Solution Of Heat Diffusion Equation Research Articles

Data-Specific Anisotropic Mexican Hat Wavelets for Structure-Preserving Image Processing

This paper proposes a novel approach for structure-sensitive image processing based on the rigorous mathematical derivation of data-specific anisotropic Mexican hat wavelets (DAM). Our DAM is derived from the negative first-order derivative of the fundamental solution of heat diffusion equation with respect to time, which not only shares similar properties with Mexican hat wavelet but also intrinsically embeds the image-specific properties. Through the scale-aware DAM transform and its inverse transform, we are capable of conducting structure-sensitive image processing. Our key idea is to represent the images as undirected graphs, whose edge weights are governed by the normalized intensity/color differences within the local neighboring pixel window. Based on the rigorous theory of global graph Laplacian and heat diffusion, our original DAM can also encode the local/global structure of images. We employ the Krylov subspace technique to reduce the computational cost of our DAM transform. Furthermore, aiming at various structure-preserving image processing applications such as filtering, detail enhancement, tone manipulation, and stylization, we conduct comprehensive experiments and make quantitative comparisons with other state-of-the-art methods, which demonstrate the versatility and superiority of our method.

Predicting the effective thermal conductivities of composite materials and porous media by machine learning methods

Composite materials have a wide range of engineering applications, and their effective thermal conductivities are important thermo-physical properties for real applications. The traditional methods to study effective thermal conductivities of composite materials, such as the effective medium theory, the direct solution of heat diffusion equation, or the Boltzmann transport equation, are all based on developing good physical understanding of heat transfer mechanisms in those composite materials. In this work, we take a completely different approach to predict the effective thermal conductivities of composite materials using machine learning methods. With a set of trustable data, the support vector regression (SVR), Gaussian process regression (GPR) and convolution neural network (CNN) are employed to train models that can predict the effective thermal conductivities of composite materials. We find that the models obtained from SVR, GPR, and CNN all have a better performance than the Maxwell-Eucken model and the Bruggeman model in terms of predicting accuracy. Our work demonstrates that machine learning methods are useful tools to fast predict the effective thermal conductivities of composite materials and porous media if the training data set is available. The machine learning approach also has the potential to be generalized and applied to study other physical properties of composite materials.

Strain localization during discontinuous plastic flow at extremely low temperatures

• The paper deals with an extended, physically based, multiaxial constitutive model of discontinuous plastic flow, including new feature of strain localization at near 0 K temperatures in polycrystalline materials. • Another new feature defines the drop of stress being entirely determined by dislocations density before and after the serration. • Regular way of nucleation and free unconstrained glide of slip bands is observed within the sample, in the absence of phase transformation. • Contrary to former views, strong coupling of discontinuous plastic flow with fcc-bcc phase transformation in metastable materials is observed. The phenomenon of strain localization in the course of discontinuous plastic flow (DPF) at extremely low temperatures is investigated. DPF is observed mainly in fcc metals and alloys strained in cryogenic conditions, practically down to absolute zero. These materials undergo at low temperatures a process similar to dynamic strain ageing, manifested by the so called serrated yielding (DPF). DPF is attributed to the mechanism of local catastrophic failure of lattice barriers (including Lomer–Cottrell locks), under the stress fields related to the accumulating edge dislocations. Failure of LC locks leads to massive motion of released dislocations, accompanied by step-wise increase of the strain rate (macroscopic slip) and drastic drop of stress. Recent experiments indicate strong strain localization in the form of shear bands propagating along the sample. The plastic power dissipated in the shear band is partially converted to heat, which results in a local drastic increase of temperature promoted by the so-called thermodynamic instability (nearly adiabatic process). The Dirac-like temperature function is measured by two thermometers located in the gage length of the sample. Spatio-temporal correlation indicates smooth shear band propagation, as long as the process of phase transformation remains on hold. A physically based multiaxial constitutive model presented in the paper describes both DPF and strain localization, accompanied by temperature distribution represented by Green-like solution of heat diffusion equation. The model accounts for the thermodynamic background, including phonon mechanism of heat transport, accompanied by specific heat vanishing with the temperature approaching absolute zero. Experimental identification of parameters of the constitutive model is carried out. A projection of the model to the range where the phase transformation takes place is discussed.

Physical properties of acerola and blueberry pulps

In this work, some physical properties of acerola and blueberry pulps were determined. The density was determined by the pycnometer method; the electrical conductivity using a conductivimeter; the thermal diffusivity by a method based on the analytical solution of heat diffusion equation; the specific heat capacity by a modified method of mixtures; and the thermal conductivity from the knowledge of other properties. Results showed that the density of acerola pulp, in the temperature range between 303 and 353K, varies between 0.97 and 1.03kgm−3; for blueberry it ranged between 0.98 and 1.05kgm−3. Electrical conductivity was between 1.69 and 8.48mScm−1 for acerola pulp and between 0.79 and 3.86mScm−1 for blueberry. Specific heat, thermal diffusivity and thermal conductivity of acerola pulp at approximately 313K showed values of 4172.49Jkg−1K−1, 1.53×10−7m2s and 0.65Wm−1K−1, respectively. For blueberry, these values were 4050.39Jkg−1K−1, 1.51×10−7m2s and 0.64Wm−1K−1.

Optical-microwave interaction modeling in high-temperature superconducting films

Optical-microwave interaction in high-T/sub c/ superconductors is investigated for performing basic optoelectronic functions in cryogenic environment. A fast bolometric photoresponse in conjunction with the unique electrical properties of high-temperature superconductor (HTS) materials allows us to explore a series of novel optoelectronic devices with low-noise/low-power and high-speed/high-frequency characteristics. After reviewing the HTS photoresponse categories, we describe the fast bolometric photoresponse and its condition with heat transfer analysis. The analytical solution of heat diffusion equation for an HTS strip mounted on a substrate will be presented for three different type of optical sources. Then the effect of optical irradiation will be incorporated in the two-fluid model by thermomodulation concept in order to model the interaction of optical radiation with electrical signal. The current-field relationship and the supercurrent response time are evaluated in the presence of both optical and electrical signals. Our numerical simulations for YBaCuO film demonstrate the possibility of RF harmonic generation when the laser beam is modulated by the RF signal in the presence of dc bias current and RF signal mixing when the HTS film is fed by a time-harmonic microwave source. The developed model can also be used to study optical control and tunability techniques for HTS microwave devices for analog signal processing.

A local analysis of solidification in horizontal continuous casting

Quasi‐steady solidification near origin of strand. Analytical solution of heat diffusion equation in solid subject to boundary conditions at solidification front and at mould. Stability of solutions. Two‐phase region (mushy‐zone) in alloy casting.

Laser irradiation effects on high dose implanted Cu and Pb in polycrystalline aluminum

Abstract High dose implanted Cu and Pb profiles show considerable rearrangement after Q-switched ruby laser pulse irradiation, when observed using 1.6 MeV 4He+ Rutherford backscattering. Cu rearranged profiles may be interpreted as due to a Cu atom diffusion into a liquid Aluminum phase (under a condition of constant concentration at the side of the implanted profile toward the bulk of the sample). Such a liquid phase is predicted by the solution of heat diffusion equation, allowing for changes of state. Numerical results are in agreement with the observed threshold for the energy density of the laser pulse in order to see a redistributed profile and yield a numerical value for the diffusion coefficient of Cu in liquid Aluminum (DL ⋍ 1.7·10−3 cm2/sec). Pb profiles undergo a more complicated process, during which, in addition to Pb-atom diffusion into the bulk, Pb atoms also move to the surface of the Al sample as a consequence of a low segregation coefficient. Experimental results are also consistent with...

Heat flow in an aluminium sample undergoing melting and resolidification under irradiation by a nanosecond laser pulse

Abstract The characteristic times and lengths involved in the problem of heat flow through a semiinfinite Al sample irradiated with nanosecond laser pulses are discussed with reference both to the underlying physics and to the numerical solution of heat diffusion equation. Laser pulse energies allow sample melting, but no vaporization. The numerical solution proceeds via subdividing the sample into layers of thickness Δx. After describing the mechanism of heat flow through these layers, the Δx-dependence of some significant quantities is discussed and found negligible. The temperature time behaviour at different sample depths is given, showing latent heat effects; results for the solid-liquid interface motion, cooling rates, energy deposition in the front layer are presented and their dependence on the laser pulse parameters discussed qualitatively. Finally the connection of the present calculations with some recent experiments is discussed and the conditions under which neglecting of undercooling effects is a consistent procedure are ascertained.