Set Of Initial Conditions Research Articles

The role of heterogeneous stress in earthquake cycle models of the Hikurangi-Kermadec subduction zone

Summary Seismic and tsunami hazard modelling and preparedness are challenged by uncertainties in the earthquake source process. Important parameters such as the recurrence interval of earthquakes of a given magnitude at a particular location, the probability of multi-fault rupture, earthquake clustering, rupture directivity and slip distribution are often poorly constrained. Physics-based earthquake simulators, such as RSQSim, offer a means of probing uncertainties in these parameters by generating long-term catalogues of earthquake ruptures on a system of known faults. The fault initial stress state in these simulations is typically prescribed as a single uniform value, which can promote characteristic earthquake behaviours and reduce variability in modelled events. Here, we test the role of spatial heterogeneity in the distribution of the initial stresses and frictional properties on earthquake cycle simulations. We focus on the Hikurangi-Kermadec subduction zone, which may produce Mw > 9.0 earthquakes and likely poses a major hazard and risk to Aotearoa New Zealand. We explore RSQSim simulations of Hikurangi-Kermadec subduction earthquake cycles in which we vary the rate and state coefficients (a and b). The results are compared with the magnitude-frequency distribution (MFD) of the instrumental earthquake catalogue and with empirical slip scaling laws from global earthquakes. Our results suggest stress heterogeneity produces more realistic and less characteristic synthetic catalogues, making them particularly well suited for hazard and risk assessment. We further find that the initial stress effects are dominated by the initial effective normal stresses, since the normal stresses evolve more slowly than the shear stresses. A heterogeneous stress model with a constant pore-fluid pressure ratio and a constant state coefficient (b) of 0.003 produces the best fit to MFDs and empirical scaling laws, while the model with variable frictional properties produces the best fit to earthquake depth distribution and empirical scaling laws. This model is our preferred initial stress state and frictional property settings for earthquake modelling of the Hikurangi-Kermadec subduction interface. Introducing heterogeneity of other parameters within RSQSim (e.g. friction coefficient, reference slip rate, characteristic distance, initial state variable, etc) could further improve the applicability of the synthetic earthquake catalogues to seismic hazard problems and form the focus of future research.

Initial state‐dependent implementation of logic gates with memristive neurons

AbstractThis study introduces a simple memristor cellular neural network structure, a minimalist configuration with only two cells, designed to concurrently address two logic problems. The unique attribute of this system lies in its adaptability, where the nature of the implemented logic gate, be it AND, OR, and XOR, is determined exclusively by the initial states of the memristors. The memristors' state, alterable through current flow, allows for dynamic manipulation, enabling the setting of initial conditions and consequently, a change in the circuit's functionality. To optimize the parameters of this dynamic system, contemporary machine learning techniques are employed, specifically gradient descent optimization. Through a case study, the potential of leveraging intricate circuit dynamics is exemplified to expand the spectrum of problems solvable with a defined number of neurons. This work not only underscores the significance of adaptability in logical circuits but also demonstrates the efficacy of memristive elements in enhancing problem‐solving capabilities.

Traveling wave solution for a nonlocal Belousov-Zhabotinskii reaction-diffusion system

We consider a Belousov-Zhabotinskii reaction-diffusion system with nonlocal effects and study the existence of traveling wave solutions. By constructing appropriate super- and sub-solutions and using Schauder’s fixed point theorem, we show that there is a critical speed c * > 0 such that when the wave speed c > c *, there exists a traveling wave solution connecting (0, 0) to a positive steady-state, while there is no traveling wave solution when c < c *. Moreover, we also examine a special case where ϕ 1(x) is the Dirac function, and demonstrate the existence of the traveling wave solution connecting the equilibria (0, 0) and (1, 1) for c > c *, whereas the traveling wave solution does not exist when c < c *. Finally, the long-time behavior of the solution is investigated through numerical simulation and theoretical analysis, and it is found that the choice of kernel functions and the setting of initial value conditions play a crucial role.

Periodicity and lifetime of orbits around elongated asteroids

This paper presents dynamics and control of orbits around an asteroid that is modelled as a uniformly rotating homogeneous rectangular parallelepiped (HRP). Aside from the non-uniform gravitational field of the asteroid, we include the solar radiation pressure (SRP) as a perturbing force. A simple model based on the polyhedral method is employed for calculating the gravity around the HRP. First, circular periodic orbits are identified both in the presence and absence of solar radiation pressure. Then, families of general non-circular periodic orbits in the presence of SRP are determined and subsequently analysed for stability. Next, for a general orbit in the equatorial plane, its stability against a catastrophic impact of an orbiting spacecraft onto the asteroid’s surface is checked in the presence of SRP. Orbits, where the solar radiation pressure is less/more dominant over the central body’s gravity, are identified with the aim of finding the best orbits for parking a spacecraft. Then, for long-period orbits, SRP is averaged and the time averaged evolution of the orbital elements is obtained. For a special set of initial condition, a closed form solution for the evolution of the orbital eccentricity is obtained. Using this solution, a lower limit for the life-time of a spacecraft that is left uncontrolled is derived in a closed form. Finally, active control strategies are developed for orbit-keeping ofspacecraft for any choice of orbital parameters. A linear-quadratic regulator (LQR) is designed to track a given Keplerian orbit with minimum fuel expenditure. Fuel expenditure on various orbits are calculated and compared to determine the orbits of cheapest operation. The work presented is applicable to small body (asteroids and comets) exploration missions which require online cancellation of the perturbing forces with minimal knowledge of the accurate shape, size, and composition of the small body prior to the mission.

Scalar quasi-normal modes of accelerating Kerr-Newman-AdS black holes

We study linear scalar perturbations of slowly accelerating Kerr-Newman-anti-de Sitter black holes using the method of isomonodromic deformations. The conformally coupled Klein-Gordon equation separates into two second-order ordinary differential equations with five singularities. Nevertheless, the angular equation can be transformed into a Heun equation, for which we provide an asymptotic expansion for the angular eigenvalues in the small acceleration and rotation limit. In the radial case, we recast the boundary value problem in terms of a set of initial conditions for the isomonodromic tau function of Fuchsian systems with five regular singular points. For the sake of illustration, we compute the quasi-normal modes frequencies.

Rock mass classification in slope engineering with special emphasis on Slope mass rating: Current status and future projections

Rock mass classification (RMC) systems in the realm of rock slope engineering have gathered a lot of attention. The present review article delves into the major RMC systems, elucidating their fundamental principles, key parameters and practical applications. Among the various RMC systems for rock slope designing, Romana's Slope mass rating (SMR) was found to be the most comprehensive; therefore, the focus of the discussion centres around the SMR method. The article provides a crisp overview of the major advancements, evolution and potential challenges of SMR. The radical concept of wedge failure in SMR and the use of continuous functions are discussed in detail. A thorough discussion is provided on the efforts made by different researchers, encompassing the inclusion of novel factors such as slope height, heterogeneity in rock mass or lithology, weighted consideration of existing discontinuities, fuzzy sets and overburden thickness. Various automated calculation techniques and empirical correlations of SMR with other classification systems and rock engineering parameters are also outlined. Moreover, a critical examination of the variations among major extensions of SMR and their geotechnical relevance have also been discussed. Based on a meticulous assessment of the susceptibility to toppling failure in SMR, two sub‐factors to include block shape and interlayer slip between discontinuities have been suggested. These sub‐factors were validated by Goodman's tests for toppling failure. The scope of future projections or possible aspects for revisiting and refinement of the SMR method are suggested to enhance the applicability of the method under a diverse initial set of geotechnical conditions.

Delay-dependent set-invariance for linear difference equations with multiple delays: a polyhedral approach

This paper revisits the set-invariance for linear delay-difference equations and proposes novel delay-dependent notions in contrast with the existing delay-independent constructions available in the literature. The main tool in this endeavour is the model transformation by means of a matrix parametrization, which opens the way to the elaboration of delay-dependent conditions for set invariance. For the class of polyhedral sets, it will be shown how these transformed models enable particularly structured invariance conditions. Aside from the mathematical developments, a discussion of the delay-dependent conditions with respect to the confinement of the state trajectories of the original system will be presented. The relationship will be established by means of constraints involving the initial states for the time-delay systems. The characterization of this set of admissible initial conditions can be analysed in terms of complexity and conservativeness with respect to the classical delay-independent set-invariance. An illustrative example is provided to underline that confinement of state trajectories in a set can be achieved even though this is not invariant according to the classical definition.

Simulation of fiber-induced melt pressure fluctuations within large scale polymer composite deposition beads

The process-structure-property relationship in Large Area Additive Manufacturing (LAAM) technology is an ongoing area of research as the inherent microstructural properties (chiefly fibers and voids) affect the performance of printed parts. Unfortunately, we currently lack adequate understanding of micro void nucleation and evolution during the LAAM and fused deposition modelling (FDM) processes. Modeling of the polymer melt flow during the extrusion process is important in understanding the underlying microstructural formation and associated properties of the print, that determines the part performance in service conditions. In this paper we compute fiber-induced local pressure fluctuations which may promote void formation in the bead’s microstructure. On a macro-scale, we determine flow fields of a purely viscous, Newtonian planar polymer deposition flow through a LAAM nozzle which are utilized on a micro-scale model where we simulate the evolution of a single ellipsoidal fiber along streamlines obtained from the macro-model. On the micro-scale, we determine instantaneous values of the translational and rotational velocities of the rigid ellipsoidal fiber that satisfies a balance of hydrodynamic forces and couples on the fiber’s surface based on a Newton Raphson algorithm and we track the fiber’s motion along the flow path via an explicit numerical iterative algorithm. Model verification is achieved by benchmarking results with solutions from well-known Jeffery’s equation of motion of a particle in homogeneous simple shear flow. We account for rotary diffusivity due to short-range fiber-fiber interaction in the FEA simulation by determining an effective fluid domain size representative of the interaction coefficient of the melt flow through a correlation analysis that yields an equivalent steady state orientation based on the Advani-Tucker equation. We also consider different possible motions of the fiber along individual LAAM flow paths from a given set of random initial fiber conditions to determine pressure bounds on the fiber surface along each streamline. For improved computational efficiency, calculations are carried out with respect to the fiber’s local coordinate axes to overcome the rigor of adaptive remeshing during the quasi-transient analysis. Results show low pressure extremes near the fiber’s surface which varies across the printed bead as well as through its thickness. Discussion is provided to gain insight into the effect of low-pressure extremes on micro void formation, particularly at the nozzle exit and during die swell/expansion.

Evaluation of ATLHAMC12 subchannel code for total loss of flow scenario

The ALTHAMC12 subchannel code is a new subchannel code developed by the ALVEL company. The code is intended for DNBR safety analyses of the Czech nuclear power plants. In order to validate the code, a code to code comparison with THALES and VIPRE-01 is provided in this work. The reactor core model was developed and set of initial and boundary conditions has been adopted from a reference study. The comparison is done for steady state nominal parameters and Total Loss of Flow (TLOF) type of accident. The results show that ALTHAMC12 provides a good agreement with the reference codes in the terms of MDNBR value and its positions in the reactor core.

Impact induced compression and decompression waves in porous meta-materials modeled using a continuum theory of phase transitions

Porous meta-materials with both regular and random microstructure are of intense research interest today due to their interesting dynamical properties, including but not limited to, their acoustic band structure, shock absorption properties, and fracture toughness. Some of these materials can exist in a rarefied or densified state depending on the state of stress, and recover their original configuration after a cycle of loading and unloading. Often, they exhibit a hysteretic stress–strain response under quasistatic uniaxial compression. As such, many aspects of their mechanical behavior can be captured using a continuum theory of phase transitions. In this work, the dynamical behavior of such materials is explored. It is shown that the impact problem for these materials can result in propagating shocks, phase boundaries, and fans. The impact problems admit multiple solutions for the same set of initial and boundary conditions leading to non-uniqueness. This non-uniqueness can be remedied using a nucleation criterion and kinetic laws, as is known from the continuum theory of phase transitions. The fan solutions which arise in decompressive impact problems have not received much attention in the literature and may be regarded as a novel contribution of this work. The analysis presented here may have applications in the dynamic behavior of a broad class of porous materials including architected truss-like metastructures and random fiber networks.

Uncovering personal circadian responses to light through particle swarm optimization

Background and objectivesKronauer's oscillator model of the human central pacemaker is one of the most commonly used approaches to study the human circadian response to light. Two sources of error when applying it to a personal light exposure have been identified: (1) as a populational model, it does not consider inter-individual variability, and (2) the initial conditions needed to integrate the model are usually unknown, and thus subjectively estimated. In this work, we evaluate the ability of particle swarm optimization (PSO) algorithms to simultaneously uncover the optimal initial conditions and individual parameters of a pre-defined Kronauer's oscillator model. MethodsA Canonical PSO, a Dynamic Multi-Swarm PSO and a novel modification of the latter, namely Hierarchical Dynamic Multi-Swarm PSO, are evaluated. Two different target models (under a regular and an irregular schedule) are defined, and the same realistic light profile is fed to them. Based on their output, a fitness function is proposed, which is minimized by the algorithms to find the optimum set of parameters and initial conditions of the model. ResultsWe demonstrate that Dynamic Multi-Swarm and Hierarchical Dynamic Multi-Swarm algorithms can accurately uncover personal circadian parameters under both regular and irregular schedules, but as expected, optimization is easier under a regular schedule. Circadian parameters play the most important role in the optimization process and should be prioritized over initial conditions, although assessment of the impact of misestimating the latter is recommended. The log-log linear relationship between mean absolute error and computational cost shows that the number of particles to use is at the discretion of the user. ConclusionsThe robustness and low errors achieved by the algorithms support their further testing, validation and systematic application to empirical data under a regular or irregular schedule. Uncovering personal circadian parameters can improve the assessment of the circadian status of a person and the applicability of personalized light therapies, as well as help to discover other factors that may lie behind the interindividual variability in the circadian response to light.

Symbolic state estimation in bounded timed labeled Petri nets

This paper addresses the state estimation of timed discrete event systems, where the occurrence of an event is associated with a time delay and the initial state of the system belongs to a set of possible initial states. A discrete event system is modeled with a bounded timed labeled Petri net whose unobservable subnet is acyclic, and the behavior of the system under a global time clock can be observed. The procedure for state estimations of partially observed Petri nets is refined by the introduction of time in discrete event systems. We apply the symbolic techniques to the representation of states and transition relations of bounded timed labeled Petri nets. Then we propose an online algorithm for the computation of state estimations generated by timed observations.

IMEX_SfloW2D v2: a depth-averaged numerical flow model for volcanic gas–particle flows over complex topographies and water

Abstract. We present developments to the physical model and the open-source numerical code IMEX_SfloW2D (de' Michieli Vitturi et al., 2019). These developments consist of a generalization of the depth-averaged (shallow-water) fluid equations to describe a polydisperse fluid–solid mixture, including terms for sedimentation and entrainment, transport equations for solid particles of different sizes, transport equations for different components of the carrier phase, and an equation for temperature/energy. Of relevance for the simulation of volcanic mass flows, vaporization and entrainment of water are implemented in the new model. The model can be easily adapted to simulate a wide range of volcanic mass flows (pyroclastic avalanches, lahars, pyroclastic surges), and here we present its application to transient dilute pyroclastic density currents (PDCs). The numerical algorithm and the code have been improved to allow for simulation of sub- to supercritical regimes and to simplify the setting of initial and boundary conditions. The code is open-source. The results of synthetic numerical benchmarks demonstrate the robustness of the numerical code in simulating transcritical flows interacting with the topography. Moreover, they highlight the importance of simulating transient in comparison to steady-state flows and flows in 2D versus 1D. Finally, we demonstrate the model capabilities to simulate a complex natural case involving the propagation of PDCs over the sea surface and across topographic obstacles, through application to Krakatau volcano, showing the relevance, at a large scale, of non-linear fluid dynamic features, such as hydraulic jumps and von Kármán vortices, to flow conditions such as velocity and runout.

A physical memristor-based chaotic system and its application in colour image encryption scheme

This work proposes a physical memristor (TaOx) based new 4D chaotic system with 3D multi-scroll, no equilibrium point, spiking behaviour, coexistence bursting oscillation and multistability. Using this physical memristor-based chaotic system, a novel and efficient colour image encryption algorithm has been developed using a unique box scrambling method and bit-wise XOR operations. Many interesting and new dynamics of a material-based memristive chaotic system are reported here, like 3D multi-scroll chaotic attractors, bursting characteristics, multistability, a neuronal system like spiking behaviours etc using Lyapunov spectrum and bifurcation plots. It is observed that the number of scrolls is changed with the total simulation time. This novel memristive chaotic system has limit cycles with controllable spikes and bursting oscillation. In addition, the system shows chaotic bursting oscillation under a different set of parameters and initial conditions. The coexistence of the bursting phenomena is studied here. The bursting and spiking characteristic is important for material-based memristors in neuromorphic applications. 3D Chaotic multi-scroll and multistability properties make the image encryption method more efficient and secure. Such characteristics are rare in physical memristor-based chaotic systems and using this, the image encryption algorithm is also rare in recent findings. Therefore, a new secure image encryption algorithm for colour images is proposed here, based on the unique box scrambling method, bitwise XOR operation and pseudo-random number generation using the proposed memristive chaotic system. Various tests like NPCR, UACI, histogram analysis, correlation study, information entropy analysis, robustness against external noise, etc have been performed to check the algorithm’s robustness and efficiency and test the capability to resist statistical and differential attacks.

The level-crossing problem of a weakly damped particle in quadratic potential well under harmonic excitation

Escape and level-crossing are fundamental and closely related problems in transient dynamics. Often, when a particle reaches a critical displacement, its escape becomes inevitable. Therefore, escape models based on truncated potentials are often used, resulting in similar problems to level-crossing formulations. Two different types of dynamics can be identified, leading to different kinds of level-crossing depending on the relationship between the damping and the excitation level. The first one (“fast escape”) is mainly governed by the initial energy of the system, which is determined through the initial conditions. The second one (“slow escape”) is governed by the beatings determined through the relationship between external excitation and damping. An analytic approach for estimating the size and location of the safe basins (SBs) in the plane of the initial conditions (ICs) of a 1-DOF externally excited oscillator is suggested. It enables the identification of the set of ICs where the particle never reaches a certain threshold under the given excitation. The SBs depend on the damping coefficient and the excitation’s amplitude, frequency, and phase. Nonetheless, one can describe the essential properties of an SBs in the case of the almost resonant excitation using only two parameters: the forced response amplitude and the damping coefficient ratio to the difference between the natural and the excitation frequencies. Although the analysis is performed for a linear oscillator, it provides insight into the rush erosion process of the SBs (“Dover cliff” phenomenon), described previously only for nonlinear systems. The analysis reveals that the “Dover cliff” phenomenon is related to the decay rate of the transient motion and that it can occur even in linear systems too. From the engineering point of view, the rush erosion of the SBs is critical in noisy environments where devices operating in regions close to the “Dover cliff” are unsafe. Due to its simplicity, the proposed mechanical model might be generic for further analysis of the escape and level-crossing problems considering various nonlinearities (e.g., Coulomb friction, small polynomial-type nonlinearities of the restoring force, or constant restoring force). Possible applications include but are not limited to avoiding collisions for systems with clearances and durability analysis of brittle materials subjected to noisy loads.

Mathematical and numerical modelling of rapid transients at partially lifted sluice gates

In the present paper, we study the mathematical and numerical modelling of rapid transients at partially lifted sluice gates in the context of one-dimensional Shallow water Equations. First, improved exact solutions of the dam-break problem with partially lifted gate are presented, assuming (i) the dependence of the gate contraction coefficient on the upstream flow depth, and (ii) a viable definition of the submerged flow equation. We show that an exact dam-break solution always exists for any set of initial conditions, but there are also initial conditions for which the solution is multiple. To cope with this case, a novel disambiguation criterion based on the continuous dependence of the solution on the initial conditions is used to select the physically congruent choice amongst the alternatives. Finally, we present a one-dimensional Finite Volume numerical model for the approximate solution of the Shallow water Equations equipped with an approximate Riemann solver for the sluice gate treatment at cells interfaces. The numerical experiments show that the embedding of the steady state gate equations (equilibrium approach) into the approximate Riemann solver leads to unsatisfactory dam-break simulations, while a novel relaxed version of the gate equations (non-equilibrium approach) supplies results that are in agreement with both the novel exact solutions and the laboratory dam-break results available from the literature.

Reflection of internal gravity waves in the form of quasi-axisymmetric beams

Preservation of the angle of reflection when an internal gravity wave hits a sloping boundary generates a focusing mechanism if the angle between the direction of propagation of the incident wave and the horizontal is close to the slope inclination (near-critical reflection). This paper provides an explicit description of the leading approximation of the unique Leray solution to the near-critical reflection of internal waves from a slope in the form of a beam wave. More precisely, our beam wave approach allows to construct a fully consistent and Lyapunov stable approximate solution, L2-close to the Leray solution, in the form of a beam wave, within a certain (nonlinear) time-scale. To the best of our knowledge, this is the first result where a mathematical study of internal waves in terms of spatially localized beam waves is performed.A beam wave is a linear superposition of rapidly oscillating plane waves, where the high frequency of oscillation is proportional to the inverse of a power of the small parameter measuring the weak amplitude of waves.Being localized in the physical space thanks to rapid oscillations (and high variations of the modulus of the wavenumber), beams are physically more relevant than plane waves/packets of waves, whose wavenumber is nearly fixed (microlocalized). At the mathematical level, this marks a strong difference between the previous plane waves/packets of waves analysis and our approach.The main novelty of this work is to exploit the spatial localization of beam waves to exhibit a spatially localized, physically relevant solution and to improve the previous mathematical results from a twofold perspective: 1) our beam wave approximate solution is the sum of a finite number of terms, each of them is a consistent solution to the system and there is no artificial/non-physical corrector; 2) thanks to the absence of artificial correctors (used in the previous results) and to the special structure of the nonlinear term, we can push the expansion of our solution to next orders, so improving the accuracy and enlarging the consistency time-scale.Finally, our results provide a set of initial conditions localized on rays, for which the Leray solution maintains approximately in L2 the same localization.

Grid-Free Computation of Probabilistic Safety With Malliavin Calculus

This work concerns continuous-time, continuous-space stochastic dynamical systems described by stochastic differential equations (SDE). It presents a new approach to compute probabilistic safety regions, namely sets of initial conditions of the SDE associated to trajectories that are safe with a probability larger than a given threshold. The approach introduces a functional that is minimised at the border of the probabilistic safety region, then solves an optimisation problem using techniques from Malliavin Calculus, which computes such region. Unlike existing results in the literature, the new approach allows one to compute probabilistic safety regions without gridding the state space of the SDE.

Set-Valued Stabilization of Reaction-Diffusion Model by Chemotherapy and or Radiotherapy

This paper aims to control partial differential equations, modeling cancer chemotherapy and or radiotherapy, so in order to asymptotically stabilize the tumor density. Viability kernel of general model on set of initial condition is used to solve the control problem, and characterize the control solution as regulation law of regulation map. Three models from the literature are considered to simulate the results. The first model includes chemotherapy effect on logistic tumor proliferation, while the second one demonstrates radiotherapy effect on exponential tumor increasing, whereas the third one models the effects of the combination of chemotherapy and radiotherapy on Gompertzian tumor growth.

Sensitivity analysis of the hyperparameters of an ensemble Kalman filter application on a semi-distributed hydrological model for streamflow forecasting

Data Assimilation (DA) is an important step for improving prediction accuracy and real-time correction of hydrological models for operational forecasting purposes. The Ensemble Kalman filter (EnKF) is one of the most popular techniques used to address the issues of updating the model states and parameters by creating a novel set of initial conditions in real-time. This study aims at identifying optimal seasonal EnKF parametrizations to reduce the uncertainty associated with the initial conditions in a semi-distributed hydrological model of a snow-dominated catchment in Canada. Sensitivity analysis is performed to evaluate the effects of the EnKF individual hyperparameters (temperature, precipitation and inflow uncertainties) and the updating of three state variables (vadose zone, saturated zone and snowpack) on the skill of short-term (up to 9 days lead-time) forecasts. Results show that the performance of the forecasts is sensitive to the individual hyperparameters and particularly so to the temperature uncertainty, which varies between seasons. Additionally, the forecast skill is related to the choice of the state variables to be updated depending on the season. The vadose zone state variable displays higher importance and sensitivity than the other states, and the results indicate that all state variables should not be systematically updated on this catchment and with the implemented hydrological model. Finally, combining the best hyperparameter values with the optimal combination of state variables to update, insight is provided on the success of the data assimilation scheme that is evaluated on a rolling horizon using a set of seasonal rules to gain forecast performance over the span of multiple years.