Deterministic Heat Research Articles

Deterministic Heat Death of Universe and Blackhole Information Paradox with Wormhole Negative Temperatures

Deterministic Heat Death of Universe and Blackhole Information Paradox with Wormhole Negative Temperatures

The predictive management in campus heating system based on deep reinforcement learning and probabilistic heat demands forecasting

As a promising technology for replacing the rule-based decision-making in region heating systems (RHS), deep reinforcement learning (DRL) is a practical solution to identify the optimal control for heating equipment. However, as residential customers perform more casual energy-consumption behaviors, the intermittency and volatility of heat demands make managing heat supply and storage much harder for DRL agents. This study proposes a novel predictive management method for campus heating systems (CHS) with air-source heat pumps (AHP) and thermostatic water tanks. The novelty of the proposed method lies in the combination of the heat demands forecasting model and DRL-based adaptively controlling for heat supply equipment, which is firstly proposed to improve the heating supply reliability and reduce the storage dependence for CHS. Specifically, an enhanced rule, namely minimum length hamming encoding, and an input array constructing method is introduced to deal with discrete feature data and then improve the accuracy of deterministic heat demands forecasting based on long-short term memory (LSTM), and the Kernel density estimation (KDE) are employed to obtain the prediction intervals (PIs) from H-step ahead heat demands forecasting series. Followed by these, the twin delayed deep deterministic policy gradient, a model-free DRL control algorithm, is adopted for adaptively adjusting the output flow rate of AHP and then the storage of the hot water tank. To demonstrate the validity of the proposed method, a case study is presented where a campus heat demands forecasting achieves a maximum accuracy gain of 4.52%, and an optimal AHP operating controlling determined from PIs achieves a better cost reduction and supply reliability, which is superior over the conventional method using real-time heat demands or deterministic forecasting results as input.

Deterministic Manipulation of Heat Flow via Three-Dimensional-Printed Thermal Meta-Materials for Multiple Protection of Critical Components.

Heat dissipation is necessary for the safer operation of high-power electronic devices and high-capacity batteries. Thermal meta-materials can efficiently manipulate heat flow by molding natural materials into specific structures. In this study, we construct a three-dimensional-printed meta-material structure with efficient and deterministic heat conduction through combining the 2D boron nitride (BN) with nano-diamond (DM) bridging. A research of thermal conductivity and dielectric properties exhibits that the nanosized diamond-bridged and oriented 2D boron nitride endows efficient heat transfer and maintains low dielectric loss with low filler loading. The composites loaded with 19 wt% BN platelets and 1 wt% DM have the highest thermal conductivity of 3.687 W/(m·K) in the heat flow orientation, while the thermal conductivity is only 0.632 W/(m·K) in the vertical heading of heat flow. The thermal conductive networks with thermal meta-materials based on the structural characteristics have been designed to secure critical device components from the heat source and dissipate heat flow in a definite way. The infrared images show that the temperature difference of monitoring points in different directions on the BN-oriented composite substrate is 9 °C, which realizes the protection of the heat source and key components. This study shows the latent capacity of 3D-printed structured materials for critical device component protection and heat administration applications in electronic devices and electric equipment.

X-ray magnetic linear dichroism as a probe for non-collinear magnetic state in ferrimagnetic single layer exchange bias systems

Ferrimagnetic alloys are extensively studied for their unique magnetic properties leading to possible applications in perpendicular magnetic recording, due to their deterministic ultrafast switching and heat assisted magnetic recording capabilities. On a prototype ferrimagnetic alloy we demonstrate fascinating properties that occur close to a critical temperature where the magnetization is vanishing, just as in an antiferromagnet. From the X-ray magnetic circular dichroism measurements, an anomalous ‘wing shape’ hysteresis loop is observed slightly above the compensation temperature. This bears the characteristics of an intrinsic exchange bias effect, referred to as atomic exchange bias. We further exploit the X-ray magnetic linear dichroism (XMLD) contrast for probing non-collinear states which allows us to discriminate between two main reversal mechanisms, namely perpendicular domain wall formation versus spin-flop transition. Ultimately, we analyze the elemental magnetic moments for the surface and the bulk parts, separately, which allows to identify in the phase diagram the temperature window where this effect takes place. Moreover, we suggests that this effect is a general phenomenon in ferrimagnetic thin films which may also contribute to the understanding of the mechanism behind the all optical switching effect.

Fault Detectability Conditions for Linear Deterministic Heat Equations

With the rise of distributed and connected modern engineering systems, the need for safe and reliable distributed parameter systems is becoming increasingly prominent. However, fault detection of partial differential equation systems remains relatively unexplored compared to its ordinary differential equation counterpart. In this letter, we attempt to advance such research by addressing the fault detectability problem for linear deterministic heat equations with additive faults. Fault detectability examines whether a fault is detectable given a system model and measured outputs. Essentially, similar to controllability and observability, fault detectability is an intrinsic property of the system and has to be verified before designing diagnostic algorithms. In this context, we derive fault detectability conditions for heat equations by utilizing the singular values of fault-to-output transfer function. We illustrate the proposed detectability conditions on battery thermal fault diagnosis case study.

Mesoscale modeling of the crystallization parameters identification during the iron-based catalyst preparation process: the dilute concentration case

ABSTRACT In this paper we model the mesoscale crystallization of the crystals in the dilute solution concentration in the sense that the microscale model is a stochastic process and meanwhile the macroscale model is a deterministic heat diffusion process. The crystallization process includes the steps of nucleation, nucleus radial growth and nuclei aggregation. In the case of the dilute solution concentration we may neglect the effect of the nuclei aggregation, i.e. the crystallization neglects the impingement. The coupled model of crystallization and heat diffusion show the mesoscale characteristic between the micro- and macro- aspect. Furthermore we reformulate the simultaneous identification of nucleation rate and crystal growth speed in the stochastic birth-growth process by the inverse approaches. The regularization strategy is adopted to implement the numerical inversion of the inverse problem. Finally, numerical examples are provided to show the effectiveness of the proposed algorithm.

A Monte Carlo-Based Probabilistic Barrier Failure Model for Arbitrary Fire Environment

Failure of building assemblies is a combined results of both heat attack and the mechanical response of the assembly components. The latter could change the integrity of a fire barrier and the pattern of heat transfer. The prediction of failure becomes more complicated when it comes to non-standard fires where real-world experiments are limited. 2-D or 3-D numerical models may provide useful results but their sophistication of use still drives the needs for simple models that offer quick results. A probabilistic barrier failure model is developed to simulate the dynamic process of barrier failure and reflect its stochastic nature. The model comprises a deterministic heat transfer and component response submodel that calculates one-dimensional heat transfer and component responses in fire such as the fall-off of gypsum boards. Further, a Monte Carlo-based probabilistic barrier failure model is created by sampling the influential factors that affect the failure of components. The fire barriers applied in the model include light timber frame and light steel frame assemblies as well as cross laminated timber assembly, but the model is open to other assemblies where data are available. The model results are validated against five room fire tests with good agreements, and an example calculation demonstrates that in a real fire the failure of fire barriers may occur earlier or later than that in the standard fire.

Can riparian vegetation shade mitigate the expected rise in stream temperatures due to climate change during heat waves in a human-impacted pre-alpine river?

Abstract. Global warming has already affected European rivers and their aquatic biota, and climate models predict an increase of temperature in central Europe over all seasons. We simulated the influence of expected changes in heat wave intensity during the 21st century on water temperatures of a heavily impacted pre-alpine Austrian river and analysed future mitigating effects of riparian vegetation shade on radiant and turbulent energy fluxes using the deterministic Heat Source model. Modelled stream water temperature increased less than 1.5 ∘C within the first half of the century. Until 2100, a more significant increase of around 3 ∘C in minimum, maximum and mean stream temperatures was predicted for a 20-year return period heat event. The result showed clearly that in a highly altered river system riparian vegetation was not able to fully mitigate the predicted temperature rise caused by climate change but would be able to reduce water temperature by 1 to 2 ∘C. The removal of riparian vegetation amplified stream temperature increases. Maximum stream temperatures could increase by more than 4 ∘C even in annual heat events. Such a dramatic water temperature shift of some degrees, especially in summer, would indicate a total shift of aquatic biodiversity. The results demonstrate that effective river restoration and mitigation require re-establishing riparian vegetation and emphasize the importance of land–water interfaces and their ecological functioning in aquatic environments.

Joint Effect of Solar UVB and Heat Stress on the Seasonal Change of Egg Hatching Success in the Herbivorous False Spider Mite (Acari: Tenuipalpidae).

Seasonal population dynamics of an herbivorous mite has been documented in terms of the relationship between thermoresponses and temporal biological factors such as resource availability or predation risk. Although recent studies emphasize the deleterious effects of solar ultraviolet-B (UVB; 280-320 nm wavelengths) radiation on plant-dwelling mites, how UVB affects mite population remains largely unknown. On a wild shrub Viburnum erosum var. punctatum in Kyoto, an herbivorous false spider mite, Brevipalpus obovatus Donnadieu, occurs only in autumn. Females of this species lay one-third of their eggs on upper leaf surfaces. Oviposition on upper surfaces is beneficial for avoiding predation by phytoseiids, but exposes eggs to solar UVB and heat stress. To test the hypothesis that the seasonal occurrence of this mite is determined by interactions between solar UVB radiation and temperature, we examined variation in egg hatching success under near-ambient and UV-attenuated sunlight conditions from spring to autumn. The UV-attenuation significantly improved hatching success. However, most eggs died under heat stress regardless of UV treatments in July and August. We established a deterministic heat stress-cumulative UVB dose-egg hatching success response model, which we applied to meteorological data. The model analyses illustrated lower and higher survivability peaks in late May and October, respectively, which partly corresponded to data for annual field occurrence, indicating the importance of solar UVB radiation and heat stress as determinants of the seasonal occurrence of this mite.

Simulation of Dendritic Growth in Multicomponent Aluminium Alloys by Point Automata Method

A numerical model is developed to describe the dendritic growth of multicomponent aluminium alloys, based on a coupled deterministic continuum mechanics heat and species transfer model and a stochastic localized growth model that takes into account the undercooling temperature, curvature, kinetic, and thermodynamic anisotropy. The stochastic model receives temperature and concentration information from the deterministic model and the deterministic heat and species diffusion equations receive the solid fraction information from the stochastic model. The heat and species transfer models are solved on a regular grid by the standard explicit Finite Difference Method (FDM). The dendritic growth model of multicomponent alloy [1,2] is solved by a novel Point Automata (PA) approach [3,4] where the regular cells of the Cellular Automata (CA) method are replaced by the randomly distributed points and neighborhood configuration, similar as appears in meshless methods. The PA method was developed in order to circumvent the mesh anisotropy problem, associated with the classical CA method. The present paper extends our previous developments of Pa method to multicomponent alloys. A comparison of the results, obtained by the PA and CA method is shown for Al-5.3% Zn-2.35% Mg-1.35% Cu-0.5% alloy.

Random homogenisation of a highly oscillatory singular potential

In this article, we consider the problem of homogenising the linear heat equation perturbed by a rapidly oscillating random potential. We consider the situation where the space-time scaling of the potential's oscillations is \textit{not} given by the diffusion scaling that leaves the heat equation invariant. Instead, we treat the case where spatial oscillations are much faster than temporal oscillations. Under suitable scaling of the amplitude of the potential, we prove convergence to a deterministic heat equation with constant potential, thus completing the results previously obtained in \cite{MR2962093}.

Dissipation and entropy production in deterministic heat conduction of quasi-one-dimensional systems

We explore the consequences of a deterministic microscopic thermostat-reservoir contact mechanism. With different temperature reservoirs at each end of a two-dimensional system, a heat current is produced and the system has an anomalous thermal conductivity. The microscopic form for the local heat flux vector is derived and both the kinetic and potential contributions are calculated. The total heat flux vector is shown to satisfy the continuity equation. The properties of this nonequilibrium steady state are studied as functions of system size and temperature gradient, identifying key scaling relations for the local fluid properties and separating bulk and boundary effects. The local entropy density calculated from the local equilibrium distribution is shown to be a very good approximation to the entropy density calculated directly from the velocity distribution even for systems that are far from equilibrium. The dissipation and kinetic entropy production and flux are compared quantitatively and the differing mechanisms discussed within the Bhatnagar-Gross-Krook approximation. For equal-temperature reservoirs the entropy production near the reservoir walls is shown to be proportional to the local phase space contraction calculated from the tangent space dynamics. However, for unequal temperatures, the connection between local entropy production and local phase space contraction is more complicated.

Solution of Dendritic Growth in Steel by the Novel Point Automata Method

The aim of this paper is the simulation of dendritic growth in steel in two dimensions by a coupled deterministic continuum mechanics heat and species transfer model and a stochastic localized phase change kinetics model taking into account the undercooling, curvature, kinetic, and thermodynamic anisotropy. The stochastic model receives temperature and concentration information from the deterministic model and the deterministic heat, and species diffusion equations receive the solid fraction information from the stochastic model. The heat and species transfer models are solved on a regular grid by the standard explicit Finite Difference Method (FDM). The phase-change kinetics model is solved by a novel Point Automata (PA) approach. The PA method was developed [1] in order to circumvent the mesh anisotropy problem, associated with the classical Cellular Automata (CA) method. The PA approach is established on randomly distributed points and neighbourhood configuration, similar as appears in meshless methods. A comparison of the PA and CA methods is shown. It is demonstrated that the results with the new PA method are not sensitive to the crystallographic orientations of the dendrite.

Thermal performance of a naturally ventilated building using a combined algorithm of probabilistic occupant behaviour and deterministic heat and mass balance models

This study explores the role of occupant behaviour in relation to natural ventilation and its effects on summer thermal performance of naturally ventilated buildings. We develop a behavioural algorithm (the Yun algorithm) representing probabilistic occupant behaviour and implement this within a dynamic energy simulation tool. A core of this algorithm is the use of Markov chain and Monte Carlo methods in order to integrate probabilistic window use models into dynamic energy simulation procedures. The comparison between predicted and monitored window use patterns shows good agreement. Performance of the Yun algorithm is demonstrated for active, medium and passive window users and a range of office constructions. Results indicate, for example, that in some cases, the temperature of an office occupied by the active window user in summer is up to 2.6 °C lower than that for the passive window user. A comparison is made with results from an alternative behavioural algorithm developed by Humphreys [H.B. Rijal, P. Tuohy, M.A. Humphreys, J.F. Nicol, A. Samuel, J. Clarke, Using results from field surveys to predict the effect of open windows on thermal comfort and energy use in buildings, Energy and Buildings 39 (7) (2007) 823-836.]. In general, the two algorithms lead to similar predictions, but the results suggest that the Yun algorithm better reflects the observed time of day effects on window use (i.e. the increased probability of action on arrival).

Shock waves in an augmented one-dimensional atom chain

We derive here a simplified discrete one-dimensional model describing some important features of shock waves. In order to avoid expensive multidimensional simulations, one-dimensional models are commonly used, but the existing ones often exhibit some spurious physically irrelevant behaviour. Here we build a one-dimensional model with perturbations arising from mean higher-dimensional behaviour. The coupling of the system with a deterministic heat bath in the Kac–Zwanzig fashion allows us to derive a generalized Langevin equation for the system, without a priori fixing the temperature in the shocked region. This deterministic problem with several degrees of freedom is then reduced to a simpler stochastic problem with memory. Some numerical results are provided, which illustrate and confirm the qualitative correctness of the model.

Comment on “Can Disorder Induce a Finite Thermal Conductivity in 1D Lattices?”

In a recent paper [Phys. Rev. Lett. 86, 63 (2001)], Li et al have reported that the nonequilibrium heat conducting steady state of a disordered harmonic chain is not unique. In this comment we point out that for a large class of stochastic heat baths the uniqueness of the steady state can be proved, and therefore the findings of Li et al could be either due to their use of deterministic heat baths or insufficient equilibration times in the simulations. We give a simple example where the uniquness of the steady state can be explicitly demonstrated.

Three-dimensional flow field downstream of an embedded stator in a multistage axial flow compressor: Part 2: Deterministic stress and heat flux distribution and average-passage equation system

The results from the area traverse measurements of the unsteady velocity and total temperature downstream of the second stator of a three-stage axial flow compressor have been correlated to derive various deterministic stress and heat flux terms. These terms are consistent with those arising from the average-passage equation system of Adamczyk. The deterministic periodic stress and heat flux terms were found to be larger than the aperiodic terms for both the normal and the shear components. Consequently the terms involving the aperiodic components in the average-passage equations could be neglected for stator exit and rotor inlet flow modelling. The deterministic periodic normal and shear stresses were seen to be most significant in the stator wakes away from the end-wall regions. The most significant shear stress correlation was between the axial and the tangential velocity components. Since the correlations involving the radial component were small, it is postulated that the dominant mechanism for mixing (in the radial direction) is due to the steady deterministic radial velocity. All three components of deterministic heat flux were found to be significant in this flow field, especially in the wakes. The dominant terms in the average-passage equation system away from the end walls were due to the tangential gradient compared with the radial gradient terms and both the terms were found to be of equal importance in the hub and casing end-wall regions.

Water temperature modelling in a small forested stream: implication of forest canopy and soil temperature

The demand for comprehensive environmental assessment of river ecosystem has increased for engineers and scientists. Accurate and versatile water temperature models are required to meet this demand. A number of hydrological models take vegetation and soil characteristics into account, but very few temperature models do. The objective of this paper is to incorporate soil temperature and vegetation as input variables in a deterministic heat budget model. The CEQUEAU hydrological and water temperature model was used to simulate water temperature in Catamaran Brook, a small catchment located in central New Brunswick. The model was modified by incorporating soil temperature as a parameter influencing the temperature of interflow, using the so-called force-restore method. Crown closure was also incorporated in the model as a factor influencing locally advected water using a negative exponential function. The modified model simulated daily water temperatures better than the original model. Root-mean-square error for a period of 5 years decreased from 2.10°C with the original model to 1.77°C with the modified model. Nash coefficient increased from 0.78 with the original model to 0.82 with the modified model. An analysis of residuals showed that the modified model is sensitive to additional parameters such as crown closure, especially for short time scales during periods of higher discharge and during extreme meteorological and hydrological events such as tropical storms.Key words: stream temperature, hydrology, deterministic model, CEQUEAU, forestry.

Finite Width For a Random Stationary Interface

We study the asymptotic shape of the solution $u(t,x) \in [0,1]$ to a one-dimensional heat equation with a multiplicative white noise term. At time zero the solution is an interface, that is $u(0,x)$ is 0 for all large positive $x$ and $u(0,x)$ is 1 for all large negitive $x$. The special form of the noise term preserves this property at all times $t \geq 0$. The main result is that, in contrast to the deterministic heat equation, the width of the interface remains stochastically bounded.

Modeling of climate change effects on stream temperatures and fish habitats below dams and near groundwater inputs

A deterministic heat transport model was developed to calculate stream water temperatures downstream of reservoir outlets (tailwaters) and groundwater sources. The model calculates heat exchange between the atmosphere, the water and the sediments and is driven by climate and stream hydrologic parameters. Past and projected climate conditions were used as input to the stream water temperature model. To produce a projected future weather scenario, output from the Columbia University Goddard Institute for Space Studies (GISS) global circulation model (GCM) for a doubling of atmospheric CO2 were used to adjust past (1955–1979) weather parameters. Stream reach lengths, within which water temperatures are suitable for survival or good growth of 28 fish species, were determined for four selected streams. Several alternative upstream inflow conditions were chosen: Discharges from surface (epilimnion) and bottom (hypolimnion) outlets of reservoirs, and two groundwater inflow scenarios. By applying water temperature criteria for fish survival and good growth (Stefanet al., 1993) to simulated stream temperatures, it was possible to estimate stream lengths with suitable habitat. When simulated suitable habitat was compared to actual fish observations, good agreement was found. For projected climate change, the simulations showed how much of the available stream habitat would be lost. In the examples presented the effect of cold hypolimnetic water release from a reservoir or groundwater discharges is felt as far as 48 km (30 miles) downstream from its source, especially in smaller shaded streams. The impact of climate change on stream temperatures below dams is more pronounced when the water release is from the epilimnion (reservoir surface) rather than the hypolimnion (deep water). Examples used for this study show elimination of coldwater habitat for rainbow trout when the upstream release is from the surface of a reservoir, but only reductions of coldwater habitat when the upstream release is from a reservoir hypolimnion.