Discontinuous Evolution Research Articles

Tunable drag drop via flow-induced snap-through in origami

We leverage the snap-through response of a bistable origami mechanism to induce a discontinuous evolution of drag with flow speed. The transition between equilibrium states is actuated passively by airflow, and we demonstrate that large shape reconfiguration over a small increment of flow velocity leads to a pronounced and sudden drop in drag. Moreover, we show that systematically varying the geometrical and mechanical properties of the origami unit enables the tuning of this drag discontinuity and the critical speed and loading at which it occurs. Experimental results are supported by a theoretical aeroelastic model, which further guides inverse design to identify the combination of structural origami parameters for targeted drag collapse. This approach sheds light on harnessing origami-inspired mechanisms for efficient passive drag control in a fluid environment, applicable for load alleviation or situations requiring swift transitions in aerodynamic performances.

Space-time CutFEM on overlapping meshes II: simple discontinuous mesh evolution

We present a cut finite element method for the heat equation on two overlapping meshes: a stationary background mesh and an overlapping mesh that evolves inside/“on top” of it. Here the overlapping mesh is prescribed by a simple discontinuous evolution, meaning that its location, size, and shape as functions of time are discontinuous and piecewise constant. For the discrete function space, we use continuous Galerkin in space and discontinuous Galerkin in time, with the addition of a discontinuity on the boundary between the two meshes. The finite element formulation is based on Nitsche’s method. The simple discontinuous mesh evolution results in a space-time discretization with a slabwise product structure between space and time which allows for existing analysis methodologies to be applied with only minor modifications. We follow the analysis methodology presented by Eriksson and Johnson (SIAM J Numer Anal 28(1):43–77, 1991; SIAM J Numer Anal 32(3):706–740, 1995). The greatest modification is the introduction of a Ritz-like “shift operator” that is used to obtain the discrete strong stability needed for the error analysis. The shift operator generalizes the original analysis to some methods for which the discrete subspace at one time does not lie in the space of the stiffness form at the subsequent time. The error analysis consists of an a priori error estimate that is of optimal order with respect to both time step and mesh size. We also present numerical results for a problem in one spatial dimension that verify the analytic error convergence orders.

Correction of the spring-dashpot-slider model

AbstractThe spring-dashpot-slider is a common way to include solid friction for discrete element method simulations of granular matter. However, the most popular model that is currently in use has a number of problems, including the spontaneous creation of energy. The main cause for these problems is the discontinuous evolution of the spring displacement. In this paper, we derive a differential equation for the displacement that yields a continuous time evolution, that fixes the problems of the discontinuous model and is simpler to implement.

Evolution of initial discontinuities in a particular case of two-step initial problem for the defocusing complex modified KdV equation

In this paper, the complete classification of solutions of defocusing complex modified KdV equation with a particular case of two-step initial condition is investigated by the finite-gap integration approach and Whitham modulation theory. The periodic wave solution and corresponding Whitham modulation equations for zero-phase, one-phase, two-phase are found. The self-similar wave structures in each case are composed of different building blocks: the plateau, vacuum, rarefaction wave, dispersive shock wave and two-genus region, which are studied in detail. The results of direct numerical simulations for the defocusing complex modified KdV equation agree well with those of Whitham modulation theory.

RoeNet: Predicting discontinuity of hyperbolic systems from continuous data

AbstractPredicting future discontinuous phenomena that are unobservable from training data sets has long been a challenging problem in scientific machine learning. We introduce a novel paradigm to predict the emergence and evolution of various discontinuities of hyperbolic partial differential equations (PDEs) based on given training data over a short window with limited discontinuity information. Our method is inspired by the classical Roe solver [P. L. Roe, J Comput Phys., vol. 43, 1981], a basic tool for simulating various hyperbolic PDEs in computational physics. By carefully designing the computing primitives, the data flow, and the novel pseudoinverse processing module, we enable our data‐driven predictor to satisfy all the essential mathematical criteria of a Roe solver and hence deliver accurate predictions of hyperbolic PDEs. We demonstrate through various examples that our data‐driven Roe predictor outperforms original human‐designed Roe solver and deep neural networks with weak priors in terms of accuracy and robustness.

An innovative quasi-bond approach to bridge continuity, anisotropic damage and macroscopic fracture of solids and structures

Spontaneous formation and evolution of discontinuities in solid media still poses one of the significant challenges in solid mechanics and computational mechanics. To facilitate numerical modeling, a new model called herein ‘quasi-bond’ model is proposed, which redefines the form of local interaction between material particles. Unlike traditional discrete methods that require direct connections between material particles, in this quasi-bond method, only one end of each bond is actually connected to a material particle, rendering great flexibility in describing bond distribution and anisotropic damage by bond breakage. Homogenization of solid body can be performed by an integral over quasi-bonds, while the process of crack nucleation, propagation and coalescence to form fracture is simulated through bond breakage. Especially, the relationship between material elastic constants and bond stiffness parameter is established in both two- and three-dimensional contexts. Furthermore, a smoothed strain-based fracture description is proposed with the ability of eliminating particle density/distribution dependence problems. Finally, several benchmark tests are conducted to demonstrate the efficiency and accuracy of the proposed approach in solving elasticity and fracture problems.

On the detection of nonlinear normal mode-related isolated branches of periodic solutions for high-dimensional nonlinear mechanical systems with frictionless contact interfaces

This contribution introduces a methodology for the detection of isolated branches of periodic solutions to the nonlinear mechanical equation of motion for systems featuring frictionless contact interfaces. This methodology relies on a harmonic balance method-based solving procedure combined with the application of the Melnikov energy principle. It is able to predict the location of isolated branches of solutions in the vicinity of families of autonomous periodic solutions, namely nonlinear normal modes. The methodology is first applied on a two-degree-of-freedom phenomenological system in order to illustrate its relevance and accuracy. In particular, for this academic application, the proposed methodology yields an understanding of the discontinuous evolution of the first nonlinear resonance frequency as the forcing amplitude increases. Isolated branches of solutions featuring high amplitudes of vibration are detected far beyond nonlinear resonance frequencies obtained with a typical application of the harmonic balance method coupled with an arc-length continuation algorithm. Demonstration of the applicability of the proposed methodology to high-dimensional industrial finite element models is made with the nonlinear vibration analysis of a transsonic compressor blade, NASA rotor 37, subjected to an harmonic loading and blade-tip/casing structural contacts. The proposed methodology yields numerous isolated branches of solutions, which relevance is assessed by means of time integration simulations. In the end, the presented results underline that typical continuation algorithms may yield a significant underestimation of nonlinear resonance frequencies.

Investigation of slip characteristics and contact area evolution of rough rock discontinuity under impact shear load

AbstractThis study investigated theshear slip behavior and contact area evolution of rough rock discontinuities with impact shear load. First, the dynamic impact shear numerical simulation of rock samples with real rough rock discontinuities was carried out. Subsequently, the variety rule of slip displacement and velocity of rock discontinuity with impact velocity, confining stress and joint roughness coefficient (JRC) was studied. The variation in contact area and shear stress of rock discontinuity during shear was assessed. Finally, the effect of frictional force on the slip displacement and velocity and the effect of contact area and frictional force on the shear stress distribution were analyzed. The results showed that the slip displacement, velocity and shear stress are rate dependent. The slip displacement and velocity increase as the impact velocity increases and decrease as the confining stress and JRC increase. The contact area and shear stress distribution range of rock discontinuities decrease slightly as the impact velocity increases but increase significantly as the confining stress and JRC increase. The shear stress distribution range of rock discontinuities closely correlates with the contact area. The shear stress in the non‐contact area is zero. The shear stress distribution range increases as the contact area increases. The average shear stress increases as the frictional force increases. Moreover, the slip displacement and velocity of rock discontinuities decrease linearly as the frictional force increases.

Continuous evolution families

Recently in relation to the theory of non-commutative probability, the notion of evolution family { ω s , t } s ≤ t \{\omega _{s,t}\}_{s \le t} is generalized assuming only continuity in parameters, namely ( s , t ) ↦ ω s , t (s,t) \mapsto \omega _{s,t} is continuous with respect to locally uniform convergence on a planar domain. In this article we present various equivalence conditions to the continuous evolution families concerned with the left and right parameters. We also provide an example of a discontinuous evolution family in the last section.

On discontinuous stress and strain evolutions in machining of dissimilar laser cladded workpiece

During subsequent machining of laser cladded workpiece, the stress transferred in depth direction is different with conventional cast workpiece due to the geometrical discontinuity, resulting in the stress difference and strain discontinuity at the interface between the cladding layer and substrate. Elastic and plastic deformation will occur in the cladding layer and substrate, respectively, which ultimately reduces the service life of the cladded workpiece. In this study, the stress and strain evolution in subsequent machining of laser cladded workpiece was investigated using an orthogonal cutting model by finite element method. A dimensionless thickness ratio between uncut chip thickness and cladding layer thickness was set and the maximum thickness ratio without equivalent plastic strain (PEEQ) discontinuity at the interface was determined. In addition, the results indicated that the maximum thickness ratio first decreased and then increased with the increase of cutting speed, while increases with the increase of the yield strength of substrate. The synergetic effects of thickness ratio, cutting speed and yield strength of substrate on the strain discontinuity at the interface were also investigated based on Taguchi method. The optimal combination of parameters is determined based on the regression model and divided into areas with considering machining efficiency as well. The map of cutting configurations facilitates the selection of proper machining parameters in order to estimate the strain discontinuity in machining laser cladded workpiece, ensuring a better service life of the workpiece.

Effects of a Late Gravitational Transition on Gravitational Waves and Anticipated Constraints

We investigate the evolution of gravitational waves through discontinuous evolution (transition) of the Hubble expansion rate H(z) at a sudden cosmological singularity, which may be due to a transition of the value of the gravitational constant. We find the evolution of the scale factor and the gravitational wave waveform through the singularity by imposing the proper boundary conditions. We also use existing cosmological data and mock data of future gravitational wave experiments (the ET) to impose current and anticipated constraints on the magnitude of such a transition. We show that mock data of the Einstein Telescope can reduce the uncertainties by up to a factor of three depending on the cosmological parameter considered.

Strongly correlated exciton-polarons in twisted homobilayer heterostructures

We consider dressing of excitonic properties by strongly correlated electrons in gate-controlled twisted homobilayer heterostructures. The combined effect of the moir\'e potential and the Coulomb interaction supports the formation of different strongly correlated phases depending on the filling, including charge-ordered metals or incompressible insulators at integer occupation. The coupling between excitons and electrons results in a splitting of the excitonic resonance into an attractive and a repulsive polaron peak. Analyzing the properties of the exciton-polarons across the different phases of the system, we reveal a discontinuous evolution of the spectrum with the formation of a double-peak structure in the repulsive polaron branch. The double-peak structure emerges for noninteger fillings and it is controlled by the energy separation between the quasiparticle states close to the Fermi level and the high-energy doublons excitations. Our results demonstrate that exciton-polarons carry a clear hallmark of the electronic correlations and, thus, provide a direct signature of the formation of correlation-driven insulators in gate-controlled heterostructures.

Relationship between fissility, composition, rock fabric and reservoir properties in Vaca Muerta Formation (Neuquén Basin, Argentina): from outcrop to subsurface core data

The fissility is the ability of some rocks to split along relatively smooth surfaces parallel to the bedding. This property observed mostly in fine-grained rocks is particularly expressed in outcrops, where rocks are subjected to weathering processes. Most authors associate the fissility to the abundance of clay minerals and their orientation parallel to the bedding. The horizontal fabric can be promoted by depositional conditions such as sediment composition, quantity of total organic carbon content (TOC) and depositional mechanisms, giving rise to a primary fissility. Alternatively, the alignment of platy minerals can be linked to the burial history of the rock, by processes such as mechanical compaction or secondary mineral growth, resulting in a secondary fissility. The present study aims to identify the main controls of fissility development at the micro- and macroscopic scale in rocks of the Vaca Muerta Formation exposed in the Cerro Mulichinco area and in a 121-meter-long core extracted from a well within the Neuquén Basin. In outcrops, fissility is related to fine-grained laminated facies with low carbonate content, revealing the strong control exerted by lithology. The TOC measurements allow establishing a positive correlation between organic matter content and fissility intensity. Moreover, the analysis of the transgressive-regressive cycles shows that fissility is higher around the maximum flooding surfaces. Regarding their mechanical characteristics, the different interfaces observed in core are classified into first and second-order, the last one including fissility planes. Some of these interfaces evolve from potential (partially open) to effective (totally open) discontinuities in response to changes of stress conditions during the core extraction and due to the stress relaxation through time: weeks (T1), months (T2) and years (T3) after extraction. The time evolution of the effective core discontinuities points out rock intervals that are variably broken and core segments that remain intact. The Drying Alcohol Discontinuities (DAD) methodology reveals potential discontinuities within apparently intact core segments. By using this technique, a 4-class index is established as a proxy for fissility degree. When integrated with geological, petrophysical and geomechanical data, this index enables characterizing the main mechanisms controlling rock fissility that express through discontinuities promoting the loss of competence of a rock. Consequently, this mechanical property is considered to influence the efficiency of hydraulic fracture in shale reservoir completion.

Investigations on the intrinsic and template-dependent transformations of AlPO4-11 molecular sieve under high pressure

In this study, aluminophosphate molecular sieve AlPO4-11, with one-dimensional elliptical channels, was investigated under high pressure in non-penetrating silicone oil by X-ray powder diffraction, infrared spectroscopy and theoretical simulation, focusing on its intrinsic and template-modified mechanical behaviors. Two distinct compressible regimes were observed for both the calcined and as-synthesized AlPO4-11 frameworks before pressure-induced amorphization (PIA). The channel cross-section in the calcined AlPO4-11 framework showed an obvious increase in the ellipticity during this process. The framework structure began to lose crystallinity at approximately 2–3 GPa and underwent significant amorphization at 6.6 GPa. PIA was mainly induced via the destruction of the constructed species along the periodic crystallographic planes which are parallel to the channel axis. The bulk moduli showed that this empty framework was rather soft in these regimes. For the as-synthesized AlPO4-11 framework, the mechanical stability of the channels was markedly improved by the template molecules. A different elliptic deformation of the cross-section with a reduced contractility in the minor axis direction was presented. Discontinuous volume evolution occurs at 3–4 GPa and significant amorphization was postponed to 13.7 GPa. The as-synthesized AlPO4-11 was stiffer than calcined AlPO4-11 and showed a soft to hard transformation due to the strengthened host-guest interaction upon compression. Moreover, infrared spectra indirectly confirmed the structural collapses by detecting the vibrational characteristics of the embedded template molecules. The present results provided a comparative and basic knowledge of the intrinsic and extrinsic stability, compressibility, channel deformation and collapse of the AlPO4-11 framework under high pressure. This study emphasized the importance of guest molecules in modifying the mechanical behaviors of zeolites and resisting framework collapse.

Experimental Study of Energy Evolution at a Discontinuity in Rock under Cyclic Loading and Unloading.

Energy is often dissipated and released in the process of rock deformation and failure. To study the energy evolution of rock discontinuities under cyclic loading and unloading, cement mortar was used as rock material and a CSS-1950 rock biaxial rheological testing machine was used to conduct graded cyclic loading and unloading tests on Barton’s standard profile line discontinuities with different joint roughness coefficients (JRCs). According to the deformation characteristics of the rock discontinuity sample, the change of internal energy is calculated and analyzed. The experimental results show that under the same cyclic stress, the samples harden with the increase in the number of cycles. With the increase of cyclic stress, the dissipated energy density of each stage gradually exceeds the elastic energy density and occupies a dominant position and increases rapidly as failure becomes imminent. In the process of increasing the shear stress step-by-step, the elastic energy ratio shows a downward trend, but the dissipated energy is contrary to it. The energy dissipation ratio can be used to characterize the internal damage of the sample under load. In the initial stage of fractional loading, the sample is in the extrusion compaction stage, and the energy dissipation ratio remains quasi-constant; then the fracture develops steadily, the damage inside the sample intensifies, and the energy dissipation ratio increases linearly (albeit at a low rate). When the energy storage limit is reached, the growth rate of energy dissipation ratio increases and changes when the stress level reaches a certain threshold. The increase of the roughness of rock discontinuity samples will improve their energy storage capacity to a certain extent.

Evolution of weak shock waves in non-ideal magnetogasdynamics

Abstract In this article, a study concerning the growth and decay of weak shock waves in non-ideal magnetogasdynamic regime has been performed. One-dimensional plane and cylindrical symmetries are assumed. The flow medium is considered as a perfectly conducting non-ideal gas permeated with either axial or azimuthal magnetic field. The Generalized Wavefront Expansion (GWE) method used in this work provides a system of coupled non-linear transport equations which completely describe the evolution of weak shocks and first order discontinuities induced behind it. The solution obtained during the process agrees with the classical decay laws for weak shocks. A general criterion for steepening of compressive waves and flattening of expansion waves has been derived. Further, the effect of geometrical spreading, magnetic field, and non-idealness of the gas on steepening or flattening of waves is discussed and illustrated via figures. Also, a comparison between growth and decay of weak shocks in ideal and non-ideal magnetogasdynamic regimes has been made. It has been observed during the study that all compressive waves evolve into shock regardless of their initial strength, and expansive waves decay and damp out eventually.

Inverted base composition skews and discontinuous mitochondrial genome architecture evolution in the Enoplea (Nematoda)

BackgroundWithin the class Enoplea, the earliest-branching lineages in the phylum Nematoda, the relatively highly conserved ancestral mitochondrial architecture of Trichinellida is in stark contrast to the rapidly evolving architecture of Dorylaimida and Mermithida. To better understand the evolution of mitogenomic architecture in this lineage, we sequenced the mitogenome of a fish parasite Pseudocapillaria tomentosa (Trichinellida: Capillariidae) and compared it to all available enoplean mitogenomes.ResultsP. tomentosa exhibited highly reduced noncoding regions (the largest was 98 bp), and a unique base composition among the Enoplea. We attributed the latter to the inverted GC skew (0.08) in comparison to the ancestral skew in Trichinellidae (-0.43 to -0.37). Capillariidae, Trichuridae and Longidoridae (Dorylaimida) generally exhibited low negative or low positive skews (-0.1 to 0.1), whereas Mermithidae exhibited fully inverted low skews (0 to 0.05). This is indicative of inversions in the strand replication order or otherwise disrupted replication mechanism in the lineages with reduced/inverted skews. Among the Trichinellida, Trichinellidae and Trichuridae have almost perfectly conserved architecture, whereas Capillariidae exhibit multiple rearrangements of tRNA genes. In contrast, Mermithidae (Mermithida) and Longidoridae (Dorylaimida) exhibit almost no similarity to the ancestral architecture.ConclusionsLongidoridae exhibited more rearranged mitogenomic architecture than the hypervariable Mermithidae. Similar to the Chromadorea, the evolution of mitochondrial architecture in enoplean nematodes exhibits a strong discontinuity: lineages possessing a mostly conserved architecture over tens of millions of years are interspersed with lineages exhibiting architectural hypervariability. As Longidoridae also have some of the smallest metazoan mitochondrial genomes, they contradict the prediction that compact mitogenomes should be structurally stable. Lineages exhibiting inverted skews appear to represent the intermediate phase between the Trichinellidae (ancestral) and fully derived skews in Chromadorean mitogenomes (GC skews = 0.18 to 0.64). Multiple lines of evidence (CAT-GTR analysis in our study, a majority of previous mitogenomic results, and skew disruption scenarios) support the Dorylaimia split into two sister-clades: Dorylaimida + Mermithida and Trichinellida. However, skew inversions produce strong base composition biases, which can hamper phylogenetic and other evolutionary studies, so enoplean mitogenomes have to be used with utmost care in evolutionary studies.

Impact assessment of the West African monsoon on convective precipitations over the far north region of Cameroon

Squall lines observed over the sahelo-sudanese regions are responsible for most of the annual rainfall recorded in these regions. They originate from the development of convective processes embedded in the Mesoscale Convective Systems (MCS). The impact assessment of the West African Monsoon (WAM) on the development of squall lines in the sahelo-sudanese regions, particularly the far north region of Cameroon is studied. In this study, the Tropical Rainfall Measuring Mission data (TRMM 3A12 and 3B43) and ERA5 reanalysis data from 1998 to 2008 have been used. The technique used is based on the use of the Climate Data Operator (CDO) software and the NCAR command language (NCL). Analysis of these data shows that the seasonal distribution of winds from the saharan heat-low and the Saint Helena high is the dominant atmospheric dynamics associated with the disturbances behind the development of squall lines. This distribution makes it possible to specifically draw up the evolution of the InterTropical Discontinuity (ITD) on the African continent, and thus, highlight the contribution of the WAM on precipitation in the far north region of Cameroon. This study is performed to contribute to the prediction of hydro-meteorological phenomena to improve disaster risks management associated with floods and landslides in this region, the most vulnerable in Cameroon.

Trigonometric shock waves in the Kaup–Boussinesq system

We consider the modulationally stable version of the Kaup-Boussinesq system which models propagation of nonlinear waves in various physical systems. It is shown that the Whitham modulation equations for this model have a new type of solutions which describe trigonometric shock waves. In the Gurevich-Pitaevskii problem of evolution of an initial discontinuity, these solutions correspond to a non-zero wave excitation on one of the sides of the discontinuity. Our analytical results are confirmed by numerical calculations.

Modeling Discontinuous Cultural Evolution: The Impact of Cross-Domain Transfer.

This paper uses autocatalytic networks to model discontinuous cultural transitions involving cross-domain transfer, using as an illustrative example, artworks inspired by the oldest-known uncontested example of figurative art: the carving of the Hohlenstein-Stadel Löwenmensch, or lion-human. Autocatalytic networks provide a general modeling setting in which nodes are not just passive transmitters of activation; they actively galvanize, or “catalyze” the synthesis of novel (“foodset-derived”) nodes from existing ones (the “foodset.”) This makes them uniquely suited to model how new structure grows out of earlier structure, i.e., cumulative, generative network growth. They have been used to model the origin and early evolution of biological life, and the emergence of cognitive structures capable of undergoing cultural evolution. We conducted a study in which six individual creators and one group generated music, prose, poetry, and visual art inspired by the Hohlenstein-Stadel Löwenmensch, and answered questions about the process. The data revealed four through-lines by which they expressed the Löwenmensch in an alternative art form: (1) lion-human hybrid, (2) subtracting from the whole to reveal the form within, (3) deterioration, and (4) waiting to be found with a story to tell. Autocatalytic networks were used to model how these four spontaneously derived through-lines form a cultural lineage from Löwenmensch to artist to audience. We used the resulting data from three creators to model the cross-domain transfer from inspirational source (sculpted figurine) to creative product (music, poetry, prose, visual art). These four spontaneously-generated threads of cultural continuity formed the backbone of this Löwenmensch-inspired cultural lineage, enabling culture to evolve even in the face of discontinuity at the level conventional categories or domains. We know of no other theory of cultural evolution that accommodates cross-domain transfer or other forms of discontinuity. The approach paves the way for a broad scientific framework for the origins of evolutionary processes.