Several results in the existing literature establish Euclidean density theorems of the following strong type. These results claim that every set of positive upper Banach density in the Euclidean space of an appropriate dimension contains isometric copies of all sufficiently large elements of a prescribed family of finite point configurations. So far, all results of this type discussed linear isotropic dilates of a fixed point configuration. In this paper, we initiate the study of analogous density theorems for families of point configurations generated by anisotropic dilations, i.e., families with power-type dependence on a single parameter interpreted as their size. More specifically, we prove nonisotropic power-type generalizations of a result by Bourgain on vertices of a simplex, a result by Lyall and Magyar on vertices of a rectangular box, and a result on distance trees, which is a particular case of the treatise of distance graphs by Lyall and Magyar. Another source of motivation for this paper is providing additional evidence for the versatility of the approach stemming from the work of Cook, Magyar, and Pramanik and its modification used recently by Durcik and the present author. Finally, yet another purpose of this paper is to single out anisotropic multilinear singular integral operators associated with the above combinatorial problems, as they are interesting on their own.

A proportion of the heat added to a body of rock during prograde metamorphism will be absorbed in the chemical work of metamorphic recrystallization. When and where heat is so absorbed will affect the exact thermal histories of the rocks, and hence the metamorphic textures. This paper reports the results of modelling of the inter-relations between reaction progress and thermal histories in a rock column. The results suggest that volumes of rock undergoing reaction at any moment act as heat sinks and absorb heat from the surrounding rock, that reaction generally takes place close to the temperature at which nucleation took place, and that steady heating of a rock pile can give rise to a reaction history in which spurts of reaction are separated by ‘quiet’, non-reactive intervals.

This article is intended to fill in the blank of the numerical schemes with second-order convergence accuracy in time for nonlinear Stokes’ first problem for a heated generalized second grade fluid with fractional derivative. A linearized difference scheme is proposed. The time fractional-order derivative is discretized by second-order shifted and weighted Gr¨unwald-Letnikov difference operator. The convergence accuracy in space is improved by performing the average operator. The presented numerical method is unconditionally stable with the global convergence order of in maximum norm, where τ and h are the step sizes in time and space, respectively. Finally, numerical examples are carried out to verify the theoretical results, showing that our scheme is efficient indeed.

In the Netherlands the present-day thermal gradient in the shallow subsurface (i.e. the upper few 100 m), is around 20°C km–1, whereas at depths between 0.5 and 3 km it is ∼33°C km–1. This large contrast in the gradient between shallow and deeper parts of the subsurface occurs throughout the country and cannot be explained by either systematic thermal property changes with depth or the depositional setting of the region. In this paper we use a 1D thermal model for the crust and demonstrate that this observed temperature-depth trend most likely reflects a transient condition inherited from past climate change. It is shown that the prolonged cold period during the Weichselian (∼110–10 kya) and the subsequent warmer conditions during the Holocene account for the increase in the thermal gradient with depth. Moreover, we demonstrate that thermal history further back in time still influences the present-day subsurface temperature. Geothermal climate-change influences on these long time scales have not been documented before for the Netherlands.

The numerical solution of the harmonic heat map flow problems with blowup in finite or infinite time is considered using an adaptive moving mesh method. A properly chosen monitor function is derived so that the moving mesh method can be used to simulate blowup and produce accurate blowup profiles which agree with formal asymptotic analysis. Moreover, the moving mesh method has finite time blowup when the underlying continuous problem does. In situations where the continuous problem has infinite time blowup, the moving mesh method exhibits finite time blowup with a blowup time tending to infinity as the number of mesh points increases. The inadequacy of a uniform mesh solution is clearly demonstrated.

The thermal properties of rocks in the upper crust of the Qaidam basin are given based on measurements of 98 thermal conductivities and 50 heat production values. Nineteen new measured heat flow data were obtained from thermal conductivity data and systematic steady-state temperature data. This paper contributes 28 calculated heat flow values for the basin for the first time. Examination of 47 heat flow values, ranging from 31.3 to 70.4 mW/m2 with an average value of 52.6±9.6 mW/m2, gives the heat flow distribution character of the basin: high heat flows over 60 mW/m2 are distributed in the western and central parts of the basin. Lower heat flow values are found in the eastern part and north marginal area of the basin, with values less 40 mW/m2. The Qaidam basin heatflow data show a linear relationship between heatflow and heat production, based on thermal structure analysis. The thermal structure of the lithosphere is characterized as having a ‘hot crust’ but ‘cold mantle’. Heat production in the upper crust is a significant source of heat in the basin and contributes up to 56.8% of the surface heat flow. The heat flow province is of great geophysical significance, and the thermal structure of the area gives clues about the regional geodynamics. Study of the Qaidam basin thermal structure shows that the crust has been highly active, particularly during its most recent geological evolution. This corresponds to Himalayan tectonic movements during latest Eocene to Quaternary times in the region of the Qinghai–Tibet Plateau. Since the Qaidam basin is in the northeastern area of the Qinghai–Tibet Plateau, the heat flow values and the thermal structure of the basin may give some insight into the thermal state of the plateau, and study of thermal regime of the Qaidam basin could in turn provide useful information about the tectonics of the Qinghai–Tibet Plateau.

We have calculated the thermal boundary resistance at the GaN/SiC, GaN/sapphire and GaN/AlN interfaces in the diffuse mismatch approximation. The obtained values were then used to examine the effect of the thermal boundary resistance on heat diffusion in AlGaN/GaN heterostructure field-effect transistors. The results show that the thermal boundary resistance at the device layer interfaces can strongly influence the temperature rise in the device channel.

Charnockite and homophanous leptynite are two quartz–feldspar neosomes in the late Archaean granulite-migmatite Eastern Ghats terrane of Orissa, India. Three phases of deformation and metamorphism are recognised to have preceded a late phase, or phases in which deformation was not intense. An early granulite facies event (D1–M1) produced basic granulites and khondalite (sillimanite-garnet aluminous paragneiss). A second event (D2–M2) involved some retrogression but temperatures and pressures remained high (possibly c. 750°C—>5 kb). D3–M3 was associated with the development of open folds (F3) with axial planar shear zones in pinched antiforms; temperatures and pressures were also falling (c. 650°C— 4kb), but the shear zones acted as a control on the development of firstly homophanous leptynite, and secondly charnockite. In both cases, neosomes of quartz and potassium feldspar have myrmekitic textures and intergranular occurrence. The palaeosome became strained and garnet–biotite and garnet–biotite–clinopyroxene ± orthopyroxene mineral assemblages were formed in association with the development, respectively, of homophanous leptynite and charnockite. The persistence of straining in the palaeosome and the presence of poikilitic textures indicate that this typical assemblage does not represent one in thermodynamic equilibrium. This has important consequences for geothermobarometry.

The structural control on neosome development reflects a regional characteristic where shear zones are the site of peralkaline plutons, fenitisation, carbonatites and epigenetic graphite development. The peculiar features of charnockite are seen as just one of several aspects related to the fluxing of hot CO2-dominated fluids from either the deep crust or mantle during the late Archaean development of the Indian craton.