14 Cycle 47 at 200°C, GRO-B14 Cycle 47 at room temperature, conclusions from qualitative analysis, future work and next steps. Conclusions are the following: Both GRO-Chipped and GRO-B14 had existing voids and cracks within the volume. These sites withmore » existing damage were selected for CT images from mechanically and thermally loaded scans since they are prone to damage initiation. The GRO-Chipped sample was loaded to 1580 N which resulted in a 14% compressive engineering strain, calculated using LVDT. Based on the CT cross sectional images, the GRO-B14 sample at 200°C has a thermal expansion of approximately 96 μm in height (i.e. ~1.6% engineering strain).« less

A nonlinear wave equation in nonadiabatic flame propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Booty, M.R.; Matalon, M.; Matkowsky, B.J.

1988-06-01

The authors derive a nonlinear wave equation from the diffusional thermal model of gaseous combustion to describe the evolution of a flame front. The equation arises as a long wave theory, for values of the volumeric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis numbers near the critical value beyond which uniformly propagating planar flames lose stability via a degenerate Hopf bifurcation. Analysis of the equation suggests the possibility of a singularity developing in finite time.

Magnetic Flux Transport at the Solar Surface

NASA Astrophysics Data System (ADS)

Jiang, J.; Hathaway, D. H.; Cameron, R. H.; Solanki, S. K.; Gizon, L.; Upton, L.

2014-12-01

After emerging to the solar surface, the Sun's magnetic field displays a complex and intricate evolution. The evolution of the surface field is important for several reasons. One is that the surface field, and its dynamics, sets the boundary condition for the coronal and heliospheric magnetic fields. Another is that the surface evolution gives us insight into the dynamo process. In particular, it plays an essential role in the Babcock-Leighton model of the solar dynamo. Describing this evolution is the aim of the surface flux transport model. The model starts from the emergence of magnetic bipoles. Thereafter, the model is based on the induction equation and the fact that after emergence the magnetic field is observed to evolve as if it were purely radial. The induction equation then describes how the surface flows—differential rotation, meridional circulation, granular, supergranular flows, and active region inflows—determine the evolution of the field (now taken to be purely radial). In this paper, we review the modeling of the various processes that determine the evolution of the surface field. We restrict our attention to their role in the surface flux transport model. We also discuss the success of the model and some of the results that have been obtained using this model.

Use of atomic force microscopy for characterizing damage evolution during fatigue

NASA Astrophysics Data System (ADS)

Cretegny, Laurent

2000-10-01

A study of the development of surface fatigue damage in PH 13-8 Mo stainless steel and copper by atomic force microscopy (AFM) was performed. AFM observations allow highly automated, quantitative characterization of surface deformation with a resolution of 5 nm or better, which is ideal for understanding fatigue damage evolution. A secondary objective was to establish a correlation between fatigue life exhausted and impedance spectroscopy. Strain controlled fatigue tests were conducted both in high and low cycle fatigue regimes, and interruptions of the fatigue tests allowed characterizing the evolution of the surface upset at various life-fractions. In the low strain amplitude tests on stainless steel (Deltaepsilonpl/2 = 0.0026%), surface damage occurred in the shape of narrow streaks at the interface between martensite laths where reverted austenite was present. The streaks eventually coalesced to form crack nuclei. In high strain amplitude tests (Deltaepsilon pl/2 = 0.049%), fatigue surface damage was essentially dominated by the formation of extrusions. In copper, both low (Deltaepsilonpl/2 = 0.061%) and high (Deltaepsilonpl/2 = 0.134%) strain amplitude tests showed the formation of slip bands (mainly extrusions) across entire grains. Protrusions were present only in copper specimens tested at the high strain amplitude. Crack nucleation in the low strain amplitude tests occurred in both materials at the interface between a region that sustained a high level of deformation and one with little evidence of surface upset. This commonality between these two materials that are otherwise very dissimilar in nature suggests a universal scheme for location of fatigue crack nucleation sites during HCF. A procedure was developed in this study to quantitatively characterize the amount of irreversible surface strain. The proposed formalism is applicable to any material, independently of the type of surface damage, and leads to a criterion for crack nucleation based on physical evidence of surface damage. A correlation between fatigue damage and impedance spectroscopy measurements was shown in copper, in particular during the primary cyclic hardening stage. The measurements were however less sensitive to the development of surface upset that occurred beyond that stage.

Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

PubMed

Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

2014-01-01

Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

Nonlinear Ocean Waves

DTIC Science & Technology

1994-09-30

equation due to Kadomtsev & Petviashvili (1970), Dx(atu + 6 ui)u + a8 3U) + 3 ay2u = 0, (KP) is known to describe approximately the evolution of...to be stable to perturbations, and their amplitudes need not be small. The Kadomtsev - Petviashvili (KP) equation is known to describe approximately the...predicted with reasonable accuracy by a family of exact solutions of an equation due to Kadomtsev and Petviashvili (1970): (ft + 6 ffx + f )x + 3fyy

3D numerical simulation of transient processes in hydraulic turbines

NASA Astrophysics Data System (ADS)

Cherny, S.; Chirkov, D.; Bannikov, D.; Lapin, V.; Skorospelov, V.; Eshkunova, I.; Avdushenko, A.

2010-08-01

An approach for numerical simulation of 3D hydraulic turbine flows in transient operating regimes is presented. The method is based on a coupled solution of incompressible RANS equations, runner rotation equation, and water hammer equations. The issue of setting appropriate boundary conditions is considered in detail. As an illustration, the simulation results for runaway process are presented. The evolution of vortex structure and its effect on computed runaway traces are analyzed.

Traveling waves in discretized Balitsky Kovchegov evolution

NASA Astrophysics Data System (ADS)

Marquet, C.; Peschanski, R.; Soyez, G.; Bialas, A.

2006-02-01

We study the asymptotic solutions of a version of the Balitsky-Kovchegov evolution with discrete steps in rapidity. We derive a closed iterative equation in momentum space. We show that it possesses traveling-wave solutions and extract their properties. We find no evidence for chaotic behaviour due to discretization.

A three-dimensional `Kaiser damage-memory' effect through true-triaxial loading

NASA Astrophysics Data System (ADS)

Meredith, P. G.; Browning, J.; Harland, S. R.; Healy, D.; Stuart, C.; Mitchell, T. M.

2017-12-01

Microcrack damage leading to failure in rocks evolves in response to differential loading. The vast majority of experimental studies investigate damage evolution, the `Kaiser damage-memory' effect, and rock failure using conventional triaxial stress states (σ1 > σ2 = σ3). Such stress states develop a crack population that displays cylindrical transverse isotropy. However, in nature the stress state is in general truly triaxial (σ1 > σ2 > σ3) and experiments that utilise such loading conditions can generate crack populations that display planar transverse isotropy which in turn influences properties such as permeability and strength. We investigate the evolution of crack damage under both conventional and true triaxial stress conditions using results from measurements made on cubic samples of sandstone deformed in three orthogonal directions with independently controlled stress paths. We have measured, simultaneously with stress and strain, the changes in ultrasonic compressional and shear wave velocities in the three principal directions, together with the bulk acoustic emission (AE) output. Changes in acoustic wave velocities are associated with both elastic closure and opening of pre-existing cracks, and the inelastic formation of new cracks. By contrast, AE is only associated with the inelastic growth of new crack damage and as such, we use the onset of AE to determine the initiation of new crack damage. By mapping these damage onsets under both conventional triaxial and true triaxial sequential cyclic loading, we have shown that `damage envelopes' evolve dynamically and can be pushed closer to the failure envelope. Whether a stress state has been `visited' before is key to determining and understanding damage states. Crack damage populations can be generated with multiple orientations depending on the arrangement of loading directions and hence principal stress directions. The sequential cyclic loading tests show that further damage in any one population commences only when the previous maximum differential stress `seen' by that population is exceeded. Understanding anisotropic damage is important for applying the results of true-triaxial tests and hence better replicating natural fractured systems.

Physical Interpretation of Laboratory Friction Laws in the Context of Damage Physics

NASA Astrophysics Data System (ADS)

Rundle, J. B.; Tiampo, K. F.; Martins, J. S.; Klein, W.

2002-12-01

Frictional on sliding surfaces is ultimately related to processes of surface damage, and can be understood in the context of the physics of dynamical threshold systems. Threshold systems are known to be some of the most important nonlinear, self-organizing systems in nature, including networks of earthquake faults, neural networks, superconductors and semiconductors, and the World Wide Web, as well as political, social, and ecological systems. All of these systems have dynamics that are strongly correlated in space and time, and all typically display a multiplicity of spatial and temporal scales. Here we discuss the physics of self-organization and damage in earthquake threshold systems at the "microscopic" laboratory scale, in which consideration of results from simulations leads to dynamical equations that can be used to derive results obtained from sliding friction experiments, specifically, the empirical "rate-and-state" friction equations of Ruina. Paradoxically, in all of these dissipative systems, long-range interactions induce the existence of locally ergodic dynamics, even though the dissipation of energy is involved. The existence of dissipative effects leads to the appearance of a "leaky threshold" dynamics, equivalent to a new scaling field that controls the size of nucleation events relative to the size of the background fluctuations. The corresponding appearance of a mean field spinodal leads to a general coarse-grained equation, which expresses the balance between rate of stress supplied, and rate of stress dissipated in the processes leading to surface damage. We can use ideas from thermodynamics and kinetics of phase transitions to develop the exact form of the rate-and-state equations, giving clear physical meaning to all terms and variables. Ultimately, the self-organizing dynamics arise from the appearance of an energy landscape in these systems, which in turn arises from the strong correlations and mean field nature of the physics.

Comparison of equilibrium ohmic and nonequilibrium swarm models for monitoring conduction electron evolution in high-altitude EMP calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pusateri, Elise N.; Morris, Heidi E.; Nelson, Eric

2016-10-17

Here, atmospheric electromagnetic pulse (EMP) events are important physical phenomena that occur through both man-made and natural processes. Radiation-induced currents and voltages in EMP can couple with electrical systems, such as those found in satellites, and cause significant damage. Due to the disruptive nature of EMP, it is important to accurately predict EMP evolution and propagation with computational models. CHAP-LA (Compton High Altitude Pulse-Los Alamos) is a state-of-the-art EMP code that solves Maxwell inline images equations for gamma source-induced electromagnetic fields in the atmosphere. In EMP, low-energy, conduction electrons constitute a conduction current that limits the EMP by opposing themore » Compton current. CHAP-LA calculates the conduction current using an equilibrium ohmic model. The equilibrium model works well at low altitudes, where the electron energy equilibration time is short compared to the rise time or duration of the EMP. At high altitudes, the equilibration time increases beyond the EMP rise time and the predicted equilibrium ionization rate becomes very large. The ohmic model predicts an unphysically large production of conduction electrons which prematurely and abruptly shorts the EMP in the simulation code. An electron swarm model, which implicitly accounts for the time evolution of the conduction electron energy distribution, can be used to overcome the limitations exhibited by the equilibrium ohmic model. We have developed and validated an electron swarm model previously in Pusateri et al. (2015). Here we demonstrate EMP damping behavior caused by the ohmic model at high altitudes and show improvements on high-altitude, upward EMP modeling obtained by integrating a swarm model into CHAP-LA.« less

Comparison of equilibrium ohmic and nonequilibrium swarm models for monitoring conduction electron evolution in high-altitude EMP calculations

NASA Astrophysics Data System (ADS)

Pusateri, Elise N.; Morris, Heidi E.; Nelson, Eric; Ji, Wei

2016-10-01

Atmospheric electromagnetic pulse (EMP) events are important physical phenomena that occur through both man-made and natural processes. Radiation-induced currents and voltages in EMP can couple with electrical systems, such as those found in satellites, and cause significant damage. Due to the disruptive nature of EMP, it is important to accurately predict EMP evolution and propagation with computational models. CHAP-LA (Compton High Altitude Pulse-Los Alamos) is a state-of-the-art EMP code that solves Maxwell's equations for gamma source-induced electromagnetic fields in the atmosphere. In EMP, low-energy, conduction electrons constitute a conduction current that limits the EMP by opposing the Compton current. CHAP-LA calculates the conduction current using an equilibrium ohmic model. The equilibrium model works well at low altitudes, where the electron energy equilibration time is short compared to the rise time or duration of the EMP. At high altitudes, the equilibration time increases beyond the EMP rise time and the predicted equilibrium ionization rate becomes very large. The ohmic model predicts an unphysically large production of conduction electrons which prematurely and abruptly shorts the EMP in the simulation code. An electron swarm model, which implicitly accounts for the time evolution of the conduction electron energy distribution, can be used to overcome the limitations exhibited by the equilibrium ohmic model. We have developed and validated an electron swarm model previously in Pusateri et al. (2015). Here we demonstrate EMP damping behavior caused by the ohmic model at high altitudes and show improvements on high-altitude, upward EMP modeling obtained by integrating a swarm model into CHAP-LA.