Exponential Temperature Dependence Research Articles

Density profiles of a self-gravitating lattice gas in one, two, and three dimensions.

We consider a lattice gas in spaces of dimensionality D=1,2,3. The particles are subject to a hardcore exclusion interaction and an attractive pair interaction that satisfies Gauss' law as do Newtonian gravity in D=3, a logarithmic potential in D=2, and a distance-independent force in D=1. Under mild additional assumptions regarding symmetry and fluctuations we investigate equilibrium states of self-gravitating material clusters, in particular radial density profiles for closed and open systems. We present exact analytic results in several instances and high-precision numerical data in others. The density profile of a cluster with finite mass is found to exhibit exponential decay in D=1 and power-law decay in D=2 with temperature-dependent exponents in both cases. In D=2 the gas evaporates in a continuous transition at a nonzero critical temperature. We describe clusters of infinite mass in D=3 with a density profile consisting of three layers (core, shell, halo) and an algebraic large-distance asymptotic decay. In D=3 a cluster of finite mass can be stabilized at T>0 via confinement to a sphere of finite radius. In some parameter regime, the gas thus enclosed undergoes a discontinuous transition between distinct density profiles. For the free energy needed to identify the equilibrium state we introduce a construction of gravitational self-energy that works in all D for the lattice gas. The decay rate of the density profile of an open cluster is shown to transform via a stretched exponential for 1<D<2, whereas it crosses over from one power-law at intermediate distances to a different power-law at larger distances for 2<D<3.

The Variational Form of the Mathematical Model of a Thermal Explosion in a Solid Body with Temperature-Dependent Thermal Conductivity

The variational form of a mathematical model of a thermal explosion has been developed based on a variational formulation of a nonlinear problem of stationary thermal conductivity in a homogeneous solid body. The model takes the temperature dependence of the thermal conductivity of a solid body into account. The presented example of quantitative analysis of the model demonstrates a method for finding the combination of parameters for determining a thermal explosion in a plate with an exponential temperature dependence of the thermal conductivity. At the same time, the analysis allows one to identify the number of steadystate temperature distributions inside a body whose energy release intensifies with a temperature increase.

Speed-dependent Voigt lineshape parameter database from dual frequency comb measurements up to 1305 K. Part I: Pure H2O absorption, 6801–7188 cm−1

We measure speed-dependent Voigt lineshape parameters with temperature-dependence exponents for several hundred spectroscopic features of pure water spanning 6801–7188 cm−1. The parameters are extracted from broad bandwidth, high-resolution dual frequency comb absorption spectra with multispectrum fitting techniques. The data encompass 25 spectra ranging from 296 K to 1305 K and 1 to 17 Torr of pure water vapor. We present the extracted parameters, compare them to published data, and present speed-dependence, self-shift, and self-broadening temperature-dependent parameters for the first time. Lineshape data is extracted using a quadratic speed-dependent Voigt profile and a single self-broadening power law temperature-dependence exponent over the entire temperature range. The results represent an important step toward a new high-temperature database using advanced lineshape profiles.

Singular ferromagnetic susceptibility of the transverse-field Ising antiferromagnet on the triangular lattice

A transverse magnetic field $\Gamma$ is known to induce antiferromagnetic three-sublattice order of the Ising spins $\sigma^z$ in the triangular lattice Ising antiferromagnet at low enough temperature. This low-temperature order is known to melt on heating in a two-step manner, with a power-law ordered intermediate temperature phase characterized by power-law correlations at the three-sublattice wavevector ${\bf Q}$: $\langle \sigma^z(\vec{R}) \sigma^z(0)\rangle \sim \cos({\mathbf Q}\cdot \vec{R}) /|\vec{R}|^{\eta(T)}$ with the temperature-dependent power-law exponent $\eta(T) \in (1/9,1/4)$. Here, we use a newly developed quantum cluster algorithm to study the {\em ferromagnetic} easy-axis susceptibility $\chi_{u}(L)$ of an $L \times L$ sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular $L$ dependence $\chi_{u}(L)\sim L^{2- 9 \eta}$ when $\eta(T)$ is in the range $(1/9,2/9)$. This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility $\chi_{u}(B)$ to a uniform field $B$ along the easy axis is singular at intermediate temperatures in the small $B$ limit, $\chi_{u}(B) \sim |B|^{-\frac{4 - 18 \eta}{4-9\eta}}$ for $\eta(T) \in (1/9, 2/9)$, although there is no ferromagnetic long-range order in the low temperature state.

Temperature dependence of wood photodegradation. Part 2: Evaluation by Arrhenius law

The temperature dependence of photodegradation for wood was evaluated applying the Arrhenius law. Hardwood (beech, Fagus sylvatica L. and poplar, Populus x euramericana cv. Pannonia) and softwood (Scots pine, Pinus sylvestris L. and spruce Picea abies Karst.) species were involved in the test. Samples were irradiated by a strong UV emitter mercury lamp at 30 °C, 80 °C, 120 °C and 160 °C. The chemical changes were detected by diffuse reflectance infrared spectroscopy. The absorption changes were determined by difference spectrum method. After IR data processing, the dominant seven IR bands were selected for generating the Arrhenius plots for all examined species.The results show that the Arrhenius law is useful in interpreting the kinetics of some photochemical reactions during the photodegradation of wood. The photodegradation of guaiacyl lignin absorbing at 1270 cm−1 was found a single rate-limited, thermally activated process for all examined species. These results indicated that the temperature dependence of this degradation was exponential. The absorption increase of quinones at 1596 cm−1 and the absorption decrease of ether bond in cellulose and hemicellulose at 1175 cm−1 also showed exponential temperature dependence for conifers.In most of the cases, at least two different (and sometimes antagonistic) types of chemical changes generated absorption change at the same wavenumber region. In these situations, the Arrhenius equation was unable to indicate whether the temperature dependence is exponential or not.

Temperature dependence of line parameters of near studied by tunable diode laser spectroscopy**Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 41205021 and 61701006), the Youth Innovation Promotion Association of the Chinese Academy of Sciences (Grant No. 2015264), and the Scientific Research Foundation of the Higher Education Institutions of Anhui Province, China

The absorption spectrum of carbon dioxide at has been recorded at sample temperatures between 218.0 K and room temperature, by using a high-resolution tunable diode laser absorption spectrometer (TDLAS) combined with a temperature controlled cryogenically cooled absorption cell. The self-, N2-, and air-broadening coefficients for nine transitions of belonging to the band in the 4987 cm−1–4998 cm−1 region have been measured at different temperatures. From these measurements, we have further determined the temperature dependence exponents of the pressure-broadening coefficients. To the best of our knowledge, the temperature dependence parameters of the collisional broadening coefficients are reported experimentally for the first time for these nine transitions. The measured halfwidth coefficients and the air temperature dependence exponents of these transitions are compared with the available values reported in the literature and HITRAN 2012 database. Agreements and discrepancies are also discussed.

Dual Variational Form of the Model of Thermal Explosion in a Quiescent Medium with Temperature-Dependent Thermal Conductivity

Based on the dual variational formulation of the nonlinear stationary heat conduction problem, a mathematical model is constructed that describes the temperature state of a stationary medium in a volume of an arbitrary shape. The thermal conductivity of the medium and the volumetric energy release depend on the temperature. This model is applied to analyzing the conditions of thermal explosion in an infinitely long circular cylinder for exponential temperature dependences of the above parameters. In the particular case of constant thermal conductivity of this cylinder, a comparison with the published results is carried out.

Electrical resistivity across the tricriticality in itinerant ferromagnet

We investigate the discontinuous ferromagnetic phase diagram near tricritical point in UCo1-xRuxAl compounds by electrical resistivity measurements. Separation of phases in UCo0.995Ru0.005Al at ambient pressure and in UCo0.990Ru0.010Al at pressure of 0.2 GPa and disappearance of ferromagnetism at 0.4 GPa is confirmed. The exponent of temperature dependence of electrical resistivity implies change from Fermi liquid-like behavior to non-Fermi liquid at 0.2 GPa and reaches minimum at 0.4 GPa. Our results are compared to results obtained on the pure UCoAl and explanation for different exponents is given.

Line shape parameters of air-broadened water vapor transitions in the ν1 and ν3 spectral region

A Bruker IFS-120HR Fourier transform spectrometer located at the Pacific Northwest National Laboratory (PNNL) in Richland, Washington was used to record a series of spectra of pure H2O and air-broadened H2O in the regions of the ν1 and ν3 bands (3450–4000 cm−1) at different pressures, temperatures and volume mixing ratios of H2O in air. Eighteen high-resolution, high signal-to-noise (S/N) ratio absorption spectra were recorded at T = 268, 296 and 353 K using two temperature-controlled absorption cells with path lengths of 9.906(1) and 19.95(1) cm. The resolution of the spectra recorded with the 9.906 cm and 19.95 cm absorption cells was 0.006 and 0.008 cm−1, respectively. A multispectrum nonlinear least squares fitting technique was employed to fit all the eighteen spectra simultaneously to retrieve 313 accurate line positions, 315 intensities, 229 Lorentz air-broadened half-width and 213 air-shift coefficients and their temperature dependences (136 for air-broadened width and 128 for air-shift coefficients, respectively). Room temperature self-broadened half-width coefficients for 209 transitions and self-shift coefficients for 106 transitions were also measured. Line mixing coefficients were experimentally determined for isolated sets of 10 transition pairs for H2O-air and 8 transition pairs for H2O-H2O using the off-diagonal relaxation matrix element formalism, and 85 quadratic speed dependence parameters were measured. Modified Complex Robert-Bonamy (MCRB) calculations of self-, and air-broadened (from N2- and O2-broadening) half-width and air-shift coefficients, and temperature dependence exponents of air-broadened half-width coefficients are made. The measurements and calculations are compared with each other and with similar parameters reported in the literature.

ENTROPY GENERATION FOR A NON-NEWTONIAN SHEAR THINNING FLUID WITH VISCOUS HEATING EFFECTS

This paper reports the entropy generation of a two-dimensional, non-isothermal, steady, hydrodynamically and thermally fully-developed flow of an incompressible, non-Newtonian shear thinning fluid between two infinite parallel plates. The inelastic fluid is modeled by a two parameter Carreau constitutive equation with an exponential temperature dependence of viscosity. Temperature dependence of the fluid is modeled through Arrhenius law. Momentum and energy balance equations, which govern the flow, are coupled, and this nonlinear boundary value problem is solved numerically using a Pseudospectral method based on the Chebyshev polynomials. The effect of various flow controlling parameters on velocity, temperature and entropy generation is analyzed. The results indicated that Brinkman number and activation energy have opposite effects on entropy generation due to heat transfer. In contrast to the power-law index, an increase in the material time constant results in a decrease in the Bejan Number.

Peculiarities of Electrical Characteristics of Semi-Insulating CdTe-Сl crystals

Electrical properties of semi-insulating CdTe-Сl crystals, grown by the vertical Bridgman and the travelling heater method, have been studied. It is found that the travelling heater method provides electron conductivity of the crystals, and the vertical Bridgman method – hole conductivity. Specific resistance of the samples is of (108-109) Ohm×сm at 300 K, and Hall mobility of the holes and electrons is of (45 - 55) cm2/V·s and (10 - 20) cm2/V·s respectively. Very low values of electron mobility and an exponential temperature dependence of µn are due to drift barriers with a height of εb ≈ 0.20 eV. Formation of the barriers is caused by the fluctuations of the potential relief resulting from the microheterogeneity of the defect-impurity system. Quasi-photochemical reactions that reduce electron mobility after photo-excitation have been observed in n-CdTe-Cl samples. In p-CdTe-Cl samples, neither drift barriers, nor quasi-photochemical reactions were detected.

Thermodynamic reassessment of the Al–Zr binary system

Based on the data of the literature reports, the Al–Zr binary system has been re-assessed thermodynamically through the CALPHAD (CALculations of PHAse Diagram) approach using Thermo-Calc software. The Redlich–Kister polynomials as well as the exponential temperature dependence model of Kaptay were used to describe the excess Gibbs energy of the liquid phase and the three terminal solid solutions: fcc_A1 (Al), bcc_A2 (βZr), and hcp_A3 (αZr). Additionally, the ten Al–Zr intermetallic compounds were treated as strict stoichiometric compounds. Finally, the comparison between the experimental and the two calculated phase diagrams, as well as the generated thermodynamic parameters, was critically discussed.

Nonisothermal filling of a planar channel with a power-law fluid

In this paper, the fountain flow of a power-law fluid during the filling of a planar vertical channel is investigated taking into account a dissipative heating. The rheological properties of the medium are defined by Ostwald de Waele power-law with an exponential temperature dependence of effective viscosity. The problem is solved numerically by means of a finite-difference method based on the SIMPLE algorithm and method of invariants for compliance with the natural boundary conditions on a free surface. The parametrical investigations of the shape of free surface as a function of the basic dimensionless criteria and nonlinearity degree of the fluid are implemented. The effect of viscous dissipation on the formation of the kinematic characteristics of the flow is shown.

Common behaviors associated with the glass transitions of water-like models

We perform molecular dynamics simulations to ascertain effects of the molecular polarity on structural and dynamical properties of water-like systems, in particular, on their glassy slowdown. To systematically vary the molecular dipole moments, we scale the partial charges of the established SPC/E and TIP4P/2005 models. In broad ranges of the molecular polarity, the studied SPC/E and TIP4P/2005 descendants show a density anomaly, which can be attributed to the removal of water molecules interstitial between the first and the second neighbor shells upon cooling. While all considered modified water models behave as typical glass formers, the structural relaxation time τ heavily depends on the molecular dipole moment. This large dynamical diversity is exploited to systematically ascertain characteristic properties of glass-forming liquids. For all studied water-like systems, we observe a close relation between the activation energy E∞ describing the Arrhenius behavior of the regular liquid and the glass transition temperature Tg characterizing the supercooled liquid, explicitly, E∞/Tg≈10. Moreover, decomposing the activation energy of the structural relaxation according to E(T)=E∞+Ec(T), we show that the glassy slowdown of all modified water molecules can fully be traced back to an exponential temperature dependence of the contribution Ec(T) related to cooperative dynamics. Extrapolation of this behavior suggests a common value at the glass transition temperature, Ec(Tg)/Tg≈25. Finally, we discuss links between the structural relaxation and the vibrational displacement, as proposed in various theoretical approaches to the glass transition.

Experimental study of carbon dioxide spectroscopic parameters around 2.0 µm region for combustion diagnostic applications

The high-resolution absorption spectra of carbon dioxide were measured at sample temperatures in the range of 296–800 K. The measurements were performed based on direct laser absorption spectroscopy using a tunable diode laser combined with a home-made heated static cell. Line strengths, self-broadening coefficients and their temperature dependences of five selected strong lines belonging to the 20012←00001 band of carbon dioxide near 2.0 µm were inferred from these measured spectra. To the best of our knowledge, this is the first study that measures the line parameters for the five selected strong CO2 lines at elevated temperature. The measured line strengths and self-broadening coefficients of these lines are compared with the available values listed in HITRAN/HITEMP database. The temperature dependence exponents of self-broadening coefficients are compared with theoretical calculations and values inferred from HITEMP2010. Agreements and discrepancies are discussed.

Effect of electron irradiation on the pseudogap temperature dependence of YBa $$_2$$ 2 Cu $$_3$$ 3 O $$_{7-\delta }$$ 7 - δ single crystals

The effect of electron irradiation on the basal-plane conductivity $$\sigma (T)$$ of YBa $$_2$$ Cu $$_3$$ O $$_{7-\delta }$$ single crystals is investigated. The excess conductivity $$\Delta \sigma (T)$$ has been revealed to obey an exponential temperature dependence in the broad temperature range $$T_f< T < T^*$$ , where $$T_f$$ is the transition temperature from the pseudogap state to the regime of fluctuation conductivity. The description of the excess conductivity by the relation $$\Delta \sigma (T) \propto (1-T/T^*)\exp (\Delta ^*_{ab}/T)$$ can be interpreted in terms of the mean-field theory where $$T^*$$ is the mean-field transition temperature to the pseudogap state and $$\Delta ^*(T)$$ is satisfactory described within the framework of the BCS-BEC crossover theory. In all, electron irradiation of the YBa $$_2$$ Cu $$_3$$ O $$_{7-\delta }$$ single crystals has been revealed to lead to an expansion of the temperature range of the pseudogap state, thereby narrowing the range of the linear dependence of $$\rho (T)$$ in the ab-plane.

ASD-1000: High-resolution, high-temperature acetylene spectroscopic databank

We present a high-resolution, high-temperature version of the Acetylene Spectroscopic Databank called ASD-1000. The databank contains the line parameters (position, intensity, Einstein coefficient for spontaneous emission, term value of the lower states, self- and air-broadening coefficients, temperature dependence exponents of the self- and air-broadening coefficients) of the principal isotopologue of C2H2. The reference temperature for line intensity is 296 K and the intensity cutoff is 10−27 cm−1/(molecule cm−2) at 1000 K. The databank has 33,890,981 entries and covers the 3–10,000 cm−1 spectral range. The databank is based on the global modeling of the line positions and intensities performed within the framework of the method of effective operators. The parameters of the effective Hamiltonian and the effective dipole moment operator have been fitted to the observed values of the line positions and intensities collected from the literature. The broadening coefficients as well as their temperature dependence exponents were calculated using the empirical equations. The databank is useful for studying high-temperature radiative properties of C2H2. ASD-1000 is freely accessible via the Internet site of V.E. Zuev Institute of Atmospheric Optics SB RAS ftp://ftp.iao.ru/pub/ASD1000/.

Dual time scales in simulated annealing of a two-dimensional Ising spin glass.

We apply a generalized Kibble-Zurek out-of-equilibrium scaling ansatz to simulated annealing when approaching the spin-glass transition at temperature T=0 of the two-dimensional Ising model with random J=±1 couplings. Analyzing the spin-glass order parameter and the excess energy as functions of the system size and the annealing velocity in Monte Carlo simulations with Metropolis dynamics, we find scaling where the energy relaxes slower than the spin-glass order parameter, i.e., there are two different dynamic exponents. The values of the exponents relating the relaxation time scales to the system length, τ∼L^{z}, are z=8.28±0.03 for the relaxation of the order parameter and z=10.31±0.04 for the energy relaxation. We argue that the behavior with dual time scales arises as a consequence of the entropy-driven ordering mechanism within droplet theory. We point out that the dynamic exponents found here for T→0 simulated annealing are different from the temperature-dependent equilibrium dynamic exponent z_{eq}(T), for which previous studies have found a divergent behavior: z_{eq}(T→0)→∞. Thus, our study shows that, within Metropolis dynamics, it is easier to relax the system to one of its degenerate ground states than to migrate at low temperatures between regions of the configuration space surrounding different ground states. In a more general context of optimization, our study provides an example of robust dense-region solutions for which the excess energy (the conventional cost function) may not be the best measure of success.

Study of thermal-field emission properties and investigation of temperature dependent noise in the field emission current from vertical carbon nanotube emitters

We have investigated temperature dependent field electron emission characteristics of vertical carbon nanotubes (CNTs). The generalized expression for electron emission from well-defined cathode surface is given by Millikan and Lauritsen [1] for the combination of temperature and electric field effect. The same expression has been used to explain the electron emission characteristics from vertical CNT emitters. Furthermore, this has been applied to explain the electron emission for different temperatures ranging from room temperature to 1500K. The real-time field electron emission images at room temperature and 1500K are recorded by using Charge Coupled Device (CCD) in order to understand the effect of temperature on distribution of electron emission spots and ring like structures in Field Emission Microscope (FEM) image. The FEM images could be used to calculate the total number of emitters per cm2 for electron emission. The calculated number of emitters per cm2 from FEM image is typically, 4.5 × 107 and the actual number emitters per cm2 present as per Atomic Force Microscopy (AFM) data is 1.2 × 1012. The measured Current-Voltage (I-V) characteristics exhibit non linear Folwer-Nordheim (F-N) type behavior. The fluctuations in the emission current were recorded at different temperatures and Fast Fourier transformed into temperature dependent power spectral density. The latter was found to obey power law relation S(f) = A(Iδ/fξ), where δ and ξ are temperature dependent current and frequency exponents respectively.

Evolution of internal strain in austenite phase during thermally induced martensitic phase transformation in NiTi shape memory alloys

New insight into the temperature dependent evolution of internal strain in the austenite phase during the martensitic phase transformation in NiTi shape memory alloys is provided via classical molecular dynamics simulations that employ well-established interatomic potentials for NiTi. It is shown, for the first time, that the developed strain tensor in the austenite phase is tetragonal in nature, with exponential temperature-dependence. Equally importantly, it is found that the developed internal strain (parallel to the habit plane) in the austenite varies linearly with the evolving martensite phase fraction. Interestingly, the Richard’s equation is found to describe the temperature dependence of the martensite phase fraction as well as the internal strain components parallel to the habit plane in the austenite phase. An analysis of the temperature dependent phonon dispersion of strained austenite revealed the competition between phonon softening of the TA2 branch and internal strain that leads to stabilization of the austenite phase in the two phase regime.