Multiple Temperature Model Research Articles

An Analytical Multiple-Temperature Model for Flash Laser Irradiation on Single-Layer Graphene.

A Multiple-Temperature Model is proposed to describe the flash laser irradiation of a single layer of graphene. Zhukovsky’s mathematical approach is applied to solve the Fourier heat equations based upon quantum concepts, including heat operators. Easy solutions were inferred with respect to classical mathematics. Thus, simple equations were set for the electrons and phonon temperatures in the case of flash laser treatment of a single layer of graphene. Our method avoids the difficulties and extensive time-consuming nonequilibrium green function method or quantum field theories when applied in a condensed matter. Simple expressions were deduced that could prove useful for researchers.

Multiple temperature model of nonlinear coupled constitutive relations for hypersonic diatomic gas flows

The rotational energy of diatomic gases would be activated by the process of intermolecular collisions in high-temperature hypersonic flows. In this paper, a multi-temperature nonlinear coupled constitutive model has been proposed for simulating the transfer of energy between translational and rotational motions in hypersonic non-equilibrium flows. In this model, the nonlinear coupled constitutive equations are modified by introducing a rotational energy relaxation model and a changeable viscosity ratio related to local temperature. To confirm its accuracy, the new model is applied to investigate steady shock wave structures and high-speed gas flows around a cylinder and across a flat plate. The computational results are compared with the multi-temperature Navier–Stokes (NS) equations, the direct simulation Monte Carlo (DSMC) solutions, and the experiment data. The final results show the new model would reproduce the NS results at low Knudsen numbers but behave quite differently from the NS results as the non-equilibrium degree is enhanced. The new model is in better agreement with the DSMC solutions and the experimental data than the NS solutions in the far-from-equilibrium regions, which demonstrates the potential of the new relaxation model in the simulation of hypersonic non-equilibrium flows.

Optical Generation and Detection of Local Nonequilibrium Phonons in Suspended Graphene.

The measured frequencies and intensities of different first- and second-order Raman peaks of suspended graphene are used to show that optical phonons and different acoustic phonon polarizations are driven out of local equilibrium inside a submicron laser spot. The experimental results are correlated with a first-principles-based multiple temperature model to suggest a considerably lower equivalent local temperature of the flexural phonons than those of other phonon polarizations. The finding reveals weak coupling between the flexural modes with hot electrons and optical phonons. Since the ultrahigh intrinsic thermal conductivity of graphene has been largely attributed to contributions from the flexural phonons, the observed local nonequilibrium phenomena have important implications for understanding energy dissipation processes in graphene-based electronic and optoelectronic devices, as well as in Raman measurements of thermal transport in graphene and other two-dimensional materials.

Multiple temperature model for the information preservation method and its application to nonequilibrium gas flows

The information preservation (IP) method has been successfully applied to various nonequilibrium gas flows. Comparing with the direct simulation Monte Carlo (DSMC) method, the IP method dramatically reduces the statistical scatter by preserving collective information of simulation molecules. In this paper, a multiple temperature model is proposed to extend the IP method to strongly translational nonequilibrium gas flows. The governing equations for the IP quantities have been derived from the Boltzmann equation based on an assumption that each simulation molecule represents a Gaussian distribution function with a second-order temperature tensor. According to the governing equations, the implementation of IP method is divided into three steps: molecular movement, molecular collision, and update step. With a reasonable multiple temperature collision model and the flux splitting method in the update step, the transport of IP quantities can be accurately modeled. We apply the IP method with the multiple temperature model to shear-driven Couette flow, external force-driven Poiseuille flow and thermal creep flow, respectively. In the former two cases, the separation of different temperature components is clearly observed in the transition regime, and the velocity, temperature and pressure distributions are also well captured. The thermal creep flow, resulting from the presence of temperature gradients along boundary walls, is properly simulated. All of the IP results compare well with the corresponding DSMC results, whereas the IP method uses much smaller sampling sizes than the DSMC method. This paper shows that the IP method with the multiple temperature model is an accurate and efficient tool to simulate strongly translational nonequilibrium gas flows.

Reducing Tile Complexity for the Self-assembly of Scaled Shapes Through Temperature Programming

This paper concerns the self-assembly of scaled-up versions of arbitrary finite shapes. We work in the multiple temperature model that was introduced by Aggarwal, Cheng, Goldwasser, Kao, and Schweller (Complexities for Generalized Models of Self-Assembly, SIAM J. Comput. 2005). The multiple temperature model is a natural generalization of Winfree’s abstract tile assembly model, where the temperature of a tile system is allowed to be shifted up and down as self-assembly proceeds. We first exhibit two constant-size tile sets in which scaled-up versions of arbitrary shapes self-assemble. Our first tile set has the property that each scaled shape self-assembles via an asymptotically “Kolmogorov-optimum” temperature sequence but the scaling factor grows with the size of the shape being assembled. In contrast, our second tile set assembles each scaled shape via a temperature sequence whose length is proportional to the number of points in the shape but the scaling factor is a constant independent of the shape being assembled. We then show that there is no constant-size tile set that can uniquely assemble an arbitrary (non-scaled, connected) shape in the multiple temperature model, i.e., the scaling is necessary for self-assembly. This answers an open question of Kao and Schweller (Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2006), pp. 571–580, 2006), who asked whether such a tile set exists.

Multiple temperature kinetic model and gas-kinetic method for hypersonic non-equilibrium flow computations

It is well known that for increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier–Stokes equations lose accuracy. For the high speed diatomic molecular flow in the transitional regime, the inaccuracies are partially attributed to the single temperature approximations in the Navier–Stokes equations. Here, we propose a continuum multiple temperature model based on the Bhatnagar–Gross–Krook (BGK) equation for the non-equilibrium flow computation. In the current model, the Landau–Teller–Jeans relaxation model for the rotational energy is used to evaluate the energy exchange between the translational and rotational modes. Due to the multiple temperature approximation, the second viscosity coefficient in the Navier–Stokes equations is replaced by the temperature relaxation term. In order to solve the multiple temperature kinetic model, a multiscale gas-kinetic finite volume scheme is proposed, where the gas-kinetic equation is numerically solved for the fluxes to update the macroscopic flow variables inside each control volume. Since the gas-kinetic scheme uses a continuous gas distribution function at a cell interface for the fluxes evaluation, the moments of a gas distribution function can be explicitly obtained for the multiple temperature model. Therefore, the kinetic scheme is much more efficient than the DSMC method, especially in the near continuum flow regime. For the non-equilibrium flow computations, i.e., the nozzle flow and hypersonic rarefied flow over flat plate, the computational results are validated in comparison with experimental measurements and DSMC solutions.

Multiple temperature model for near continuum flows

In the near continuum flow regime, the flow may have different translational temperatures in different directions. It is well known that for increasingly rarefied flow fields, the predictions from continuum formulation, such as the Navier-Stokes equations, lose accuracy. These inaccuracies may be partially due to the single temperature assumption in the Navier-Stokes equations. Here, based on the gas-kinetic Bhatnagar-Gross-Krook (BGK) equation, a multi-translational temperature model is proposed and used in the flow calculations. In order to fix all three translational temperatures, two constraints are additionally proposed to model the energy exchange in different directions. Based on the multiple temperature assumption, the Navier-Stokes relation between the stress and strain is replaced by the temperature relaxation term, and the Navier-Stokes assumption is recovered only in the limiting case when the flow is close to the equilibrium with the same temperature in different directions. In order to validate the current model, both the Couette and Poiseuille flows are studied in the transition flow regime.

Analysis of the Far‐Infrared/Submillimeter Polarization Spectrum Based on Temperature Maps of Orion

We compile polarization data on Galactic molecular clouds from instruments spanning the wavelength range 60-1300 μm. The polarization spectrum in these clouds falls from 60 to 350 μm but rises from 350 to 1300 μm. To explain this spectrum, we require a model in which the emission arises from dust grains at multiple temperatures along the line of sight and in which the polarizing efficiency of these grains is correlated with their temperature. In order to test this hypothesis, we collect flux data from the literature and create spectral energy distributions (SEDs) in a region of the Orion A molecular cloud. Dust temperature distributions (DTDs) are estimated from these SEDs on a point-by-point basis within the cloud. We find cold, dense cores associated with submillimeter flux peaks and warm dust associated with the M42 H II region. The SEDs are well fitted by both one- and two-temperature components in the DTD. While the results are consistent with the multiple-temperature model, they do not provide a conclusive test. However, we show that this problem should be resolved with improved data.