Search

In this study, we investigate the diversity of the bifurcations and deformations during evolution of periodic patterns on compressed films bonded to compliant substrates. Three-dimensional finite element analysis is performed assuming that the first bifurcation has either the hexagonal or square (i.e., checkerboard) dimple mode. Step-by-step eigenvalue buckling analysis is performed to explore sequential bifurcations on the bifurcated paths. It is found that at the second bifurcation, a rectangular checkerboard or stripe mode occurs depending not only on the Young's modulus ratio of the film and substrate, but also on the magnitude of the imperfection prescribed by the first bifurcation mode. Different bifurcation modes give a family of herringbone deformation patterns with different dimensions, i.e., the evolutional process is multiple and robust. Further, superposition of the identical modes in symmetric directions elucidates the existence of distinctive patterns cognate with the herringbone pattern, including a variety of experimentally observed patterns.

In this study, we investigate the diversity of the bifurcations and deformations during evolution of periodic patterns on compressed films bonded to compliant substrates. Three-dimensional finite element analysis is performed assuming that the first bifurcation has either the hexagonal or square (i.e., checkerboard) dimple mode. Step-by-step eigenvalue buckling analysis is performed to explore sequential bifurcations on the bifurcated paths. It is found that at the second bifurcation, a rectangular checkerboard or stripe mode occurs depending not only on the Young's modulus ratio of the film and substrate, but also on the magnitude of the imperfection prescribed by the first bifurcation mode. Different bifurcation modes give a family of herringbone deformation patterns with different dimensions, i.e., the evolutional process is multiple and robust. Further, superposition of the identical modes in symmetric directions elucidates the existence of distinctive patterns cognate with the herringbone pattern, including a variety of experimentally observed patterns.

We investigate bifurcations of periodic solutions observed in the forced Wilson-Cowan neuron pair by both the brute-force computation and the shooting method. By superimposing the results given by both methods, a detailed topological classification of periodic solutions is achieved that includes tori and chaos attractors in the parameter space is achieved. We thoroughly explore the parameter space composed of threshold values, amplitude, and angular velocity of an external forcing term. Many bifurcation curves that are invisible when using brute-force method are solved by the shooting method. We find out a typical bifurcation structure including Arnold tongue in the angular velocity and the amplitude of the external force parameter plane, and confirm its fractal structure. In addition, the emergence of periodic bursting responses depending on these patterns is explained.

Aoi Shinya, Yabuuchi Yuki, Morozumi Daiki, et al. Maneuverable and Efficient Locomotion of a Myriapod Robot with Variable Body-Axis Flexibility via Instability and Bifurcation. Soft Robotics 6, NT64 (2023); https://doi.org/10.1089/soro.2022.0177.

BackgroundTechniques for provisional and dual-stent left main bifurcation stenting require optimization. AimTo identify technical variables influencing procedural outcomes and periprocedural myocardial infarction following left main bifurcation intervention. MethodsProcedural and outcome data were analyzed in 438 patients from the per-protocol cohort of the European Bifurcation Club Left Main Trial (EBC MAIN). These patients were randomized to the provisional strategy or a compatible dual-stent extension (T, T-and-protrude, or culotte). ResultsMean age was 71 years and 37.4% presented with an acute coronary syndrome. Transient reduction of side vessel thrombolysis in myocardial infarction flow occurred after initial stent placement in 5% of procedures but was not associated with periprocedural myocardial infarction. Failure to rewire a jailed vessel during any strategy was more common when jailed wires were not used (9.5% vs. 2.5%, odds ratio [OR]: 6.4, p = 0.002). In the provisional cohort, the use of the proximal optimization technique was associated with less subsequent side vessel intervention (23.3% vs. 41.9%, OR: 0.4, p = 0.048). Side vessel stenting was predominantly required for dissection, which occurred more often following side vessel preparation (15.3% vs. 4.4%, OR: 3.1, p = 0.040). Exclusive use of noncompliant balloons for kissing balloon inflation was associated with reduced need for side vessel intervention in provisional cases (20.5% vs. 38.5%, OR: 0.4, p = 0.013), and a reduced risk of periprocedural myocardial infarction across all strategies (2.9% vs. 7.7%, OR: 0.2, p = 0.020). ConclusionWhen performing provisional or compatible dual-stent left main bifurcation intervention, jailed wire use is associated with successful jailed vessel rewiring. Side vessel preparation in provisional patients is linked to increased side vessel dissection requiring stenting. Use of the proximal optimization technique may reduce the need for additional side vessel in

We study the existence, exact multiplicity, and structure of the set of positive solutions to the periodic problem u" = p(t)u + h(t)|u|(lambda) sgn u + mu f (t); u(0) = u(omega), u0(0) = u'(omega), where mu is an element of R is a parameter. We assume that p, h, f is an element of L([0, omega]), lambda > 1, and the function h is non-negative. The results obtained extend the results known in the existing literature. We do not require that the Green's function of the corresponding linear problem be positive and we allow the forcing term f to change its sign.

In this paper, we study the number of steady solutions of a non-linear model arising in Climatology. By applying a shooting method we show the existence of infinitely many steady solutions for some values of a parameter (the solar constant). This method allows us to determine how many times a solution attains the critical temperature (-10degreesC) at which the coalbedo is assumed to be discontinuous., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

This article seeks the deepening of Deleuzian chaosmosis through its comparison with Prigogine's proposal around dissipative systems. Thus, we will explore the aporia between determinism and chance that occurs in Prigogine when it comes to affirming the life-giving character of matter throughout his work. In this sense, we will observe the way in which Deleuze solves it from an ontology of difference that includes the Bergsonian concept of virtuality. The horizon will consist of looking for the link between the notion of chaosmos and (neo)baroque that Deleuze exposed in his last work dedicated to Leibniz., El presente artículo busca la profundización de la caosmosis deleuziana a través de su puesta en comparación con la propuesta de Prigogine en torno a los sistemas disipativos. Así, exploraremos la aporía entre determinismo y azar que acontece en Prigogine a la hora de afirmar el carácter vivificador de la materia a lo largo de su obra. En este sentido, observaremos el modo en que Deleuze la resuelve desde una ontología de la diferencia que incluye el concepto bergsoniano de virtualidad el cual implica una concepción del tiempo también vivificado. El horizonte, no será otro que buscar el engarce entre la noción de caosmos y la de (neo)barroco de la que Deleuze se ocupó en su última obra dedicada a Leibniz.

Aims: Ischaemic heart disease results from insufficient coronary blood flow. Direct measurement of absolute flow (mL/min) is feasible, but has not entered routine clinical practice in most catheterization laboratories. Interventional cardiologists, therefore, rely on surrogate markers of flow. Recently, we described a computational fluid dynamics (CFD) method for predicting flow that differentiates inlet, side branch, and outlet flows during angiography. In the current study, we evaluate a new method that regionalizes flow along the length of the artery. Methods and results: Three-dimensional coronary anatomy was reconstructed from angiograms from 20 patients with chronic coronary syndrome. All flows were computed using CFD by applying the pressure gradient to the reconstructed geometry. Side branch flow was modelled as a porous wall boundary. Side branch flow magnitude was based on morphometric scaling laws with two models: a homogeneous model with flow loss along the entire arterial length; and a regionalized model with flow proportional to local taper. Flow results were validated against invasive measurements of flow by continuous infusion thermodilution (Coroventis™, Abbott). Both methods quantified flow relative to the invasive measures: homogeneous (r 0.47, P 0.006; zero bias; 95% CI -168 to +168 mL/min); regionalized method (r 0.43, P 0.013; zero bias; 95% CI -175 to +175 mL/min). Conclusion: During angiography and pressure wire assessment, coronary flow can now be regionalized and differentiated at the inlet, outlet, and side branches. The effect of epicardial disease on agreement suggests the model may be best targeted at cases with a stenosis close to side branches.

This paper presents a study of the existence conditions of limit cycles and mechanisms when losing their stability in an open-loop DC–DC boost converter loaded with a constant power load and operating in discontinuous conduction mode. First, the existence conditions are determined. Then, boundaries associated with different kinds of instabilities such as the classical smooth fold and period-doubling bifurcations and nonsmooth border-collision bifurcations such as fold border-collision bifurcations are elucidated. To perform the stability analysis, an implicit 1D map for the system is derived. From this model, it is obtained that smooth period-doubling and fold bifurcations may occur at certain values of the circuit parameters. Some results from numerical simulations performed on the circuit-based switched model are provided showing consistency with the theoretical analysis from the derived model., Postprint (author's final draft)

We introduce a different class of thresholdless three-dimensional soliton states that form in higher-order topological insulators based on a two-dimensional Su-Schrieffer-Heeger array of coupled waveguides. The linear spectrum of such structures is characterized by the presence of a topological gap with corner states residing in them. We find that a focusing Kerr nonlinearity allows families of light bullets bifurcating from the linear corner states to exist as stable three-dimensional solitons, which inherit topological protection from their linear corner counterparts and, remarkably, survive even in the presence of considerable disorder. The light bullets exhibit a spatial localization degree that depends strongly on the array dimerization, and may feature large temporal widths in the topological gap near the bifurcation point, thus drastically reducing the otherwise strong instabilities caused by higher-order effects., This research was funded by the Russian Science Foundation under Grant No. 21-12-00096 and partially by Research Project No. FFUU-2021-0003 of the Institute of Spectroscopy of the Russian Academy of Sciences. Support by Agencia Estatal de Investigación Grants No. CEX2019-000910-S and No. PGC2018-097035-B-I00 funded by MCIN/AEI/10.13039/501100011033/FEDER, Departament de Recerca i Universitats de la Generalitat de Catalunya (Grant No. 47Y48R6YK), and Generalitat de Catalunya (CERCA), Fundacio Cellex and Fundacio Mir-Puig, is acknowledged., Peer Reviewed, Postprint (author's final draft)

This study analyzes a basic mathematical model for the dynamic interactions among tumor cells, infected tumor cells and viruses population, focusing on the viral lytic cycle for oncolytic virotherapy. I study the time delay effect of viral infection on tumor cell populations by identifying bifurcation thresholds in both the burst rate and time delay of viral infection in oncolytic virus therapy. Time delay plays an important role in changing the structure of tumor cell populations in a dynamical system. The multi-bifurcation thresholds of the time delay are observed and also dependent on the bursting rate. This study demonstrates a strong relationship between viral burst rates and time delays in population dynamics. The results of this study show that time delay affects oscillation generation and results in back-to-back Hopf bifurcation. This study provides insight into understanding the relationship between the two control parameters, in which tumor cell populations pattern from equilibrium steady-state solutions to periodic solutions and from periodic solutions to equilibrium-state solutions.

This study analyzes a basic mathematical model for the dynamic interactions among tumor cells, infected tumor cells and viruses population, focusing on the viral lytic cycle for oncolytic virotherapy. I study the time delay effect of viral infection on tumor cell populations by identifying bifurcation thresholds in both the burst rate and time delay of viral infection in oncolytic virus therapy. Time delay plays an important role in changing the structure of tumor cell populations in a dynamical system. The multi-bifurcation thresholds of the time delay are observed and also dependent on the bursting rate. This study demonstrates a strong relationship between viral burst rates and time delays in population dynamics. The results of this study show that time delay affects oscillation generation and results in back-to-back Hopf bifurcation. This study provides insight into understanding the relationship between the two control parameters, in which tumor cell populations pattern from equilibrium steady-state solutions to periodic solutions and from periodic solutions to equilibrium-state solutions.

Background: The impact of intracoronary imaging on outcomes, after provisional versus dual-stenting for bifurcation left main (LM) lesions, is unknown. Objectives: We investigated the effect of intracoronary imaging in the EBC MAIN trial (European Bifurcation Club LM Coronary Stent study). Methods: Four hundred and sixty-seven patients were randomized to dual-stenting or a stepwise provisional strategy. Four hundred and fifty-five patients were included. Intravascular ultrasound (IVUS) or optical coherence tomography (OCT) was undertaken at the operator's discretion. The primary endpoint was death, myocardial infarction or target vessel revascularization at 1-year. Results: Intracoronary imaging was undertaken in 179 patients (39%; IVUS = 151, OCT = 28). As a result of IVUS findings, operators reintervened in 42 procedures. The primary outcome did not differ with intracoronary imaging versus angiographic-guidance (17% vs. 16%; odds ratio [OR]: 0.92 (95% confidence interval [CI]: 0.51-1.63) p = 0.767), nor for reintervention based on IVUS versus none (14% vs. 16%; OR: 0.88 [95% CI: 0.32-2.43] p = 0.803), adjusted for syntax score, lesion calcification and ischemic symptoms. With angiographic-guidance, primary outcome events were more frequent with dual versus provisional stenting (21% vs. 10%; adjusted OR: 2.11 [95% CI: 1.04-4.30] p = 0.039). With intracoronary imaging, there were numerically fewer primary outcome events with dual versus provisional stenting (13% vs. 21%; adjusted OR: 0.56 [95% CI: 0.22-1.46] p = 0.220). Conclusions: In EBC MAIN, the primary outcome did not differ with intracoronary imaging versus none. However, in patients with angiographic-guidance, outcomes were worse with a dual-stent than provisional strategy When intracoronary imaging was used, there was a trend toward better outcomes with the dual-stent than provisional strategy.

Provisional stenting has become the default technique for the treatment of most coronary bifurcation lesions. However, the side branch (SB) can become compromised after main vessel (MV) stenting and restoring SB patency can be difficult in challenging anatomies. Angiographic and intracoronary imaging criteria can predict the risk of side branch closure and may encourage use of side branch protection strategies. These protective approaches provide strategies to avoid SB closure or overcome compromise following MV stenting, minimising periprocedural injury. In this article, we analyse the strategies of SB preservation discussed and developed during the most recent European Bifurcation Club (EBC) meetings.

Background: Stepwise provisional stenting is the gold standard for percutaneous coronary intervention (PCI) on bifurcation lesions, but the optimal ballooning technique for eventual side branch treatment is not established. The objective of the present study was to compare the stent configuration obtained by 2 different side branch optimization techniques performed after main vessel (MV) stent implantation: proximal optimization technique+kissing balloon inflation+final proximal optimization technique (POT/KBI/POT [PKP]) versus proximal optimization technique+isolated side branch dilation+final proximal optimization technique (POT-side-POT [PSP]). Methods: We realized a 1:1 prospective randomized trial comparing bifurcation PCI conducted (under angiographic and angioscopic visualization) with either PKP or PSP in reanimated swine hearts using commercially available drug-eluting stents. After PCI, the obtained stent configuration (expansion, eccentricity, apposition) was assessed by optical coherence tomography and micro-computed tomography dividing the stent in 4 segments. Primary study end point was minimum stent expansion at the distal MV segment. Results: A total of 30 PCIs were successfully performed according to randomization obtaining overall good results (average minimum stent expansion >90% at optical coherence tomography and micro-computed tomography) with PSP or PKP. Minimum stent expansion at the distal MV segment was significantly higher with PKP as compared with PSP at optical coherence tomography (97.9±4.2% versus 91.0±7.7%; P=0.002) and micro-computed tomography (98.1±4.1% versus 91.3±7.9%; P=0.006). Other significant findings included higher stent eccentricity index at proximal MV with PSP, higher side branch scaffolding length and lower malapposition (at bifurcation core and distal MV) with PKP. Conclusions: This first prospective randomized trial in a unique non-atherosclerotic preclinical environment showed that bifurcation PCI conducted with P

The objective of this work was to investigate the dynamics of host–parasitoid model with spatial refuge effect. For this, two discrete host–parasitoid models were considered under spatial refuge effect. Suppose that a constant population of hosts may seek refuge and protection from an attack of parasitoids. We found the parametric factors affecting the existence of the equilibrium points and uniqueness of equilibrium points. A local stability analysis of host–parasitoid models was also carried out. Bifurcation theory was used to observe that the host–parasitoid models undergo Neimark–Sacker bifurcation. The effect of the existence of constant refuge effect on the local stability and bifurcation of models was also explored. Hybrid chaos control methodology was used to control the chaotic behavior of model. In addition, numerical simulations, bifurcation diagrams, and phase portraits of the models are also presented.

We investigate bifurcations of periodic solutions observed in the forced Wilson-Cowan neuron pair by both the brute-force computation and the shooting method. By superimposing the results given by both methods, a detailed topological classification of periodic solutions is achieved that includes tori and chaos attractors in the parameter space is achieved. We thoroughly explore the parameter space composed of threshold values, amplitude, and angular velocity of an external forcing term. Many bifurcation curves that are invisible when using brute-force method are solved by the shooting method. We find out a typical bifurcation structure including Arnold tongue in the angular velocity and the amplitude of the external force parameter plane, and confirm its fractal structure. In addition, the emergence of periodic bursting responses depending on these patterns is explained.

In this study, we investigate the bifurcation and deformation during the evolution of periodic patterns on a gel film bonded to a soft substrate. 3D finite element analysis is performed using an inhomogeneous field theory for polymeric gels. Step-by-step eigenvalue buckling analysis is conducted to explore not only the first bifurcation, but also sequential bifurcations on bifurcated paths. When the hexagonal dimple mode occurs as the first bifurcation, the second bifurcation consists of rectangular checkerboard modes in three symmetric directions. The resulting deformation patterns are in good agreement with experiments and, surprisingly, are analogous to the in-plane buckling behavior of hexagonal honeycombs. Uniaxial, biaxial, and equibiaxial (flower-like) patterns are produced by the periodic arrangements of distorted dimples. The third and fourth bifurcations cause the coalescence of the selected dimples. This reveals the occurrence of the rectangular checkerboard modes at the second bifurcation to be the missing link in the pattern evolution from hexagonal dimples to herringbone and labyrinth patterns.

N/A

From population collapses to cell-fate decision, critical phenomena are abundant in complex real-world systems. Among modelling theories to address them, the critical transitions framework gained traction for its purpose of determining classes of critical mechanisms and identifying generic indicators to detect and alert them (“early warning signals”). This thesis contributes to such research field by elucidating its relevance within the systems biology landscape, by providing a systematic classification of leading mechanisms for critical transitions, and by assessing the theoretical and empirical performance of early warning signals. The thesis thus bridges general results concerning the critical transitions field – possibly applicable to multidisciplinary contexts – and specific applications in biology and epidemiology, towards the development of sound risk monitoring system.

This project is about transforming existing buildings that are facing demolition. In opposition to the constant renewing of our physical world for better performing building, this graduation proposes a gradual mutation of a locality., Architecture, Urbanism and Building Sciences | Explorelab

This project is about transforming existing buildings that are facing demolition. In opposition to the constant renewing of our physical world for better performing building, this graduation proposes a gradual mutation of a locality., Architecture, Urbanism and Building Sciences | Explorelab

In the conventional implementations for solving bifurcation problems, Jacobian matrix and its partial derivatives regarding the given problem should be provided manually. This process is not so easy, thus it often induces human errors like computation failures, typing error, especially if the system is higher order. In this paper, we develop a preprocessor that gives Jacobian matrix and partial derivatives symbolically by using SymPy packages on the Python platform. Possibilities about the inclusion of errors are minimized by symbolic derivations and reducing loop structures. It imposes a user only on putting an expression of the equation into a JSON format file. We demonstrate bifurcation calculations for discrete neuron dynamical systems. The system includes an exponential function, which makes the calculation of derivatives complicated, but we show that it can be implemented simply by using symbolic differentiation.

info:eu-repo/semantics/published

We investigate the local self-sustained process underlying spiral turbulence in counter-rotating Taylor–Couette flow using a periodic annular domain, shaped as a parallelogram, two of whose sides are aligned with the cylindrical helix described by the spiral pattern. The primary focus of the study is placed on the emergence of drifting–rotating waves (DRW) that capture, in a relatively small domain, the main features of coherent structures typically observed in developed turbulence. The transitional dynamics of the subcritical region, far below the first instability of the laminar circular Couette flow, is determined by the upper and lower branches of DRW solutions originated at saddle-node bifurcations. The mechanism whereby these solutions self-sustain, and the chaotic dynamics they induce, are conspicuously reminiscent of other subcritical shear flows. Remarkably, the flow properties of DRW persist even as the Reynolds number is increased beyond the linear stability threshold of the base flow. Simulations in a narrow parallelogram domain stretched in the azimuthal direction to revolve around the apparatus a full turn confirm that self-sustained vortices eventually concentrate into a localised pattern. The resulting statistical steady state satisfactorily reproduces qualitatively, and to a certain degree also quantitatively, the topology and properties of spiral turbulence as calculated in a large periodic domain of sufficient aspect ratio that is representative of the real system., Postprint (author's final draft)

In this study, the non-linear dynamics of Taylor–Couette flow in a very small-aspect-ratio wide-gap annulus in a counter-rotating regime under the influence of radial through-flow are investigated by solving its full three-dimensional Navier-Stokes equations. Depending on the intensity of the radial flow, either an axisymmetric (pure m = 0 mode) pulsating flow structure or an axisymmetric axially propagating vortex will appear subcritical, i.e. below the centrifugal instability threshold of the circular Couette flow. We show that the propagating vortices can be stably existed in two separate parameter regions, which feature different underlying dynamics. Although in one regime, the flow appears only as a limit cycle solution upon which saddle-node-invariant-circle bifurcation occurs, but in the other regime, it shows more complex dynamics with richer Hopf bifurcation sequences. That is, by presence of incommensurate frequencies, it can be appeared as 1-, 2- and 3-torus solutions, which is known as the Ruelle–Takens–Newhouse route to chaos. Therefore, the observed bifurcation scenario is the Ruelle-Takens-Newhouse route to chaos and the period doubling bifurcation, which exhibit rich and complex dynamics., Postprint (published version)

Over time, the mammalian circadian system has evolved to anticipate a 24 hour day. These rhythms are robust and not easily perturbed, but as a consequence, are also difficult to reset. Until the modernization of society and the advent of artificial light, the inability to reset rhythms has not been a problem. This inflexibility has the potential to induce health complications like mental illness and metabolic dysfunction when there is desynchrony between internal rhythms and the outside world is chronic, such as in shift workers whose schedules do not align with a normal day. Studies on the flexibility of circadian rhythms have mainly focused on standard 24 hour entrainment paradigms, but few have considered how plasticity may change under non-standard environmental conditions. Chapter 2 introduces the idea that bifurcation of circadian waveforms in peripheral tissues induces extraordinary flexibility in clock gene expression rhythms when challenged with simulated jet-lag. Bifurcated clock gene expression rhythms are low amplitude, which may enable such rapid resetting in peripheral tissues. Chapter 3 describes that the implementation of an 18 hour light and food restricted schedule can, remarkably, entrain low amplitude hepatic clock gene expression rhythms to an 18 hour day (T18). Entrainment to T18 is well beyond the established limits of entrainment for the liver (T=22-26 hours), and was not achieved in previous studies on T18 photoperiod without time restricted eating. Together, this thesis demonstrates increased circadian plasticity of mammalian peripheral clock gene expression rhythms beyond what was previously thought to be possible under standard environmental conditions. Enhanced flexibility of entrainment may be due to low amplitude clock gene expression rhythms, but the mechanism remains unknown. These results broaden the understanding of circadian flexibility and provide insight on mitigation of circadian disruption.

With the drive for more efficent slender structures, nonlinear dynamic phenomena are increasingly being observed in, and sometimes designed into, engineering systems. The objective of this thesis is to develop a better theoretical understanding of nonlinear systems that manifest internal resonance and provides practical insights into the exploitation of such nonlinear behaviours in engineering practice. To achieve this, an analytical approach is employed, that is based on nonlinear normal mode, or backbone curve, analysis. The geometry, i.e. synchronicity and asynchronicity, of internal resonances is investigated using conceptually simple, two-mode systems. Special dynamic behaviours that emerge from internal resonance are studied, including isolated backbone curves and backbone solutions where the phases of modal coordinates vary. The underpinning mechanisms that govern their existence are analytically derived and demonstrated using relevant engineering systems. These geometric features are generalised to account for arbitrary types of internal resonances for two-mode interactions with arbitrary eigenfrequency ratios; an analytical technique is proposed for the efficient and robust determination of internal resonances. The research scope is then extended to forced-damped scenarios. By employing an energy-based method, the relationships between backbone curves and forced periodic responses are established. A semi-analytical, energy balancing method is formulated by combining the energy balancing principle across multiple harmonics with quadrature criteria. With known NNM solutions, it allows for efficient prediction of forced responses with the applicability and accuracy estimated via harmonic phase-shifts. Based on the concept of resonant capture, backbone curves are used to interpret damped transient responses with applications of Targeted Energy Transfer (TET). The required backbone curves for realising TET are identified from a symmetry-breaking p

We study boundedness of solutions to a linear boundary value problem (BVP) modelling a two-layer ocean with a uniform eddy viscosity in the lower layer and variable eddy viscosity in the upper layer. We analyse bounds of solutions to the given problem on the examples of different eddy viscosity profiles in the case of their parameter dependence., Mathematical Physics

Channels in rivers and estuaries are the main paths of fluvial and tidal currents that transport sediment through the system. While network representations of multi-channel systems and their connectivity are quite useful for characterisation of braiding patterns and dynamics, the recognition of channels and their properties is complicated because of the large bed elevation variations, such as shallow shoals and bed steps that render channels visually disconnected. We present and analyse two mathematically rigorous methods to identify channel networks from a terrain model of the river bed. Both methods construct a dense network of locally steepest-descent channels from saddle points on the terrain, and select a subset of channels with a certain minimum sediment volume between them. This is closely linked to the main mechanism of channel formation and change by displacement of sediment volume. The two methods differ in how they compute these sediment volumes: either globally through the entire length of the river, or locally. We compare the methods for the measured bathymetry of the Western Scheldt estuary, The Netherlands, over the past decades. The global method is overly sensitive to small changes elsewhere in the network compared to the local method. We conclude that the local method works best conceptually and for stability reasons. The associated concept of alluvial connectivity between channels in a network is thus the inverse of the volume of sediment that must be displaced to merge the channels. Our method opens up possibilities for new analyses as shown in two examples. First, it shows a clear pattern of scale dependence on volume of the total network length and of the number of nodes by a power law relation, showing that the smaller channels are relatively much shorter. Second, channel bifurcations were found to be predominantly mildly asymmetrical, which is unexpected from fluvial bifurcation theory.

We study boundedness of solutions to a linear boundary value problem (BVP) modelling a two-layer ocean with a uniform eddy viscosity in the lower layer and variable eddy viscosity in the upper layer. We analyse bounds of solutions to the given problem on the examples of different eddy viscosity profiles in the case of their parameter dependence., Mathematical Physics

In the present work, starting from the 1D evolutionary Muthian cobweb model in [Hommes & Wagener, 2010], where the economy is populated by biased firms and unbiased fundamentalist firms, we investigate the effects generated by adaptively adjusted beliefs on the long-period price of the goods produced. As in [Hommes & Wagener, 2010], we focus on the case in which the Muthian model is globally stable in the sense of Guesnerie [2002], stable under naive expectations. Coupling into the details, we first assume that just biased producers, being aware of the systematic errors they make in their forecasts, partially rely on an adaptive adjustment of beliefs, obtaining a 3D model, which has a unique steady state. Although in [Hommes & Wagener, 2010] the fundamental steady state is always stable and at most it can coexist with a period-two cycle, we show that the complexity degree increases in our case, where on increasing the reactivity of the evolutionary mechanism, there may be up to two stability thresholds for the steady state, both corresponding to flip bifurcations, and the equilibrium can coexist with a quasiperiodic attractor. On checking the robustness of such outcomes, we contrast them with those we find for the 4D setting, obtained by assuming that unbiased fundamentalists update their belief about the fundamental value partially relying on the same adaptive adjustment mechanism used by biased producers. The outcomes are similar to those of the 3D framework. For instance, in both cases, there exists just the fundamental equilibrium, which can coexist with a quasiperiodic attractor.

Friction-induced vibrations, apparent for example as squeal noise in car braking systems, have seen a significant amount of research effort in the past and remain an area of active research today. Due to the huge bifurcation parameter space and model parameter uncertainties, the instability mechanisms of these vibrations remain elusive. Particularly, bifurcation parameters and critical sensitivities vary from brake system to brake system. Numerical simulations cannot resolve all aspects for robust instability predictions today. Recent work has illustrated how data-driven approaches to friction-induced noise modeling can be an alternative approach to conventional physics-based modeling: A digital twin representing a specific brake system was shown to predict instabilities and mode coupling associated with squeal occurrence with high accuracy. This work builds upon previous data-driven approaches to obtain a digital twin from measurement data of a real-world disc brake system. After validation, this data-based model is exploited to study the effect of various loading conditions on the predicted squealing behavior of the system. By gradually altering the loading conditions, we generate stability maps that encode information about the stability regions of the respective brake system. These stability maps provide a data-driven perspective on the mechanisms underlying frictioninduced noise, fostering a deeper understanding of the bifurcation parameter space of the underlying system., Bundesministerium für Bildung und Forschung (BMBF)

This material may be downloaded for personal use only. Any other use requires prior permission of the American Society of Civil Engineers. This material may be found at https://ascelibrary.org/doi/abs/10.1061/%28ASCE%29HY.1943-7900.0001993, The large pier of an emblematic bridge built in 2008 in the Ebro River (Zaragoza, Spain) obstructs the flow in high floods. Clear-water scour experiments in a scale model were conducted to anticipate maximum local scour depths and design riprap protections. These proved to be effective during a large flood event in 2015, but bed aggradation under the left bridge span and deep scour under the right one, not mirroring the bed deformation observed in the model, raised concerns about the bridge safety. The effects of the protected pier on the changes in the aftermath of the 2015 flood are discussed. It is shown that a large meander upstream generated an imbalance in the spanwise bedload distribution, leading to sedimentation on the left and contraction scour on the right. The paper argues for the need to take into account the effects of large piers on river morphology at the bridge planning phase. The case study shows that using a clear-water model to design the riprap protection is adequate, but more importantly, that the fluvial processes during a flood could only be studied with a live-bed model with geometrical detail of the full river reach, namely, the upstream meander., Thanks to the insightful, helpful comments by the Associate Editor. Thanks to the Ebro Water Authority (Marisa Moreno and Miriam Pardos) and Zaragoza Municipality (Luis Manso) for providing hydrological data and field surveys. We also thank the financial support of the FEDER-COMPETE2020 (POCI) and Portuguese funds (Foundation for Science and Technology, IP) through project PTDC/ECI-EGS/29835/2017—POCI-01-0145-FEDER-029835., Peer Reviewed, Postprint (published version)

Channels in rivers and estuaries are the main paths of fluvial and tidal currents that transport sediment through the system. While network representations of multi-channel systems and their connectivity are quite useful for characterisation of braiding patterns and dynamics, the recognition of channels and their properties is complicated because of the large bed elevation variations, such as shallow shoals and bed steps that render channels visually disconnected. We present and analyse two mathematically rigorous methods to identify channel networks from a terrain model of the river bed. Both methods construct a dense network of locally steepest-descent channels from saddle points on the terrain, and select a subset of channels with a certain minimum sediment volume between them. This is closely linked to the main mechanism of channel formation and change by displacement of sediment volume. The two methods differ in how they compute these sediment volumes: either globally through the entire length of the river, or locally. We compare the methods for the measured bathymetry of the Western Scheldt estuary, The Netherlands, over the past decades. The global method is overly sensitive to small changes elsewhere in the network compared to the local method. We conclude that the local method works best conceptually and for stability reasons. The associated concept of alluvial connectivity between channels in a network is thus the inverse of the volume of sediment that must be displaced to merge the channels. Our method opens up possibilities for new analyses as shown in two examples. First, it shows a clear pattern of scale dependence on volume of the total network length and of the number of nodes by a power law relation, showing that the smaller channels are relatively much shorter. Second, channel bifurcations were found to be predominantly mildly asymmetrical, which is unexpected from fluvial bifurcation theory.

The study of bifurcations of differential-algebraic equations (DAEs) is the topic of interest for many applied sciences, such as electrical engineering, robotics, etc. While some of them were investigated already, the full classification of such bifurcations has not been done yet. In this paper, we consider bifurcations of quasilinear DAEs with a singularity and provide a full list of all codimension-one bifurcations in lower-dimensional cases. Among others, it includes singularity-induced bifurcations (SIBs), which occur when an equilibrium branch intersects a singular manifold causing certain eigenvalues of the linearized problem to diverge to infinity. For these and other bifurcations, we construct the normal forms, establish the non-degeneracy conditions and give a qualitative description of the dynamics. Also, we study singular homoclinic and heteroclinic bifurcations, which were not considered before., Deutsche Forschungsgemeinschaft (DFG)

This project is about transforming existing buildings that are facing demolition. In opposition to the constant renewing of our physical world for better performing building, this graduation proposes a gradual mutation of a locality., Architecture, Urbanism and Building Sciences | Explorelab

This project is about transforming existing buildings that are facing demolition. In opposition to the constant renewing of our physical world for better performing building, this graduation proposes a gradual mutation of a locality., Architecture, Urbanism and Building Sciences | Explorelab

We bring to the forefront of educational thought a specific attitude toward the COVID-19 crisis that harnesses the symbolism of wind and water to navigate the cultural storm interfering upon our mathematical and pedagogical craft. The purpose of our paper is to open up space for opportunities in mathematics education using integral mindfulness as the rudder to readjust our bearings. More specifically, through conceptual analyses and making explicit the currents of change, disorder, and technology, we can apply discernment to these metaphors that intersect our pedagogy to re-align efforts and attitudes toward an integrated (aperspectival) culture of mathematics education. Through shared responsibility during these tumultuous times, we can once again strive toward the pursuit of excellence in mathematics education.

A mathematical aspect of the anharmonic downward distortion following (ADDF) path is discussed. The ADDF method is utilized as an automated reaction path search method, which can explore transition state geometries on a potential energy surface from a potential minimum. We show that the maximum number of the ADD stationary paths intersecting the potential minimum is 2(f + 1) - 2, where f denotes the degree of freedom of the system. We also show that the bifurcation of the ADD stationary path is essential to detect all the transition states connected from a given minimum. The ADDF computation is demonstrated for a H2O molecule in which pitchfork bifurcation is observed.

Various collective motions of camphor boats have been studied. Camphor boats are self-driven particles that interact with each other through the change of surface tension on water surface by camphor molecules. Consequently, even in a one-dimensional circuit, a congested state or jamming can be observed (Suematsu et al. in Phys Rev E 81:056210, 2010). In this phenomenon, the unidirectional motion of each particle is considered a traveling wave, and the concentration of camphor molecules forms a pulse shape. Hence, each pair of particles interacts with each other like a pulse-pulse interaction. Thus, we expect that the center manifold theories proposed in Ei (J Dyn Differ Equ 14:85-137, 2002) and Ei et al. (Physica D 165:176-198 2002) are applicable for the analysis of the collective motion of camphor boats. However, spatial discontinuity in our model, in particular the existence of Dirac delta functions in a linearized operator, does not fulfill the requirement in the reduction process because the authors developed their theories in L2-framework and for smooth nonlinearity in Ei (2002) and Ei et al. (2002). In this article, we extend the results obtained in Ei (2002) and Ei et al. (2002) and establish a new center manifold approach in (H1)*-framework. Finally, we succeed to rigorously reduce a mathematical model (Nagayama et al. in Physica D: Nonlinear Phenom 194:151-165, 2004) coupled with a Newtonian equation and a reaction-diffusion equation including delta functions to an ordinary differential system that represents the motions of camphor boats.

Various collective motions of camphor boats have been studied. Camphor boats are self-driven particles that interact with each other through the change of surface tension on water surface by camphor molecules. Consequently, even in a one-dimensional circuit, a congested state or jamming can be observed (Suematsu et al. in Phys Rev E 81:056210, 2010). In this phenomenon, the unidirectional motion of each particle is considered a traveling wave, and the concentration of camphor molecules forms a pulse shape. Hence, each pair of particles interacts with each other like a pulse-pulse interaction. Thus, we expect that the center manifold theories proposed in Ei (J Dyn Differ Equ 14:85-137, 2002) and Ei et al. (Physica D 165:176-198 2002) are applicable for the analysis of the collective motion of camphor boats. However, spatial discontinuity in our model, in particular the existence of Dirac delta functions in a linearized operator, does not fulfill the requirement in the reduction process because the authors developed their theories in L2-framework and for smooth nonlinearity in Ei (2002) and Ei et al. (2002). In this article, we extend the results obtained in Ei (2002) and Ei et al. (2002) and establish a new center manifold approach in (H1)*-framework. Finally, we succeed to rigorously reduce a mathematical model (Nagayama et al. in Physica D: Nonlinear Phenom 194:151-165, 2004) coupled with a Newtonian equation and a reaction-diffusion equation including delta functions to an ordinary differential system that represents the motions of camphor boats.

A mathematical aspect of the anharmonic downward distortion following (ADDF) path is discussed. The ADDF method is utilized as an automated reaction path search method, which can explore transition state geometries on a potential energy surface from a potential minimum. We show that the maximum number of the ADD stationary paths intersecting the potential minimum is 2(f + 1) - 2, where f denotes the degree of freedom of the system. We also show that the bifurcation of the ADD stationary path is essential to detect all the transition states connected from a given minimum. The ADDF computation is demonstrated for a H2O molecule in which pitchfork bifurcation is observed.

application/pdf, Nonlinear Dynamics. 2021, 106 (3), P.2363-2376

Mean-field models describe bulk neural activity in terms of population-average action potential (spike) rates, but do not attempt to address the variations in the firing activity of individual neurons and the interactions among them. In 2016, Waikato Cortical Modelling group published a purely theoretical model [Steyn-Ross et al, Phys. Rev. E 93.2 (2016): 022402] that provides a more accurate mapping of spiking dynamics, scaling from single neuron to the macroscopic level by regridding the system using a spatial blocking: a bottom-up neural regridding referred to as True-field. A 2D continuum of identical neurons is constructed from a lattice of spiking neurons that are coupled both synaptically (via chemical synapses) and diffusively (via electrical synapses). The spiking behaviour at the single-neuron level is modelled using the Wilson point neuron equations, steered by incoming electrical impulses from adjacent neurons. These equations are then reblocked to form a coarser-spatial resolution by eliminating the high-frequency spatial modes. The existence of diffusive terms in voltage and recovery equations is crucial for this spatial coarse-graining procedure. The purpose of this thesis is to conduct a preliminary analysis of the True-field model, which has never been tested in simulations before. The coarse-graining procedure employed in this framework results in a set of nonlinear corrections in the model equations. My first challenge is to recover those corrections and conduct numerical investigations to identify the most significant ones. My next challenge is to tune parameters of the True-field model via a comprehensive series of simulations, looking for “realistic” cortical behaviours. Two approaches are used: point simulations of the homogeneous two-neuron cortex, and full 2D grid simulations of a sheet of cortical tissue. Point simulations are straightforward and time efficient but do not provide any information about spatial variations in firing activity

This study investigates the mechanisms by which small-scale turbulence and cloud physics determine the organization of large-scale convection in radiative-convective equilibrium (RCE), an idealization of the tropical atmosphere. Under uniform forcings similar to typical tropical conditions, the atmosphere in RCE might spontaneously separate into dry and moist regions on scales of 100–1,000 km, with convective clouds aggregating into a cluster in the latter. This phenomenon is known as convective self-aggregation. Herein, we demonstrate that subtle changes in assumptions related to cloud physics and turbulence on scales of E 1 km can dictate the emergence or suppression of convective self-aggregation, resulting from a bifurcation of the dynamical system. The bifurcation occurs when a small dry patch forms in the domain and is sustained because it contributes to negative effective diffusivity of the circulation. Cloud-radiation feedbacks and turbulence circulation interactions govern the formation of such dry patches, thereby modulating the bifurcation. This sensitive dependence on subgrid process models might be a fundamental barrier to climate predictability in light of inherent uncertainties in microscale processes. Because without the capability to include exact representations of those processes in climate models, slight differences in the different approximations used by modelers can lead to qualitative changes in climate predictions, at least for some processes.

For a family of two-dimensional predator-prey models of Gause type, we investigate the simultaneous occurrence of a center singularity and a limit cycle. The family is characterized by the fact that the functional response is nonanalytical and ehibits group defense. We prove the eistence and uniqueness of the limit cycle using a new theorem for Liénard systems. The new theorem gives conditions for the uniqueness of a limit cycle which surrounds a period annulus. The results of this paper provide a mechanism for studying the global behavior of solutions to Gause systems through bifurcation of an integrable system which contains a center and a limit cycle., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Network Architectures and Services

It is well known that the existence of traveling wave solutions (TWS) for many partial differential equations (PDE) is a consequence of the fact that an associated planar ordinary differential equation (ODE) has certain types of solutions defined for all time. In this paper we address the problem of persistence of TWS of a given PDE under small perturbations. Our main results deal with the situation where the associated ODE has a center and, as a consequence, the original PDE has a continuum of periodic traveling wave solutions. We prove that the TWS that persist are controlled by the zeroes of some Abelian integrals. We apply our results to several famous PDE, like the Ostrovsky, Klein-Gordon, sine-Gordon, Korteweg-de Vries, Rosenau-Hyman, Camassa-Holm, and Boussinesq equations., Mathematical Physics