Constant Cp Research Articles

Mechanical Properties of TiC Nanowire from DFT Calculations

Mechanical properties of TiC nanowire (TiCNW) have been investigated using the density functional theory, the full-potential augmented plane wave plus local orbital method (FLAPW + lo), by means of Wein2 k package. Infinite and free-standing nanowire in periodic positions was simulated by supercell approach, and the optimized structure and bond length were calculated. Young’s modulus of TiC nanowire and bulk TiC is obtained by the generalized gradient approximation and bulk modulus using the phonopy package. Additional modules are also obtained using these two modules. Gruneisen parameter γ and heat capacity at constant pressure CP at temperatures (0–1000 K) were calculated by the quasi-harmonic approximation. According to our results, the mechanical properties of bulk TiC are in good agreement with the available theoretical and experimental data. Young’s modulus of TiC nanowire is 4.09 times bigger than that of bulk TiC. Bulk modulus and shear modulus of TiCNW are 4.78 and 3.96 times bigger than those of bulk TiC, respectively. The increase in Young’s modulus, bulk modulus, and shear modulus is due to the bonding of Ti atoms to each other in relaxed structure. CP and γ of TiCNW increase with temperature; however, at a specific temperature, γ of TiCNW is more, and CP of TiCNW is less than those of bulk TiC.

Thermodynamic Parameters of Lead Sulfide Chrystals in the Cubic Phase

Geometric and thermodynamic parameters of cubic PbS crystals were obtained using thecomputer calculations of the thermodynamic parameters within density functional theory methodDFT. Cluster models for the calculation based on the analysis of the crystal and electronicstructure. Temperature dependence of energy ΔE and enthalpy ΔH, Gibbs free energy ΔG, heatcapacity at constant pressure CP and constant volume CV, entropy ΔS were determined on thebasis of ab initio calculations of the crystal structure of molecular clusters. Analytical expressions oftemperature dependences of thermodynamic parameters which were approximated withquantum-chemical calculation points have been presented. Experimental results compared withtheoretically calculated data.

Lp-Boundedness for the Littlewood-Paley g-Function Connected with the Riemann-Liouville Operator

We study the Gauss and Poisson semigroups connected with the Riemann- Liouville operator deflned on the half plane. Next, we establish a principle of maximum for the singular partial difierential operator ¢fi = @ 2 @r2 + 2fi + 1 r @ @r + @ 2 @x2 + @ 2 @t2 ; (r;x;t) 2 )0;+1(£R£)0;+1(: Later, we deflne the Littlewood-Paley g-function and using the principle of maximum, we prove that for every p 2 )1;+1(, there exists a positive constant Cp such that for every f 2 L p (dfi), 1 Cp jjfjjp; fi 6 jjg(f)jjp;fi 6 Cp jjfjjp;fi:

Heat capacity of one-dimensional chains of methane molecules in the outer grooves of carbon nanotube bundles

The heat capacity at constant pressure CP of 1D-chains of methane molecules adsorbed in the grooves on the outer surface of the bundles of closed single-walled nanotubes was measured in the temperature range from 2 to 60 K for the first time. The behavior of the temperature dependence of CP below 12 K indicates the presence of a Schottky-type anomaly originated from the tunneling between the lowest energy levels of the rotational spectra of the A, T, and E nuclear-spin species of methane molecules. The feature observed in the vicinity of 14 K is presumably caused by an orientational phase transition, in which the nature of the rotational motion of the molecules changes from libration to hindered rotation. It was found that the rotational heat capacity in the temperature range of 30–40 K is close to that of freely rotating methane molecules. An increase in the derivative dCP(T)/dT above 40 K and the feature in the CP(T) near 52 K are due to the decay of 1D chains of CH4.

Thermodynamic Parameters of Lead Sulfide Crystals in the Cubic Phase

Geometric and thermodynamic parameters of cubic PbS crystals were obtained using the computer calculations of the thermodynamic parameters within density functional theory method DFT. Cluster models for the calculation were based on the analysis of the crystal and electronic structure. Temperature dependence of energy ΔE and ΔH enthalpy, Gibbs free energy ΔG, heat capacity at constant pressure CP and volume CV, entropy ΔS were determined on the basis of ab initio calculations of the crystal structure of molecular clusters. Analytical expressions of temperature dependences of thermodynamic parameters which were approximated with quantum-chemical calculation points using mathematical package Maple 14 were presented. Experimental results compared with theoretically calculated data.

The pressure dependence of physical properties of La2Zr2O7: First-principles calculations and Quasi-harmonic Debye approximation

The pressure_induced physical properties of La2Zr2O7 pyrochlore were investigated by local density approximation (LDA) theory combining with Quasi-harmonic Debye approximation (QHA). It has been shown that there is a linear increase in the molar Gibbs free energy with the increasing pressure and the value of molar Gibbs free energy is larger than zero when the pressure reaches a particular value. The calculated transformation pressure values are 0.35, 0.65, 1.81 and 3.35 GPa at the temperatures of 300, 500, 1000 and 1500 K, respectively. The calculated results show that the bulk modulus increases with the increasing pressure at a given temperature while decreases with increasing temperature at given pressure. The deviation between constant pressure heat capacity Cp and constant volume heat capacity Cv at different pressure is not sensitive at normal temperature. Analysis shows that lower thermal expansion coefficients at higher pressure results from the strong interaction among the atoms in compound.

On Schatten p-norms of commutators

For any odd integer d≥3, we determine the sharpest constant Cp,q,r such that‖XY−YX‖p≤Cp,q,r‖X‖q‖Y‖r for all X,Y∈Md, where Md denotes the set of all d×d complex matrices, ‖⋅‖p, 1≤p≤∞, denotes the Schatten p-norm on Md, and 1≤p,q,r≤∞ satisfy 1p>1q+1r. This is a continuation of the study of the problem considered in Wenzel and Audenaert (2010) [8].

Net energy content of dry extruded-expelled soybean meal fed with or without enzyme supplementation to growing pigs as determined by indirect calorimetry.

Two experiments were conducted to determine the NE content of dry extruded-expelled soybean (DESBM) and the effect of a multienzyme carbohydrase (MC) mixture on the NE content of DESBM and to determine the effect of diet design on NE values in growing pigs using indirect calorimetry (IC). In Exp. 1, 24 barrows (19.6 ± 0.51 kg BW) were allotted in a completely randomized design to 4 dietary treatments: a corn–soybean meal basal diet (Diet A), a diet containing Diet A and DESBM in an 80:20 ratio with a constant CP (Diet B), a diet with an 80:20 ratio of Diet A and DESBM with a constant corn:soybean meal ratio (Diet C), and a diet with simple substitution of Diet A with DESBM in an 80:20 ratio (Diet D). Pigs were fed in metabolism crates for a period of 16 d to determine the DE and ME and thereafter were moved into an indirect calorimeter where O2 consumption and CO2 production were measured to determine heat production and fasting heat production. The NE content of DESBM was calculated (difference method) to be 2,632, 2,548 and 2,540 kcal/kg DM in diets B, C, and D, respectively. Respective values obtained with published prediction equations were 2,624, 2,530 and 2,436 kcal/kg. In Exp. 2, 24 barrows (16.9 ± 0.76 kg BW) were randomly allotted to 1 of 4 treatments. The diets were a corn–soybean meal basal diet and a diet containing the basal diet and DESBM in an 80:20 ratio with a constant corn:soybean meal ratio with or without 2 levels (0.05% and 0.1%) of MC. The experimental procedures were similar to those described in Exp. 1. Enzyme supplementation improved (P < 0.0001) the DE, ME, and NE content of the DESBM. Multienzyme carbohydrase at 0.05% and 0.1% of the diet improved NE values of DESBM by 4.9% and 3.7%, respectively. In conclusion, the NE values of DESBM obtained with the IC method were higher than the values obtained with prediction equations; the disparity was least when diets were formulated with a constant CP level. However, as the difference method was used to determine the NE of ingredient, it is more appropriate to maintain a constant ratio between the ingredients. Also, the NE value of DESBM obtained for diets C and D were not different. Hence, the average NE value of DESBM evaluated was 2,544 kcal/kg DM. Enzyme supplementation improved the NE content of DESBM fed to growing pigs.

A sharp maximal inequality for one-dimensional Dunkl martingales

Let X=(Xt)t≥0 be a one-dimensional Dunkl process of parameter k≥0, starting from 0. For any p≥1, we find the least constant Cp,k∈(0,∞] in the Doob-type inequality E(sup0≤t≤τXτ)p≤Cp,kE∣Xτ∣p where τ runs over all p/2-integrable stopping times of X. The proof exploits optimal stopping techniques.

Lysine requirement relative to total dietary protein for optimum performance and carcass protein deposition of Iberian piglets

This work aims at establishing dietary Lys requirements [g Lys/kg crude protein (CP, N×6.25)] of post-weaned Iberian piglets based on responses on growth performance, carcass nutrient deposition and plasma metabolites. Sixty piglets (10.7±0.1kg initial BW) were randomly assigned into six isoenergetic diets based on corn, barley and soybean meal. Diets contained increasing Lys concentrations at a constant dietary CP content (165±0.7g/kg DM). l-Lys HCl was added at the expense of corn starch providing Lys:CP ratios (g/kg) of 43, 47, 52, 57, 64 and 72g/kg. Other amino acids and nutrients remained constant. Six additional piglets were slaughtered at the start of the experiment to estimate initial carcass composition. Piglets were individually housed in 2m2 pens in an environmentally controlled room until slaughter (25.3±0.4kg BW) to analyze carcass composition. Average daily gain, G:F and Gain:ME intake (g/MJ) increased linearly (P<0.001) on increasing Lys concentration. Using average daily gain as a response, the linear broken-line regression and the first derivative of the quadratic function gave the same estimation for Lys requirement (71.0g Lys/kg dietary CP, respectively). Lysine content of dietary protein has no effect upon the apparent digestibility of DM, OM and nitrogen. Carcass protein deposition (PD) increased linearly (P<0.001) and quadratically (P<0.05) on increasing dietary Lys, reaching maximum values (39.3–40.2g protein/d) with diets providing 57, 64 and 72g Lys/kg CP. Carcass PD:CP intake, and carcass PD:digestible protein intake increased linearly (P<0.001) and quadratically (P<0.05) on increasing dietary Lys concentration. The linear broken-line regression using carcass PD (g/d) as response criterion estimated Lys requirement as 58.6g Lys/kg dietary CP with a plateau PD value of 39.9g/d. The first derivative of the quadratic function relating carcass PD and dietary Lys content gave a value of 63.7g Lys/kg CP. Plasma urea concentration tended to decrease on increasing Lys concentration (P=0.06 and P=0.10, for linear and quadratic effects). For plasmatic urea, both linear and quadratic approach gave a similar estimate for Lys requirements, 61.2g Lys/kg dietary CP. It is concluded that the preferred estimate based on carcass PD – the more reliable measure of metabolic Lys utilization – is 63.7g Lys/kg CP, somewhat below the established for conventional piglets.

Thermodynamic Parameters of PbTe Crystals: DFT-Calculations

Based on the analysis of the crystal NaCl type and electronic structure of cubic phase CdS crystals the cluster models have been built for calculation of the geometric and thermodynamic parameters. According to density functional theory (DFT) and using the hybrid valence base set B3LYP the temperature dependence of the energy ΔE and the enthalpy ΔH of formation, Gibbs free energy ΔG, entropy ΔS, specific heat at constant volume CV and pressure CP of the crystals have been found. The analytical expressions of the temperature dependences of presented thermodynamic parameters which was approximated from the quantum- chemical calculations data and with using mathematical package Maple 14 have been received.

Sharp L p Bound for Holomorphic Functions on the Unit Disc

For any 1 < p < ∞ and any \({X, Y\in \mathbb{R}}\) satisfying \({|X|\leq Y}\) , we determine the optimal constant Cp(X,Y) such that the following holds. If F is a holomorphic function on the unit disc satisfying ReF(0) = X and \({||{\rm Re}F||_{L^{p}(\mathbb{T})}=Y}\) , then $$||F||_{L^p(\mathbb{T})}\geq C_p(X,Y).$$ This can be regarded as a reverse version of the classical estimates of Riesz and Essen. The proof rests on the exploitation of certain families of special subharmonic functions on the plane.

The best constants for operator Lipschitz functions on Schatten classes

Suppose that f is a Lipschitz function on R with ‖f‖Lip≤1. Let A be a bounded self-adjoint operator on a Hilbert space H. Let p∈(1,∞) and suppose that x∈B(H) is an operator such that the commutator [A,x] is contained in the Schatten class Sp. It is proved by the last two authors, that then also [f(A),x]∈Sp and there exists a constant Cp independent of x and f such that‖[f(A),x]‖p≤Cp‖[A,x]‖p. The main result of this paper is to give a sharp estimate for Cp in terms of p. Namely, we show that Cp∼p2p−1. In particular, this gives the best estimates for operator Lipschitz inequalities.We treat this result in a more general setting. This involves commutators of n self-adjoint operators A1,…,An, for which we prove the analogous result. The case described here in the abstract follows as a special case.

Study of Thermodynamic Properties of AuCu Superlattice by the Statistical Moment Method

We have investigated the thermodynamic quantities of AuCu superlattice using the statistical moment method in the statistical physics. The free energy, thermal lattice expansion coefficients, mean-square atomic displacements, and specific heats at the constant volume and those at the constant pressure, Cv and Cp, are derived in closed analytic forms in terms of the power moments of the atomic displacements. The present analytic formulas including the anharmonic effects of the lattice vibration give the predicted values of these quantities.

First-principle calculations of the thermal properties of SrTiO3 and SrO(SrTiO3)n (n=1,2)

The thermal properties of SrTiO3 and SrO(SrTiO3)n (n=1,2) with layered perovskite structure are analyzed using the Debye–Grüneisen model combined with ab initio calculations. The thermal expansion coefficient, specific heat at constant pressure CP and specific heat at constant volume CV, adiabatic bulk modulus BS and isothermal bulk modulus BT, entropy, and Debye temperature are investigated. At temperatures higher than 550°C, the thermal expansion coefficient and the discrepancies between CP and CV, as well as that between BS and BT, of Sr3Ti2O7 increase the fastest as the temperature rises, followed by those of Sr2TiO4, and those of SrTiO3 increase the slowest. The bulk module and Debye temperature of Sr2TiO4, Sr3Ti2O7, and SrTiO3 increase with decreasing SrO/SrTiO3 ratio at 0K. With increasing temperature, however, the bulk modulus and Debye temperature of Sr3Ti2O7 both rapidly decrease and even fall below those of Sr2TiO4 when the temperature is higher than specific values. We also analyzed the thermal properties of these three compounds in the pressure range from 0GPa to 16GPa at 300K.

Thermodynamic parameters of CdTe crystals in the cubic phase

Based on the analysis of the crystal and electronic structures of CdTe crystals in the cubic phase cluster models have been built for calculation of the geometric and thermodynamic parameters. According to density functional theory (DFT) and by using the hybrid B3LYP functional the temperature dependences of formation energy ∆E, formation enthalpy ∆H, Gibbs free energy ∆G, entropy ∆S, specific heat capacity at constant volume CV and pressure CP have been defined. Also, in the work analytical expressions of temperature dependences of the presented thermodynamic parameters have been derived, which have been approximated by quantum-chemical calculation data using the mathematical package Maple 14. The results of ab initio calculations are compared with experimental data.

Weak-type inequalities for maximal operators acting on Lorentz spaces

We prove sharp a priori estimates for the distribution function of the dyadic maximal function Mφ, when φ belongs to the Lorentz space L, 1 < p < ∞, 1 ≤ q < ∞. The approach rests on a precise evaluation of the Bellman function corresponding to the problem. As an application, we establish refined weak-type estimates for the dyadic maximal operator: for p, q as above and r ∈ [1, p], we determine the best constant Cp,q,r such that for any φ ∈ L p,q , ||Mφ||r,∞ ≤ Cp,q,r||φ||p,q .

Ehrenfest scheme for the extended phase space of f(R) black holes

In this letter, the original expressions of Erhenfest equations have been introduced directly into the black-hole research by treating the cosmological constant and its conjugate quantity as thermodynamic pressure and volume, respectively. The nature of phase transition at the critical point of criticality of AdS black holes in f(R) gravity has been investigated as an example. The specific heat at constant pressure CP, the volume expansion coefficient α and the isothermal compressibility coefficient are found to diverge at the critical point. An analytical check of Ehrenfest equations has been carried out and it has been proved that both Ehrenfest equations are satisfied. So AdS black holes in f(R) gravity undergo a second-order phase transition at the critical point. This result is consistent with the nature of liquid-gas phase transition at the critical point and would help deepen the understanding of the relations between AdS black holes and liquid-gas system. Moreover, the influences of f(R) correction on the thermodynamics and the phase transition of AdS black holes in f(R) gravity have also been shown in this letter.

A STOCHASTIC GRONWALL LEMMA

We prove a stochastic Gronwall lemma of the following type: if Z is an adapted non-negative continuous process which satisfies a linear integral inequality with an added continuous local martingale M and a process H on the right-hand side, then for any p ∈ (0, 1) the pth moment of the supremum of Z is bounded by a constant κp (which does not depend on M) times the pth moment of the supremum of H. Our main tool is a martingale inequality which is due to D. Burkholder. We provide an alternative simple proof of the martingale inequality which provides an explicit numerical value for the constant cp appearing in the inequality which is at most four times as large as the optimal constant.

Multiple solutions for a nonhomogeneous Schrödinger–Maxwell system in [formula omitted

The paper considers the following nonhomogeneous Schrödinger–Maxwell system: (SM){−Δu+u+λϕ(x)u=|u|p−1u+g(x),x∈R3,−Δϕ=u2,x∈R3, where λ>0, p∈(1,5), and 0≤g(x)=g(|x|)∈L2(R3). There seem to be no results on the existence of multiple solutions to problem (SM) for p∈(1,3). In this paper, we find that there is a constant Cp>0 such that problem (SM) has at least two solutions for all p∈(1,5) provided that ‖g‖L2≤Cp, however, for p∈(1,2] we need λ>0 is small. Moreover, Cp=(p−1)2p[(p+1)Sp+12p]1/(p−1), where S is the Sobolev constant.