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Boundary value problems of heat conduction
01 Jan 1968-
About: The article was published on 1968-01-01 and is currently open access. It has received 846 citations till now. The article focuses on the topics: Boundary value problem & Thermal conduction.
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TL;DR: In this article, a rigorous pseudo-two-dimensional model to simulate the cycling performance of a lithium ion cell is compared with two simplified models and the advantage of using simplified models is illustrated and their limitations are discussed.
661 citations
Cites methods from "Boundary value problems of heat con..."
...A very good approximation of the concentration profile within the solid phase was presented independently by Wang et al. [9] and Subramanian et al. [10] based on the integral approach outlined by Ozisik [ 11 ]....
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...In all these models, the concentration of lithium within the solid phase was either calculated using the superposition principle [ 11 ] or solved for rigorously, using a pseudo second dimension along the radius of the particle....
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TL;DR: In this article, the authors explored solutions to the He production-diffusion equation to characterize the response of apatite He ages to thermal histories involving partial He retention, and showed that He ages within the partial retention zone ultimately achieve a balance between He production and loss, yielding a steady state age.
551 citations
TL;DR: In this paper, it was shown that non-Newtonian properties of lava are mainly responsible for the shape of lava flows and not just the surface properties of the lava itself.
Abstract: Summary It is postulated that lavas are non-Newtonian liquids with a yield stress and that it is the yield stress which determines flow dimensions. An appropriate theory was developed for the unconfined flow of ideal Bingham liquids on inclined planes. The occurrence of structures similar to IevCes on lava flows was predicted. The theory was verified by laboratory measurements on flows of suspensions of kaolin. These flows showed similarities to lava flows. Data from lava flows was also found to be in general agreement with the theory which was then used to interpret the shapes of two lunar lava flows. It was possible to estimate yield stresses and flow rates for these lavas. 1. Effects limiting the flow of lava Lava flows show great variations in size, shape and surface features. The final form of a flow must be determined by the physical properties of the lava, its temperature and rate of extrusion and local conditions such as gravitational field strength and topography. The aim of the work presented in this paper is to isolate the parameters which have the greatest effect on flow morphology and to elucidate the relationship between the conditions at the start of a flow and the final form of the flow. At present there is no detailed knowledge of this kind but, were it available, the value of air- and satellite-photographs of lava flows would be greatly enhanced. The hypothesis on which this work is based is that flowing lava is a non-Newtonian liquid and it is its non-Newtonian properties which are mainly responsible for the shapes of flows. If lava were an ideal Newtonian liquid it would flow downhill and would continue to flow even after the supply at the vent had ceased until it ponded in a depression. Furthermore the flow would spread laterally until it was restricted by topography or until surface tension prevented spreading by which time it would be extremely thin. Observations show that lava does not behave like this. Commonly it comes to rest on a slope as soon as the supply of fresh lava ceases and many flow fronts are high and steep although unconfined by topographic features. It is clear that there is some process which limits the flow of lava, brings it to rest on slopes and prevents its lateral spreading. The most obvious and apparently generally accepted process is the solidification of lava due to cooling. For this to be a feasible process the time taken for the development of a strong enough skin to prevent lateral motion must be realistic. The solid skin of a flow experiences an outward force due to the hydrostatic pressure of the lava and this must be balanced by an inward force which is the result of tension in the curved skin. If the skin can withstand the tension the lava will not flow laterally.
447 citations
25 Sep 2006
TL;DR: A brief discussion of key sources of power dissipation and their temperature relation in CMOS VLSI circuits, and techniques for full-chip temperature calculation with special attention to its implications on the design of high-performance, low-power V LSI circuits is presented.
Abstract: The growing packing density and power consumption of very large scale integration (VLSI) circuits have made thermal effects one of the most important concerns of VLSI designers The increasing variability of key process parameters in nanometer CMOS technologies has resulted in larger impact of the substrate and metal line temperatures on the reliability and performance of the devices and interconnections Recent data shows that more than 50% of all integrated circuit failures are related to thermal issues This paper presents a brief discussion of key sources of power dissipation and their temperature relation in CMOS VLSI circuits, and techniques for full-chip temperature calculation with special attention to its implications on the design of high-performance, low-power VLSI circuits The paper is concluded with an overview of techniques to improve the full-chip thermal integrity by means of off-chip versus on-chip and static versus adaptive methods
420 citations
Cites methods from "Boundary value problems of heat con..."
...The heat diffusion equation is in general used to describe the heat conduction in a chip and calculate the temperature profile [19]...
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Book•
01 Jul 2009TL;DR: A detailed discussion of magnetic field gradient methods applied to Magnetic Resonance Imaging (MRI) is included, alongside extensive referencing throughout, providing a timely, definitive book to the subject, ideal for researchers in the fields of physics, chemistry and biology.
Abstract: Translational motion in solution, either diffusion or fluid flow, is at the heart of chemical and biochemical reactivity. Nuclear Magnetic Resonance (NMR) provides a powerful non-invasive technique for studying the phenomena using magnetic field gradient methods. Describing the physical basis of measurement techniques, with particular emphasis on diffusion, balancing theory with experimental observations and assuming little mathematical knowledge, this is a strong, yet accessible, introduction to the field. A detailed discussion of magnetic field gradient methods applied to Magnetic Resonance Imaging (MRI) is included, alongside extensive referencing throughout, providing a timely, definitive book to the subject, ideal for researchers in the fields of physics, chemistry and biology.
371 citations