Discontinuous Evolution Research Articles

A COMPARISON BETWEEN THE NMM AND THE XFEM IN DISCONTINUITY MODELING

Discontinuities such as voids, cracks, material interfaces, and joints widely exist in nature. Conventional finite element method (FEM) requires the finite element mesh to coincide with the discontinuities, which often complicates the meshing task. When evolution of discontinuities are necessary, remeshing is inevitable, which makes the simulation tedious and time-consuming. In order to overcome such inconveniences, the extended finite element method (XFEM) and the generalized finite element method (GFEM) were developed by incorporating special functions into the standard finite element approximation space based on partition of unity. The finite element mesh is allowed to be totally independent of the discontinuities and remeshing is totally avoided for discontinuity evolution. The numerical manifold method (NMM) can also be viewed as an extension or generalization to the conventional FEM. Different from the XFEM/GFEM, the approximation in the NMM is based on covers. The NMM models discontinuities by its dual cover system. In this paper, a detailed comparison between the NMM and the XFEM in discontinuity modeling is presented. Their advantages and disadvantages are pointed out. How the dual cover system in the NMM favors the complex crack modeling is emphasized. Potential extensions to the XFEM and the NMM are suggested.

Numerical integration of elasto-plasticity coupled to damage using a diagonal implicit Runge–Kutta integration scheme

This article is concerned with the numerical integration of finite strain continuum damage models. The numerical sensitivity of two damage evolution laws and two numerical integration schemes are investigated. The two damage models differ in that one of the models includes a threshold such that the damage evolution is suppressed until a certain effective plastic strain is reached. The classical integration scheme based on the implicit Euler scheme is found to suffer from a severe step-length dependence. An alternative integration scheme based on a diagonal implicit Runge--Kutta scheme originally proposed by Ellsiepen ( 1999 ) is investigated. The diagonal implicit Runge--Kutta scheme is applied to the balance of momentum as well as the constitutive evolution equations. When applied to finite strain multiplicative plasticity, the diagonal implicit Runge--Kutta scheme destroys the plastic incompressibility of the underlying continuum evolution laws. Here, the evolution laws are modified such that the incompressibility of the plastic deformation is preserved approximately. The presented numerical examples reveal that a significant increase in accuracy can be obtained at virtually no cost using the diagonal implicit Runge--Kutta scheme. It is also shown that for the model including a discontinuous evolution law, the superiority of the diagonal implicit Runge--Kutta scheme over the implicit Euler scheme is reduced.

Environmental Heterogeneity and Phenotypic Divergence: Can Heritable Epigenetic Variation Aid Speciation?

The dualism of genetic predisposition and environmental influences, their interactions, and respective roles in shaping the phenotype have been a hot topic in biological sciences for more than two centuries. Heritable epigenetic variation mediates between relatively slowly accumulating mutations in the DNA sequence and ephemeral adaptive responses to stress, thereby providing mechanisms for achieving stable, but potentially rapidly evolving phenotypic diversity as a response to environmental stimuli. This suggests that heritable epigenetic signals can play an important role in evolutionary processes, but so far this hypothesis has not been rigorously tested. A promising new area of research focuses on the interaction between the different molecular levels that produce phenotypic variation in wild, closely-related taxa that lack genome-wide genetic differentiation. By pinpointing specific adaptive traits and investigating the mechanisms responsible for phenotypic differentiation, such study systems could allow profound insights into the role of epigenetics in the evolution and stabilization of phenotypic discontinuities, and could add to our understanding of adaptive strategies to diverse environmental conditions and their dynamics.

Hydrocarbon-Generation in Cambrian-Silurian High- to Over- Mature Source Rocks, Middle and Upper Yangtze Region, China

Two main Cambrian-Silurian high- to over-mature hydrocarbon source rocks occur in the Middle and Upper Yangtze region: the Lower Cambrian Niutitang Formation (mostly shale), and the Lower Silurian Longmaxi and Upper Ordovician Wufeng formations (mostly graptolite shale). Due to several complicated tectonic events occurred in the study area, the source rocks experienced inhomogeneous uplift, deformation, and burial, resulting in discontinuous and episodic hydrocarbon generation evolution. Based on a detailed study of the tectonic burial history and an analysis of the current degree of thermal evolution of the source rocks, this paper studied the burial history, the thermal history, and the hydrocarbon-generation history of the Cambrian-Silurian source rocks. It used basin modeling technology and thermal simulation tests on source rocks to reveal the process and the regional regularity of the hydrocarbon-generation evolution, and to expound the tectonic phases and the time-spatial distribution of hydrocarbon generation. It shows that the region from western Hubei to eastern Chongqing is the major source area of Lower Cambrian rocks, and the region from southeastern Sichuan to central Guizhou is the major source area of Lower Silurian rocks. Reconstruction of hydrocarbon-generation history allows simulated estimation of the remaining hydrocarbon-generation potential of the high-over mature marine source rocks.

Measuring BAO and non-Gaussianity via QSO clustering

Our goals are (i) to search for BAO and large-scale structure in current QSO survey data and (ii) to use these and simulation/forecast results to assess the science case for a new, >10x larger, QSO survey. We first combine the SDSS, 2QZ and 2SLAQ surveys to form a survey of ~60000 QSOs. We find a hint of a peak in the QSO 2-point correlation function, xi(s), at the same scale (~105h^-1 Mpc) as detected by Eisenstein et al (2005) in their sample of DR5 LRGs but only at low statistical significance. We then compare these data with QSO mock catalogues from the Hubble Volume simulation used by Hoyle et al (2002) and find that both routes give statistical error estimates that are consistent at ~100h^-1 Mpc scales. Mock catalogues are then used to estimate the nominal survey size needed for a 3-4 sigma detection of the BAO peak. We find that a redshift survey of ~250000 z<2.2 QSOs is required over ~3000 deg^2. This is further confirmed by static log-normal simulations where the BAO are clearly detectable in the QSO power spectrum and correlation function. The nominal survey would on its own produce the first detection of, for example, discontinuous dark energy evolution in the so far uncharted 1<z<2.2 redshift range. A survey with ~50% higher QSO sky densities and 50% bigger area will give an ~6sigma BAO detection, leading to an error ~60% of the size of the BOSS error on the dark energy evolution parameter, w_a. Another important aim for a QSO survey is to place new limits on primordial non-Gaussianity at large scales, testing tentative evidence we have found for the evolution of the linear form of the combined QSO xi(s) at z~1.6. Such a QSO survey will also determine the gravitational growth rate at z~1.6 via z-space distortions, allow lensing tomography via QSO magnification bias while also measuring the exact luminosity dependence of small-scale QSO clustering.

IS THERE A HIDDEN HOLE IN TYPE Ia SUPERNOVA REMNANTS?

In this paper we report on the bulk features of the hole carved by the companion star in the material ejected during a Type Ia supernova explosion. In particular we are interested in the long term evolution of the hole as well as in its fingerprint in the geometry of the supernova remnant after several centuries of evolution, which is a hot topic in current Type Iasupernovae studies. We use an axisymmetric smoothed particle hydrodynamics code to characterize the geometric properties of the supernova remnant resulting from the interaction of this ejected material with the ambient medium. Our aim is to use supernova remnant observations to constrain the single degenerate scenario for Type Ia supernova progenitors. Our simulations show that the hole will remain open during centuries, although its partial or total closure at later times due to hydrodynamic instabilities is not excluded. Close to the edge of the hole, the Rayleigh-Taylor instability grows faster, leading to plumes that approach the edge of the forward shock. We also discuss other geometrical properties of the simulations, like the evolution of the contact discontinuity.

Muon spin relaxation and susceptibility measurements of an itinerant-electron system Sr1−xCaxRuO3: Quantum evolution from ferromagnet to paramagnet

Muon spin relaxation ($\ensuremath{\mu}$SR) and magnetic susceptibility measurements have been performed in the itinerant-electron magnet Sr${}_{1\ensuremath{-}x}$Ca${}_{x}$RuO${}_{3}$, with $x=$ 0.0, 0.3, 0.5, 0.65, 0.7, 0.75, 0.8, 0.9, and 1.0. SrRuO${}_{3}$ is a ferromagnet with the critical temperature ${T}_{c}\ensuremath{\sim}160$ K. Upon (Sr, Ca) substitution, ${T}_{c}$ decreases monotonically with increasing Ca concentration $x$ and the ferromagnetic order disappears around $x=$ 0.7. Very weak static magnetism is observed in the $x=$ 0.75 and 0.8 systems, while the $x=$ 0.9 and 1.0 systems remain paramagnetic in their full volume. Phase separation between volumes with and without static magnetism was observed in the $x=$ 0.65, 0.7, 0.75, and 0.8 systems, near the magnetic crossover around $x=$ 0.7. In this concentration region, $\ensuremath{\mu}$SR measurements revealed discontinuous evolution of magnetic properties in contrast to magnetization measurements, which exhibit seemingly continuous evolution. Unlike the volume-integrated magnetization measurements, $\ensuremath{\mu}$SR can separate the effects of the ordered moment size and the volume fraction of magnetically ordered regions. The muon spin relaxation rate $1/{T}_{1}$ exhibits critical slowing down of spin fluctuations near ${T}_{c}$ in the ferromagnetic systems with $x=$ 0.0--0.65, consistent with the behavior expected in the self-consistent renormalization theory of itinerant electron ferromagnets. The lack of maximum of $1/{T}_{1}$ in the $x=$ 0.7 system indicates the disappearance of critical slowing down. These results demonstrate a first-order quantum evolution in the ferromagnet to paramagnet crossover near $x=$ 0.7.

Flatfishes, Turtles, and Bolyerine Snakes: Evolution by Small Steps or Large, or Both?

Step size in evolution is rapidly becoming a major subject of interest to biologists. Traditionally, small changes alone were seen as significant in evolution, and any large differences between an ancestor and its descendant could be explained entirely by the accumulation of many small steps. Whether the evolution of major adaptations is mainly a matter of amassing such small increments of change, or if a significant proportion occurs through the inclusion of one or more large steps, is vital to the understanding of how evolution works. This paper begins by examining four “classic” examples of animals—flatfishes, turtles, bolyerine snakes, and gastropod molluscs—each of which has seemed difficult to interpret as resulting from a continuous series of tiny increments. Recently, however, arguments have appeared to contradict those views, and to propose instead that each of these animal groups arose through continuous adaptive modifications. While some of these arguments are more plausible than others, the view of the present author is that in none of them is there convincing evidence to conclude that the groups arose solely through gradual changes. More specifically, there is no basis to reject an evolutionary origin of the major traits in each group that included at least one principal inovation, occurring in a large, discontinuous step, preceded and followed by relatively small, more gradual changes. The broader question of how discontinuous evolution may occur is addressed through several means. These include considerations of epigenetic (sensu Waddington) development, comparative embryology, population genetics, and other approaches. Overall the phenomenon of adaptive accommodation is seen as of major importance, and its implications for ameliorating possible deleterious attributes of novel phenotypes are discussed. In the course of these analyses the doctrine that all adaptive evolution is driven by external environmental change is reviewed. It is suggested that while small adaptive changes are often closely related to shifts in specific environmental facets, the modifications associated with more major adaptations may be less so.

Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution

Cam-Clay plasticity is a well-established model for the description of the mechanics of fine grained soils. As solutions can develop discontinuities in time, a weak notion of solution, in terms of a rescaled time s, has been proposed in Dal Maso, DeSimone and Solombrino (Calc Var Partial Equ 40:125–181, 2011) to give a meaning to this discontinuous evolution. In this paper we first prove that this rescaled evolution satisfies the flow-rule for the rate of plastic strain, in a suitable measure-theoretical sense. In the second part of the paper we consider the behavior of the evolution in terms of the original time variable t. We prove that the unrescaled solution satisfies an energy-dissipation balance and an evolution law for the internal variable, which can be expressed in terms of integrals depending only on the original time. Both these integral identities contain terms concentrated on the jump times, whose size can only be determined by looking at the rescaled formulation.

Weak first-order quantum phase transition in the spin-tetrahedron system Cu2Te2O5Br2without lattice contributions

Under pressure the spin tetrahedron system Cu${}_{2}$Te${}_{2}$O${}_{5}$Br${}_{2}$ shows a softening of the collective magnetic mode whereas the energy of local spin-exchange processes increases. This apparent contradiction is due to the system's proximity to a quantum critical point induced by competing interactions that effectively decouple the tetrahedra. The high-pressure state is therefore nonmagnetic and dominated by valence bond excitations. Anomalies in the frequency and the intensity of magnetic Raman scattering are evidence for a weakly discontinuous evolution of the quantum critical state. In contrast, structural parameters as well as optical phonon modes evolve continuously with pressure without any sign for discontinuous criticality. No new low-energy excitations are observed. In contrast, the expected fingerprints of the spin-liquid phase are broadened due to Dzyaloshinskii-Moriya interactions.

Inferences on pathogenic fungus population structures from microsatellite data: new insights from spatial genetics approaches

Landscape genetics, which combines population genetics, landscape ecology and spatial statistics, has emerged recently as a new discipline that can be used to assess how landscape features or environmental variables can influence gene flow and spatial genetic variation. We applied this approach to the invasive plant pathogenic fungus Mycosphaerella fijiensis, which causes black leaf streak disease of banana. Around 880 isolates were sampled within a 50 × 50 km area located in a fragmented banana production zone in Cameroon that includes several potential physical barriers to gene flow. Two clustering algorithms and a new F(ST) -based procedure were applied to define the number of genetic entities and their spatial domain without a priori assumptions. Two populations were clearly delineated, and the genetic discontinuity appeared sharp but asymmetric. Interestingly, no landscape features matched this genetic discontinuity, and no isolation by distance (IBD) was found within populations. Our results suggest that the genetic structure observed in this production area reflects the recent history of M. fijiensis expansion in Cameroon rather than resulting from contemporary gene flow. Finally, we discuss the influence of the suspected high effective population size for such an organism on (i) the absence of an IBD signal, (ii) the characterization of contemporary gene-flow events through assignation methods of analysis and (iii) the evolution of the genetic discontinuity detected in this study.

Validation of a new automated neonatal seizure detection system: A clinician’s perspective

Objective To validate an improved automated electroencephalography (EEG)-based neonatal seizure detection algorithm (NeoGuard) in an independent data set. Methods EEG background was classified into eight grades based on the evolution of discontinuity and presence of sleep–wake cycles. Patients were further sub-classified into two groups; gpI: mild to moderate (grades 1–5) and gpII: severe (grades 6–8) EEG background abnormalities. Seizures were categorised as definite and dubious. Seizure characteristics were compared between gpI and gpII. The algorithm was tested on 756 h of EEG data from 24 consecutive neonates (median 25 h per patient) with encephalopathy and recorded seizures during continuous monitoring (cEEG). No selection was made regarding the quality of EEG or presence of artefacts. Results Seizure amplitudes significantly decreased with worsening EEG background. Seizures were detected with a total sensitivity of 61.9% (1285/2077). The detected seizure burden was 66,244/97,574 s (67.9%). Sensitivity per patient was 65.9%, with a mean positive predictive value (PPV) of 73.7%. After excluding four patients with severely abnormal EEG background, and predominantly having dubious seizures, the algorithm showed a median sensitivity per patient of 86.9%, PPV of 89.5% and false positive rate of 0.28 h −1. Sensitivity tended to be better for patients in gpI. Conclusions The algorithm detects neonatal seizures well, has a good PPV and is suited for cEEG monitoring. Changes in electrographic characteristics such as amplitude, duration and rhythmicity in relation to deteriorating EEG background tend to worsen the performance of automated seizure detection. Significance cEEG monitoring is important for detecting seizures in the neonatal intensive care unit (NICU). Our automated algorithm reliably detects neonatal seizures that are likely to be clinically most relevant, as reflected by the associated EEG background abnormality.

Homogenization of coupled heat and moisture transport in masonry structures including interfaces

Homogenization of a simultaneous heat and moisture flow in a masonry wall is presented in this paper. The principle objective is to examine an impact of the assumed imperfect hydraulic contact on the resulting homogenized properties. Such a contact is characterized by a certain mismatching resistance allowing us to represent a discontinuous evolution of temperature and moisture fields across the interface, which is in general attributed to discontinuous capillary pressures caused by different pore size distributions of the adjacent porous materials. In achieving this, two particular laboratory experiments were performed to provide distributions of temperature and relative humidity in a sample of the masonry wall, which in turn served to extract the corresponding jumps and subsequently to obtain the required interface transition parameters by matching numerical predictions and experimental results. The results suggest a low importance of accounting for imperfect hydraulic contact for the derivation of macroscopic homogenized properties. On the other hand, they strongly support the need for a fully coupled multi-scale analysis due to significant dependence of the homogenized properties on actual moisture gradients and corresponding values of both macroscopic temperature and relative humidity.

Extending Spatial Interaction Models with Agents for Understanding Relationships in a Dynamic Retail Market

For many years, effective model‐based representations of the dynamics and evolution of urban spatial structure have proved elusive. While some progress has been made through the deployment of spatial interaction models, these approaches have been limited by the difficulty of representing behavioural mechanisms and processes. In this paper, it is demonstrated that evolutionary models grounded in the principles of spatial interaction are compatible with the more novel approaches of agent‐based modelling. The incorporation of agents provides a much more flexible means for the representation of behavioural mechanisms. The paper illustrates the way in which three more complicated situations can be handled through the fusion of spatial interaction and agent modelling perspectives. These situations comprise discontinuous evolution (in which structural adjustment takes place in discrete steps, and not as a continuously smooth process); nonequilibrium dynamics (in which the underlying system parameters continue to evolve through time); the incorporation of new decision variables (which we illustrate through the addition of land rents into the model). The conclusion of the paper is that the combination of spatial interaction and agent‐based modelling methods provides encouraging prospects for the social simulation of real urban systems.

Evolution is Viral: The Theory of Collective Discontinuous Evolution

Evolution is Viral: The Theory of Collective Discontinuous Evolution

Evolution is Viral: The Theory of Collective Discontinuous Evolution

AbstractHerein will be discussed the problems associated with the origin of species according to Darwinist processes of individual mutations. We will argue that individual mutations cannot be the driving force of species origination. A far more probable explanation is a process of collective mutation that affects numerous individuals near simultaneously akin to an infectious disease. These types of mutations might be precipitated by viruses which would create a discontinuous leap into another species. Such a mechanism also sheds light on the increased rate of evolution observed currently.

On the evolution of weak discontinuities in radiative magnetogasdynamics

A method of wavefront analysis is used to analyze the formation of shock waves in a two-dimensional steady supersonic flow past plane and axisymmetric bodies in radiative magnetogasdynamics. The gas is assumed to be perfectly conducting and to be permeated by a magnetic field orthogonal to the trajectories of the gas particles. The medium is taken to be sufficiently hot for the effects of thermal radiation to be significant, which is treated by the optically thin approximation to the radiative transfer equation. Transport equations, which lead to the determination of the distance at which the first characteristic could intersect with a successive one and also to conditions, which insure that no shock will ever evolve on the wave front, are derived. The effect of upstream flow Mach number and the magnetic field strength on the behavior of the wavefront are examined.

Evolution of weak discontinuities in a non-ideal radiating gas

A method of wavefront analysis is used to study the formation of shock waves in a two-dimensional steady supersonic flow of a non-ideal radiating gas past plane and axisymmetric bodies. The gas is taken to be sufficiently hot for the effect of thermal radiation to be significant, which is, of course, treated by the optically thin approximation to the radiative transfer equation. Transport equations, which lead to the determination of the shock formation distance and also to conditions which insure that no shock will ever evolve on the wavefront, is derived. The influence of the parameter of the non-idealness, upstream flow Mach number in the presence of thermal radiation on the behavior of the wavefront are examined.

Discontinuous quantum evolutions in the presence of closed timelike curves

We consider Deutsch's computational model of a quantum system evolving in a spacetime containing closed timelike curves. Although it is known that this model predicts nonlinear and nonunitary evolutions of the system, we demonstrate that it also gives rise to evolutions which are a discontinuous function of the input state. These discontinuities persist for the most natural modifications of Deutsch's approach.

Evolution of weak discontinuities in shallow water equations

In this paper, we determine the critical time, when a weak discontinuity in the shallow water equations culminates into a bore. Invariance group properties of the governing system of partial differential equations (PDEs), admitting Lie group of point transformations with commuting infinitesimal operators, are presented. Some appropriate canonical variables are characterized that transform equations at hand to an equivalent form, which admits non-constant solutions. The propagation of weak discontinuities is studied in the medium characterized by the particular solution of the governing system.