Search

This paper presents numerical simulations of the Taylor vortex flow under the influence of an externally applied alternating axial mass flux (through-flow) in a Taylor–Couette system with axial periodic boundary conditions. Such an axially modulating flow can lead to a significant variation in the onset of primary instabilities. Depending on the system parameters, the effect can be both stabilizing and destabilizing, i.e., shifting the bifurcation threshold to larger or smaller control parameters, respectively. It is found that the system response around the primary instability is sensitive to and critically influenced by an alternating mass flux, particularly the modulation frequency. We show that such an alternating axial flow represents an easily and, more importantly, precisely controllable key parameter to change the nonlinear system response from subcritical to supercritical behavior and vice versa. Furthermore, we observe different parameter regimes with regular and irregular intermittent flow dynamics. [ABSTRACT FROM AUTHOR]

We illustrate how an alternating magnetic field can restrict and suppress the generation of vortex formation in ferrofluidic Couette flow. Therefore, the initial rotating outer cylinder (inner cylinder at rest) is brought to an abrupt stop, which results in the generation of more complex vortex dynamics in the system, evolving out of the initially fully laminar flow regime. The generated vortex flow structures appear to be axisymmetric Taylor vortices. Different stages during the spin-down process are described and characterised through dynamic quantities, such as the kinetic energy, cross-flow energy, and angular velocity flux. The presence of an alternating magnetic field modifies these dynamics during the spin-down, which is mainly dominated by the modulation amplitude of the alternating field. While moderate modulation amplitudes tend to minimise the vortex formation, i.e. weaken the flow dynamics, large modulation amplitudes suppress any vortex formation. The driving frequency only has a minor effect in general, but may allow to select between different flow pattern within the process. [ABSTRACT FROM AUTHOR]

We present direct numerical simulations of the Taylor–Couette flow of a dilute polymer solution when only the inner cylinder rotates and the curvature of the system is moderate (η=0.77). The finitely extensible nonlinear elastic-Peterlin closure is used to model the polymer dynamics. The simulations have revealed the existence of a novel elasto-inertial rotating wave characterized by arrow-shaped structures of the polymer stretch field aligned with the streamwise direction. This rotating wave pattern is comprehensively characterized, including an analysis of its dependence on the dimensionless Reynolds and Weissenberg numbers. Other flow states having arrow-shaped structures coexisting with other types of structures have also been identified for the first time in this study and are briefly discussed. This article is part of the theme issue 'Taylor–Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 2)'. [ABSTRACT FROM AUTHOR]

Many natural and industrial flows are subject to time-dependent boundary conditions and temporal modulations (e.g. driving frequency), which significantly modify the dynamics compared with their static counterparts. The present problem addresses ferrofluidic wavy vortex flow in Taylor-Couette geometry, with the outer cylinder at rest in a spatially homogeneous magnetic field subject to an alternating modulation. Using a modified Niklas approximation, the effect of frequency modulation on nonlinear flow dynamics and appearing resonance phenomena are investigated in the context of either period doubling or inverse period doubling. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

There is a huge number of natural and industrial flows, which are subjected to time-dependent boundary conditions. The flow of a magnetic fluid under the influence of temporal modulations is such an example. Here, we perform numerical simulations of ferrofluidic Couette flow subject to time-periodic modulation (with frequency Ω H ) in a spatially homogeneous magnetic field and report how such a modulation can lead to a significant Reynolds number Re enhancement. Consider a modified Niklas approximation we explain the relation between modulation amplitude, driving frequency and stabilization effect. From this, we describe the system response around the primary instability to be sensitive/critical by an alternating field. We detected that such an alternating field provides an easy and in particular accurate controllable key parameter to trigger the system to change from subcritical to supercritical and vice versa. Our findings provide a framework to study other types of magnetic flows driven by time-dependent forcing. [ABSTRACT FROM AUTHOR]

Shared caches in multicore processors introduce serious difficulties in providing guarantees on the real-time properties of embedded software due to the interaction and the resulting contention in the shared caches. To address this problem, we develop a new schedulability analysis for real-time multicore systems with shared caches, globally scheduled by Earliest Deadline First (EDF) and Fixed Priority (FP) algorithms. We construct an integer programming formulation, which can be transformed to an integer linear programming formulation, to calculate an upper bound on cache interference exhibited by a task within a given execution window. Using the integer programming formulation, an iterative algorithm is presented to obtain the upper bound on cache interference a task may exhibit during one job execution. The upper bound on cache interference is subsequently integrated into the schedulability analysis to derive a new schedulability condition. A range of experiments is performed to investigate how the schedulability is degraded by shared cache interference. We also evaluate the schedulability performance of EDF against FP scheduling over randomly generated tasksets. Our empirical evaluations show that EDF is better than FP scheduling in terms of the number of task sets deemed schedulable. [ABSTRACT FROM AUTHOR]

• Up to date most numerical simulations considere ferrofluids as point size objects. • Real ferrofluids consist of a suspension of particles with a finite size. • Particle-particle interactions, agglomeration and chain formation are crucial. • Consider agglomeration effects flow structures and dynamics significant change. • Primary (supercritical) onsets of flow instabilities are altered. We study flow structure modifications due to agglomeration , aggregation and chain formation, also known as elongational flow effect for the flow of a ferrofluid in the gap between two concentric rotating cylinders. The system is subjected to either transverse, axial and oblique magnetic field. Consider elongational flow the torque is found to increase or decrease with variation of elongational flow parameter. Furthermore the 3D flow structures themselves are modified, e.g. resulting in variation of different energy portions/contents and the angular momentum transport. The detected modifications are explained by the fact that real ferrofluids consist of a suspension of particles with a finite size in an almost ellipsoid shape as well as with particle–particle interactions that tend to form chains of various lengths and also have a tendency to agglomerate. To come close to such realistic situation for ferrofluids, we consider elongational flow effects incorporated by the symmetric part of the velocity gradient field tensor, which can be scaled by a so-called transport coefficient λ 2 . The complexity of structures and modifications depend on the magnetic field configuration. In general complexer oblique fields result in stronger interactions and modifications. [ABSTRACT FROM AUTHOR]

Time-dependent boundary conditions are ubiquitous in numerous natural and industrial flows. However, to date, the influence of such temporal modulations has been given minor attention. This research addresses ferrofluidic Couette flow in between co-rotating cylinders in a spatially homogeneous magnetic field subject to time-periodic modulation. Using a modified Niklas approximation, we study the effect of amplitude and frequency modulation onto the transition scenarios between different toroidal flow structures, non-propagating vortex (nV) states, via vortex merging and splitting. Thereby, the system response appears to be quite sensitive/dependent on the driving frequency Ω H , which can cause a notable "delay" in the system response. Further, as a result of the inertia of the ferrofluid, resisting the fast-changing accelerating Kelvin force, new, temporal nV states appear within an alternating field. These states are unstable under static fields. Finally, we show that within the same nV state, while keeping similar flow dynamics, large discrepancies in angular momentum and torque can be observed. • Ferrofluidic Couette flow subject to time-periodic modulation introduced by an external applied alternating magnetic field. • Modified Niklas approximation to study the effect of amplitude and frequency modulation onto the transition scenarios between different toroidal flow structures, non-propagating vortex (nV) states, via vortex merging and splitting. • The system is found to respond quite sensitive on the driving frequency, which can cause a notable delay in the system response. [ABSTRACT FROM AUTHOR]

This study treats with the influence of a symmetry-breaking transversal magnetic field on the nonlinear dynamics of ferrofluidic Taylor-Couette flow – flow confined between two concentric independently rotating cylinders. We detected alternating ‘flip’ solutions which are flow states featuring typical characteristics of slow-fast-dynamics in dynamical systems. The flip corresponds to a temporal change in the axial wavenumber and we find them to appear either as pure 2-fold axisymmetric (due to the symmetry-breaking nature of the applied transversal magnetic field) or involving non-axisymmetric, helical modes in its interim solution. The latter ones show features of typical ribbon solutions. In any case the flip solutions have a preferential first axial wavenumber which corresponds to the more stable state (slow dynamics) and second axial wavenumber, corresponding to the short appearing more unstable state (fast dynamics). However, in both cases the flip time grows exponential with increasing the magnetic field strength before the flip solutions, living on 2-tori invariant manifolds, cease to exist, with lifetime going to infinity. Further we show that ferrofluidic flow turbulence differ from the classical, ordinary (usually at high Reynolds number) turbulence. The applied magnetic field hinders the free motion of ferrofluid partials and therefore smoothen typical turbulent quantities and features so that speaking of mildly chaotic dynamics seems to be a more appropriate expression for the observed motion. [ABSTRACT FROM AUTHOR]

We investigate transient behaviors induced by magnetic fields on the dynamics of the flow of a ferrofluid in the gap between two concentric, independently rotating cylinders. Without applying any magnetic fields, we uncover emergence of flow states constituted by a combination of a localized spiral state in the top and bottom of the annulus and different multi-cell flow states with toroidally closed vortices in the interior of the bulk. However, when a magnetic field is presented, we observe the transient behaviors between multi-cell states passing through two critical thresholds in a strength of an axial (transverse) magnetic field. Before the first critical threshold of a magnetic field strength, multi-stable states with different number of cells could be observed. After the first critical threshold, we find the transient behavior between the three- and two-cell flow states. For more strength of magnetic field or after the second critical threshold, we discover that multi-cell states are disappeared and a localized spiral state remains to be stimulated. The studied transient behavior could be understood by the investigation of various quantities including a modal kinetic energy, a mode amplitude of the radial velocity, wavenumber, angular momentum, and torque. In addition, the emergence of new flow states and the transient behavior between their states in ferrofluidic flows indicate that richer and potentially controllable dynamics through magnetic fields could be possible in ferrofluic flow. [ABSTRACT FROM AUTHOR]

We investigate the Taylor-Couette system where the radius ratio is close to unity. Systematically increasing the Reynolds number, we observe a number of previously known transitions, such as one from the classical Taylor vortex flow (TVF) to wavy vortex flow (WVF) and the transition to fully developed turbulence. Prior to the onset of turbulence, we observe intermittent bursting patterns of localized turbulent patches, confirming the experimentally observed pattern of very short wavelength bursts (VSWBs). A striking finding is that, for a Reynolds number larger than that for the onset of VSWBs, a new type of intermittently bursting behavior emerges: patterns of azimuthally closed rings of various orders. We call them ring-bursting patterns, which surround the cylinder completely but remain localized and separated in the axial direction through nonturbulent wavy structures. We employ a number of quantitative measures including the cross-flow energy to characterize the ring-bursting patterns and to distinguish them from the background flow. These patterns are interesting because they do not occur in the wide-gap Taylor-Couette flow systems. The narrow-gap regime is less studied but certainly deserves further attention to gain deeper insights into complex flow dynamics in fluids. [ABSTRACT FROM AUTHOR]

Despite time-dependent boundary conditions being ubiquitous in natural and industrial flows, to date the influence of such temporal modulations (e.g. with driving frequency Ω H) has been given minor attention. The present problem addresses ferrofluidic Couette flow in between counter-rotating cylinders in a spatially homogeneous magnetic field subject to time-periodic modulation. Such a modulation can lead to a significant inner Reynolds number (R e i ) enhancement for both, either helical and toroidal flow structures. Using a modified Niklas approximation, the effect of low- and high-frequency modulation onto the primary instabilities, stability boundaries as well as on the non-linear oscillations that may occur is investigated. Focusing on bi-stable co-existing solutions, around their stability thresholds quite complex non-linear system response and flow dynamics is detected. For the system remaining supercritical always a single solution is selected by Ω H , while crossing the bifurcation thresholds within a modulation period the triggered system response is more complex, reaching from alternation between different solutions towards the appearance of intermittent behavior. • Natural and industrial flows subjected to time-dependent boundary conditions are ubiquitous. • Main focus of this work is the study of ferrofluidic Couette flow subject to time-periodic modulation introduced by an external applied alternating magnetic field. • Such a modulation is found to enhance the critical Reynolds number on the primary stabilization threshold in the system of various flow structures. • Further a variation in the modulation frequency allows to trigger different non-linear system response. • The latter reaching from alternation of different solutions, either between two supercritical solutions or between supercritical and subcritical solutions, and eventually the appearance of intermittent behavior. • These findings provide a framework to study other types of magnetic flows driven by time-dependent forcing. [ABSTRACT FROM AUTHOR]

This work investigates the transition between different traveling helical waves (spirals, SPIs) in the setup of differentially independent rotating cylinders. We use direct numerical simulations to consider an infinite long and periodic Taylor–Couette apparatus with fixed axial periodicity length. We find so-called mixed-cross-spirals (MCSs), that can be seen as nonlinear superpositions of SPIs, to establish stable footbridges connecting SPI states. While bridging the bifurcation branches of SPIs, the corresponding contributions within the MCS vary continuously with the control parameters. Here discussed MCSs presenting footbridge solutions start and end in different SPI branches. Therefore they differ significantly from the already known MCSs that present bypass solutions (Altmeyer and Hoffmann 2010 New J. Phys.12 113035). The latter start and end in the same SPI branch, while they always bifurcate out of those SPI branches with the larger mode amplitude. Meanwhile, these only appear within the coexisting region of both SPIs. In contrast, the footbridge solutions can also bifurcate out of the minor SPI contribution. We also find they exist in regions where only one of the SPIs contributions exists. In addition, MCS as footbridge solution can appear either stable or unstable. The latter detected transient solutions offer similar spatio-temporal characteristics to the flow establishing stable footbridges. Such transition processes are interesting for pattern-forming systems in general because they accomplish transitions between traveling waves of different azimuthal wave numbers and have not been described in the literature yet. [ABSTRACT FROM AUTHOR]

Abstract: Tasks in an embedded system are scheduled either preemptively or non-preemptively. In case of preemptive scheduling, interferences on the cache of the preempted and preempting task may extend the execution times. The corresponding delay is referred to as cache-related preemption delay (CRPD). Lee et al. presented a CRPD analysis using the concept of useful cache block (UCB): a cache block is useful if it may be in the cache before a program point and may be reused after this point. If a preemption occurs at that point, the number of additional cache misses is bounded by the number of UCBs. An upper bound on the CRPD of the whole task is thus given by the program point with the largest set of UCBs. In this article, we provide a survey of the state of the art techniques to bound the CRPD, based on, but not limited to UCBs. Based on this survey we present an alternative definition of UCBs to improve the CRPD bounds substantially. [Copyright &y& Elsevier]

This work provides a numerical investigations of propagating vortex flow states (pVs) for ferrofluidic Couette flow with small aspect ratio and fixed non-rotating end-walls. The system is subjected to oblique magnetic fields as superposition of axial and transverse orientated fields. Such field configuration breaks the basic system symmetries and renders all flow structures to be inherently three-dimensional with complexer flow dynamics. Under oblique field configuration pV states are not direct present at onset. Instead oscillating flow states (oVs) bifurcate out of the stationary state. Basically these oVs hold same symmetries as pVs, which eventually evolve in a smooth transformation out of the oVs. pVs under oblique fields appear periodic or quasi-periodic, which render them topological speaking to exist on either two- or one-dimensional invariant manifolds as 2-torus or limit cycle (1-torus) solutions, respectively. In detail, structural modifications and changes in spatial and temporal behavior for pV solutions are studied with changing the magnetic field strength of the applied magnetic field. [ABSTRACT FROM AUTHOR]

• This article provides a numerically investigation of the impact of either pure axial or pure transverse (breaking the basic system symmetries) magnetic fields onto ferrofluidic Couette flow of propagating vortex states (pVs) in a finite-length cavity with small aspect ratio and fixed non-rotating end-walls. • Under axial magnetic fields, as is the case for no magnetic field, remain pure 2D structures without any azimuthal variation involved, while for transversal field pVs are fully 3D. • We find pVs to appear in a pitchfork bifurcation in two different configurations. • Either as symmetric (in vortex generation, propagation and annihilation) pVs with respect to system mid-height, or as asymmetric pVs, i.e. with alternation in vortex cycle generation, propagation and annihilation in upper and lower system half. • Asymmetric pVs are only found to exist stable in transversal magnetic fields. • Both, symmetric and asymmetric pVs are stable coexisting over certain parameter range. • All pVs are periodic states and therefore topological identified as limit cycle solutions. Numerical investigations of propagating vortex states (pVs) for ferrofluidic Couette flow with small aspect ratio and fixed non-rotating end-walls are presented. We study structural modifications and changes in spatial and temporal behavior for pV solutions. The system is subjected to either pure axial or pure transverse magnetic field, with the latter already breaking the basic system symmetries. While under axial magnetic field pVs remain basically the same, they are found to appear in various configurations with different symmetry variation in flow structure and flow dynamics under symmetry breaking transversal magnetic field. pVs appearing in a pitchfork bifurcation are found either symmetric or asymmetric/alternating, regarding the full cycle of vortex generation, propagation and annihilation, in upper and lower system half. [ABSTRACT FROM AUTHOR]

• Flow dynamic changes due to interaction of radial mass flux and magnetic field. • Magnetic field stabilizes basic states; Radial flow can be both (de-)stabilizing. • Combination of both effects result in further variation in stability and bifurcation. We study ferrofluidic Taylor Couette flow under the influence of radial inflow and outflow in combination with an external applied magnetic field in a finite-length cavity via direct numerical simulations. As is the case for no magnetic field, the base state (cylindrical Couette flow and modified circular-Couette flow in presence of a transverse magnetic field component, respectively) with an external magnetic field is stabilized for any radial inflow and strong radial outflow, while the system becomes slightly destabilized for weak radial outflow. The particular parameter range for destabilization depends on the field strength of the applied magnetic field. Slightly increasing the field strength shrinks the range, while it grows for larger field strengths. In general, a larger field strength tends to minimize and compensate the effect of any radial flow, resulting in bifurcation thresholds (critical Reynolds number vs. radial flow) which have less curvature, i.e. they are more flat. We elucidate the origin of this effect to be in the symmetry breaking nature of the transverse magnetic field itself. Azimuthal velocity isocontours are shifted different strong due to radial flow, either in the part of the annulus that is aligned with the direction of the applied magnetic field or perpendicular to it. In particular, the modulation amplitude in the isocontours perpendicular to the field increase. As a result the flow is locally stabilized with different strength, so that the overall stabilization is weaker relative to the situation without any applied field. This diminishing curvature effect with variation of the radial flow becomes more pronounced with stronger applied magnetic fields. [ABSTRACT FROM AUTHOR]

In this paper we investigate the effects of an externally imposed axial mass flux (axial pressure gradient, axial through flow) on ferrofluidic Taylor-Couette flow under the influence of either an axial or a transverse magnetic field. Without an imposed axial through flow, due to the symmetry-conserving axial field and the symmetry-breaking transverse field, it gives rise to various vortex flows in ferrofluidic Taylor-Couette flow such as wavy Taylor vortex flow (wTVF), wavy spiral vortex flow (wSPI) and wavy vortex flows (wTV F H x and wSP I H x ), which are typically produced by a nonlinear interaction of rotational, shear and magnetic instabilities. In addition, when an axial through flow is imposed to a ferrofluidic Taylor-Couette flow in the presence of either an axial or a transverse magnetic field, previously unknown new helical vortex structures are observed. In particular, we uncover 'modulated Mixed-Cross-Spirals' with a combination of at least three different dominant azimuthal wavenumbers. Emergence of such new flow states indicates richer but potentially more controllable dynamics in ferrofluidic flows, i.e., an imposed axial through flow will be a new controllable factor/parameter in applications of a ferrofluidic and magnetic flows flow. [ABSTRACT FROM AUTHOR]

We investigate fundamental nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined be-tween two concentric independently rotating cylinders - consider small aspect ratio by solving the ferro-hydrodynamical equations, carrying out systematic bifurcation analysis. Without magnetic field, we find steady flow patterns, previously observed with a simple fluid, such as those containing normal one- or two vortex cells, as well as anomalous one-cell and twin-cell flow states. However, when a symmetry-breaking transverse magnetic field is present, all flow states exhibit stimulated, finite two-fold mode. Various bifurcations between steady and unsteady states can occur, corresponding to the transitions between the two-cell and one-cell states. While unsteady, axially oscillating flow states can arise, we also detect the emergence of new unsteady flow states. In particular, we uncover two new states: one contains only the azimuthally oscillating solution in the configuration of the twin-cell flow state, and an-other a rotating flow state. Topologically, these flow states are a limit cycle and a quasiperiodic solution on a two-torus, respectively. Emergence of new flow states in addition to observed ones with classical fluid, indicates that richer but potentially more controllable dynamics in ferrofluidic flows, as such flow states depend on the external magnetic field. [ABSTRACT FROM AUTHOR]

It is known that in classical fluids turbulence typically occurs at high Reynolds numbers. But can turbulence occur at low Reynolds numbers? Here we investigate the transition to turbulence in the classic Taylor-Couette system in which the rotating fluids are manufactured ferrofluids with magnetized nanoparticles embedded in liquid carriers. We find that, in the presence of a magnetic field transverse to the symmetry axis of the system, turbulence can occur at Reynolds numbers that are at least one order of magnitude smaller than those in conventional fluids. This is established by extensive computational ferrohydrodynamics through a detailed investigation of transitions in the flow structure, and characterization of behaviors of physical quantities such as the energy, the wave number, and the angular momentum through the bifurcations. A finding is that, as the magnetic field is increased, onset of turbulence can be determined accurately and reliably. Our results imply that experimental investigation of turbulence may be feasible by using ferrofluids. Our study of transition to and evolution of turbulence in the Taylor-Couette ferrofluidic flow system provides insights into the challenging problem of turbulence control. [ABSTRACT FROM AUTHOR]

Model-Driven Engineering (MDE) is widely applied in the industry to develop new software functions and integrate them into the existing run-time environment of a Cyber-Physical System (CPS). The design of a software component involves designers from various viewpoints such as control theory, software engineering, safety, etc. In practice, while a designer from one discipline focuses on the core aspects of his field (for instance, a control engineer concentrates on designing a stable controller), he neglects or considers less importantly the other engineering aspects (for instance, real-time software engineering or energy efficiency). This may cause some of the functional and non-functional requirements not to be met satisfactorily. In this work, we present a co-design framework based on timing tolerance contract to address such design gaps between control and real-time software engineering. The framework consists of three steps: controller design, verified by jitter margin analysis along with co-simulation, software design verified by a novel schedulability analysis, and the run-time verification by monitoring the execution of the models on target. This framework builds on CPAL (Cyber-Physical Action Language), an MDE design environment based on model-interpretation, which enforces a timing-realistic behavior in simulation through timing and scheduling annotations. The application of our framework is exemplified in the design of an automotive cruise control system. [ABSTRACT FROM AUTHOR]

The primary challenge in the majority of heat transfer applications, in view of design perspective, is to maximize the thermal transport with the minimum generation of entropy. This paper addresses the numerical investigation of buoyant convection and entropy generation processes of Al2O3–water nanofluid inside a vertical annular configuration having two coaxial cylinders. The vertical cylindrical surfaces are imposed with sinusoidal thermal distribution having different phase deviation and amplitude, while the horizontal surfaces are retained adiabatic. In this analysis, the numerical computations of conservation equations governing the physical process are performed using the time‐splitting technique and line overrelaxation methods. Detailed numerical simulations are performed for broad ranges of critical parameters, such as Rayleigh number, phase deviation, amplitude ratio, and nanoparticle volume fraction. From the vast numerical experiments, we systematically identified the suitable parameter regimes at which enhanced thermal transport has been produced with minimum entropy generation. Furthermore, the critical quantities, such as thermal dissipation and entropy generation, could be effectively monitored by a particular selection of phase deviation (γ) and amplitude ratio (ε). It has been identified that these parameters have more influence on thermal transport as well as entropy production as compared to other parameters of the analysis. [ABSTRACT FROM AUTHOR]

This survey provides an overview of the scientific literature on timing verification techniques for multi-core real-time systems. It reviews the key results in the field from its origins around 2006 to the latest research published up to the end of 2018. The survey highlights the key issues involved in providing guarantees of timing correctness for multi-core systems. A detailed review is provided covering four main categories: full integration, temporal isolation, integrating interference effects into schedulability analysis, and mapping and allocation. The survey concludes with a discussion of the advantages and disadvantages of these different approaches, identifying open issues, key challenges, and possible directions for future research. [ABSTRACT FROM AUTHOR]