Energy diffusion controlled reaction rate in dissipative Hamiltonian systems

In this paper the energy diffusion controlled reaction rate in dissipative Hamiltonian systems is investigated by using the stochastic averaging method for quasi Hamiltonian systems. The boundary value problem of mean first- passage time （MFPT） of averaged system is formulated and the energy diffusion controlled reaction rate is obtained as the inverse of MFPT. The energy diffusion controlled reaction rate in the classical Kramers bistable potential and in a two-dimensional bistable potential with a heat bath are obtained by using the proposed approach respectively. The obtained results are then compared with those from Monte Carlo simulation of original systems and from the classical Kraraers theory. It is shown that the reaction rate obtained by using the proposed approach agrees well with that from Monte Carlo simulation and is more accurate than the classical Kramers rate.

Finite Deformation, Finite Strain Nonlinear Dynamics and Dynamic Bifurcation in TVE Solids with Rheology

This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencing dynamic response and dynamic bifurcation for TVES with rheology are identified and are also demonstrated through model problem studies. A simple model problem consisting of a rod (1D) of TVES material with memory fixed at one end and subjected to harmonic excitation at the other end is considered to study nonlinear dynamics of TVES with rheology, frequency response as well as dynamic bifurcation phenomenon.

QSBR Study on the Biodegradation Rate Constant of Chloro-phenol Compounds

Structural and thermodynamic parameters of 16 chloro-phenol compounds in water solution were calculated and fully optimized by using Onsager model in self-consistent reaction field（SCRF） based on the B3LYP/6-311G＊＊ level.These quantum chemical parameters were used as theoretical descriptors to correlate with the experimental biodegradation rate constant（Kb） of 16 compounds by stepwise multiple linear regression.As a result,a three-parameter model including molecular average polarizability（α）,entropy（Sθ）,and molar heat capacity at constant volume（CVθ） were established for Kb prediction,which was proposed with correlation coefficient R2 = 0.894.α exhibits the most significant effect on Kb.Variance analysis and standard t-value test were applied to validate the model.As expected,this model exhibits good robustness and prediction ability,which can be used in Kb prediction of analogs.

Rate Constitutive Theories of Orders n and 1n for Internal Polar Non-Classical Thermofluids without Memory

In recent papers, Surana et al. presented internal polar non-classical Continuum theory in which velocity gradient tensor in its entirety was incorporated in the conservation and balance laws. Thus, this theory incorporated symmetric part of the velocity gradient tensor (as done in classical theories) as well as skew symmetric part representing varying internal rotation rates between material points which when resisted by deforming continua result in dissipation (and/or storage) of mechanical work. This physics referred as internal polar physics is neglected in classical continuum theories but can be quite significant for some materials. In another recent paper Surana et al. presented ordered rate constitutive theories for internal polar non-classical fluent continua without memory derived using deviatoric Cauchy stress tensor and conjugate strain rate tensors of up to orders n and Cauchy moment tensor and its conjugate symmetric part of the first convected derivative of the rotation gradient tensor. In this constitutive theory higher order convected derivatives of the symmetric part of the rotation gradient tensor are assumed not to contribute to dissipation. Secondly, the skew symmetric part of the velocity gradient tensor is used as rotation rates to determine rate of rotation gradient tensor. This is an approximation to true convected time derivatives of the rotation gradient tensor. The resulting constitutive theory: (1) is incomplete as it neglects the second and higher order convected time derivatives of the symmetric part of the rotation gradient tensor;(2) first convected derivative of the symmetric part of the rotation gradient tensor as used by Surana et al. is only approximate;(3) has inconsistent treatment of dissipation due to Cauchy moment tensor when compared with the dissipation mechanism due to deviatoric part of symmetric Cauchy stress tensor in which convected time derivatives of up to order n are considered in the theory. The purpose of this paper is to present ordered rate constitutive theories for deviatoric Cauchy strain tensor, moment tensor and heat vector for thermofluids without memory in which convected time derivatives of strain tensors up to order n are conjugate with the Cauchy stress tensor and the convected time derivatives of the symmetric part of the rotation gradient tensor up to orders 1n are conjugate with the moment tensor. Conservation and balance laws are used to determine the choice of dependent variables in the constitutive theories: Helmholtz free energy density Φ, entropy density η, Cauchy stress tensor, moment tensor and heat vector. Stress tensor is decomposed into symmetric and skew symmetric parts and the symmetric part of the stress tensor and the moment tensor are further decomposed into equilibrium and deviatoric tensors. It is established through conjugate pairs in entropy inequality that the constitutive theories only need to be derived for symmetric stress tensor, moment tensor and heat vector. Density in the current configuration, convected time derivatives of the strain tensor up to order n, convected time derivatives of the symmetric part of the rotation gradient tensor up to orders 1n, temperature gradient tensor and temperature are considered as argument tensors of all dependent variables in the constitutive theories based on entropy inequality and principle of equipresence. The constitutive theories are derived in contravariant and covariant bases as well as using Jaumann rates. The nth and 1nth order rate constitutive theories for internal polar non-classical thermofluids without memory are specialized for n = 1 and 1n = 1 to demonstrate fundamental differences in the constitutive theories presented here and those used presently for classical thermofluids without memory and those published by Surana et al. for internal polar non-classical incompressible thermofluids.

Theoretical approach to the study of vibrational effects on strong field ionization of molecules with alignment-dependent tunneling ionization rates

The tunneling ionization rates of vibrationally excited N2 molecules at the ground electronic state are calculated using molecular orbital Ammosov–Delone–Krainov theory considering R-dependence. The results show that molecular alignment significantly affects the ionization rate, as the rate is mainly determined by the electron density distribution of the highest occupied molecular orbital. The present work indicates that the ratios of alignment-dependent rates of different vibrational levels to that of the vibrational ground level increase for the aligned N2 at the angle θ = 0？, and suggests that the alignment-dependent tunneling ionization rates can be used as a diagnostics for the influence of vibrational excitation on the strong field ionization of molecules.

The Accumulation of He on a W Surface During keV-He Irradiation:Cluster Dynamics Modeling

The accumulation of He on a W surface during keV-He ion irradiation has been simulated using cluster dynamics modeling. This is based mainly on rate theory and improved by involving different types of objects, adopting up-to-date parameters and complex reaction processes, as well as considering the diffusion process along with depth. These new features make the simulated results compare very well with the experimental ones. The accumulation and diffusion processes are analyzed, and the depth and size dependence of the He concentrations contributed by different types of He clusters is also discussed. The exploration of the trapping and diffusion effects of the He atoms is helpful in understanding the evolution of the damages in the near-surface of plasma-facing materials under He ion irradiation.

Enhanced Constitutive Theories for Classical Thermoviscoelastic Polymeric Fluids

This paper presents ordered rate nonlinear constitutive theories for thermoviscoelastic fluids based on Classical Continuum Mechanics (CCM). We refer to these fluids as classical thermoviscoelastic polymeric fluids. The conservation and balance laws of CCM constitute the core of the mathematical model. Constitutive theories for the Cauchy stress tensor are derived using the conjugate pair in the entropy inequality, additional desired physics, and the representation theorem. The constitutive theories for the Cauchy stress tensor consider convected time derivatives of Green’s strain tensor or the Almansi strain tensor up to order n and the convected time derivatives of the Cauchy stress tensor up to order m. The resulting constitutive theories of order (m, n) are based on integrity and are valid for dilute as well as dense polymeric, compressible, and incompressible fluids with variable material coefficients. It is shown that Maxwell, Oldroyd-B, and Giesekus constitutive models can be described by a single constitutive theory. It is well established that the currently used Maxwell and Oldroyd-B models predict zero normal stress perpendicular to the flow direction. It is shown that this deficiency is a consequence of not retaining certain generators and invariants from the integrity (complete basis) in the constitutive theory and can be corrected by including additional generators and invariants in the constitutive theory. Similar improvements are also suggested for the Giesekus constitutive model. Model problem studies are presented for BVPs consisting of fully developed flow between parallel plates and lid-driven cavities utilizing the new constitutive theories for Maxwell, Oldroyd-B, and Giesekus fluids. Results are compared with those obtained from using currently used constitutive theories for the three polymeric fluids.

Mode-Coupling Analysis of Parametric Decay Instability in Magnetized Plasmas

In this paper, derived from Maxwell and fluid equations of plasmas, unified nonlinear wave equations are used to describe the parametric decay instability （PDI） in magnetized plasmas, and in view of mode-coupling, we can obtain all the possible PDI channels. By solving the nonlinear equations with a mode-coupling method, we obtain the growth rate of the PDI, of which all of the three waves are ordinary mode （O-mode） or extraordinary mode （X-mode） wave. Under the dipole approximation, an explicit formula of the growth rate of the X-mode and the condition of the equilibrium density scale are obtained. According to the existence conditions of three X-mode waves, this kind of instability might exist in ECRH with the second harmonic X-mode wave.

Effects of Cooling Rate and Component on the Microstructure and Mechanical Properties of Mg–Zn–Y Alloys

The microstructure and mechanical properties of Mg–6Zn–1Y and Mg–6Zn–3Y（wt%） alloys under different cooling rates were investigated. The results show that the second dendrite arm spacing（SDAS） of Mg–6Zn–1Y and Mg–6Zn–3Y is reduced by 32 and 30% with increasing cooling rates（Rc） from 10.2 to 23 K/s, which can be predicted using a empirical model of SDAS=68 R 0：45：45cand SDAS=73 R 0c, respectively. The compressive strength of both alloys increases with increasing the cooling rate, which is attributed to the increase of volume fraction（Vf） of secondary phases under high cooling rate. The interaction of the cooling rate and component with SDAS has been theoretically analyzed using interdependence theory.

A Cluster Dynamics Model for Accumulation of Helium in Tungsten under Helium Ions and Neutron Irradiation

A cluster dynamics model based on rate theory has been developed to describe the accumulation and diffusion processes of helium in tungsten under helium implantation alone or synergistic irradiationwith neutron,by involving different types of objects,adopting up-to-date parameters and complex reaction processes as well as considering the diffusion process along with depth.The calculated results under different conditions are in good agreement with experiments much well.The model describes the behavior of helium in tungsten within 2D space of defect type/size and depth on different ions incident conditions(energies and fluences)and material conditions(system temperature and existent sinks),by including the synergistic effect of helium-neutron irradiations and the influence of inherent sinks(dislocation lines and grain boundaries).The model,coded as IRadMat,would be universally applicable to the evolution of defects for ions/neutron irradiated on plasma-facing materials.

Experimental and theoretical analysis of equilibrium segregation and radiation-induced segregation of Cr at grain boundariesin a reduced activation ferritic/martensitic(RAFM)steel

Helium ion irradiation at 350℃was performed to study equilibrium segregation and radiation-induced segregation(RIS)of Cr at grain boundaries in reduced activation ferritic/martensitic steels.Cr concentration at grain boundary was measured by scanning transmission electron microscopy with an energy-dispersive spectrometer.The measured Cr concentration at grain boundaries in heat treated zone was 11.7 and 12.8 wt.%in irradiated zone,respectively,which matched well to the calculated results from Mclean and modified Perk model.Equilibrium segregation and RIS of Cr mechanisms were theoretically analysed.The analysis indicates that as temperature rises,equilibrium Cr segregation decreases monotoni-cally,while RIS of Cr has a bell-shape profile,which increases first and then decreases.It is also shown that at low and high temperatures,equilibrium segregation of Cr is higher than that of RIS;at intermediate temperatures,equilibrium Cr segregation is lower than RIS.

Potassium carbonate-based ternary transition temperature mixture(deep eutectic analogues)for CO_(2)absorption:Characterizations and DFT analysis

Is it possible to improve CO_(2)solubility in potassium carbonate(K_(2)CO_(3))-based transition temperature mixtures(TTMs)?To assess this possibility,a ternary transition-temperature mixture(TTTM)was prepared by using a hindered amine,2-amino-2-methyl-1,3-propanediol(AMPD).Fourier transform infrared spectroscopy(FT-IR)was employed to detect the functional groups including hydroxyl,amine,carbonate ion,and aliphatic functional groups in the prepared solvents.From thermogravimetric analysis(TGA),it was found that the addition of AMPD to the binary mixture can increase the thermal stability of TTTM.The viscosity findings showed that TTTM has a higher viscosity than TTM while their difference was decreased by increasing temperature.In addition,Eyring’s absolute rate theory was used to compute the activation parameters(∆G^(*),∆H^(*),and ∆S^(*)).The CO_(2)solubility in liquids was measured at a temperature of 303.15 K and pressures up to 1.8 MPa.The results disclosed that the CO_(2)solubility of TTTM was improved by the addition of AMPD.At the pressure of about 1.8 MPa,the CO_(2)mole fractions of TTM and TTTM were 0.1697 and 0.2022,respectively.To confirm the experimental data,density functional theory(DFT)was employed.From the DFT analysis,it was found that the TTTM+CO_(2)system has higher interaction energy(|∆E|)than the TTM+CO_(2)system indicating the higher CO_(2)affinity of the former system.This study might help scientists to better understand and to improve CO_(2)solubility in these types of solvents by choosing a suitable amine as HBD and finding the best combination of HBA and HBD.

A new stationary droplet evaporation model and its validation

The liquid droplet evaporation character is important for not only combustion chamber design process but also high-accuracy spray combustion simulation. In this paper, the suspended droplets＇ evaporation character was measured in a quiescent high-temperature environment by micro high-speed camera system. The gasoline and kerosene experimental results are consistent with the reference data. Methanol, common kerosene and aviation kerosene droplet evaporation characteristics, as well as their evaporation rate changing with temperature, were obtained. The evaporation rate experimental data were compared with the prediction result of Ranz-Marshall boiling temperature model（RMB）, Ranz-Marshall low-temperature model（RML）, drift flux model（DFM）, mass analogy model（MAM）, and stagnant film model（SFM）. The disparity between the experimental data and the model prediction results was mainly caused by the neglect of the natural convection effect, which was never introduced into the droplet evaporation concept. A new droplet evaporation model with consideration of natural convection buoyancy force effect was proposed in this paper. Under the experimental conditions in this paper, the calculation results of the new droplet evaporation model were agreed with the experimental data for kerosene, methanol and other fuels, with less than 20% relative deviations. The relative deviations between the new evaporation model predictions for kerosene and the experimental data from the references were within 10%.

Universality of slip avalanches in a ductile Fe-based bulk metallic glass

Intermittent serrated flows of a novel ductile Fe60Ni20P13C7 bulk metallic glass（BMG）at variant strain rates were investigated by statistics analysis.Peak and clutter distribution of slip-avalanche magnitudes are displayed during stable plastic flows at strain rates of 2×10-4 s-1 and 5×10-5 s-1,respectively,which means that serration behavior depends on the strain rate.However,the remarkable agreement between measured slip-avalanche magnitudes and the scaling behavior,i.e.a universal complementary cumulative distribution function（CCDF）predicted by mean-field theory（MFT）model,indicates that the plasticity of the present Fe-based BMGs can be tuned by imposed strain rates：Smax^6）ε-λ.This tuned plasticity is elucidated with expended free-volume model.Moreover,the scaling behavior of serrated flows for other strain rates can be predicted as well.