Inertial Constants Research Articles

Inertia of the oscillatory mechanisms of giant nonlinearities of optical materials in the terahertz spectral range

Subject of study. The inertia of the oscillatory mechanisms of the nonlinearities of isotropic dielectric media in the field of the terahertz-frequency electromagnetic waves was investigated for resonant and nonresonant interactions between radiation and matter. The purpose of this work was to construct a dynamic model of the nonlinear polarization responses of optical media with oscillatory nature in the field of terahertz pulses and to estimate the time constants characterizing the inertia of such responses during resonant and nonresonant interactions between radiation and media molecular vibrations. Method. The model of anharmonic vibrations of the atoms of each molecule as an oscillator in the general case for an isotropic medium, with both quadratic and cubic nonlinearities, was reduced for a macroscopic optical characteristic—its polarization—to a model as a system of parametrically coupled equations with only cubic nonlinearities. The system parameters were determined from well-known characteristics of a medium, such as its thermal expansion coefficient, stretching molecular vibration frequency, and refractive index. Main results. Expressions were obtained for the inertial time constants of the cubic susceptibilities of optical media with nonlinear vibrations in two- and one-photon resonant interactions with quasi-monochromatic terahertz pulses as well as in nonresonant interactions with broadband terahertz pulsed radiation through the thermal, spectral, and optical characteristics of materials known in the literature. Numerical estimates were obtained for the inertial time constants of the nonlinear susceptibilities of media with particularly high vibrational nonlinearities in the refractive indices, namely, α-pinene and water, as well as silicon dioxide. For these materials, the inertial time constants of the resonant oscillatory mechanisms of the nonlinearities for radiation in the terahertz spectral range were shown to be of the order of hundreds of femtoseconds; for the nonresonant interactions, the time constants decreased to ten femtoseconds or less. Practical significance. The obtained inertial time constant estimations of the polarization responses of materials indicate that their giant nonlinearities in the far infrared spectral range could be used to develop ultrafast photonic devices for pulsed terahertz radiation parameter control.

Exponential Cluster Phase Synchronization Conditions for Second-Order Kuramoto Oscillators

This brief delivers cluster phase synchronization conditions for the second-order Kuramoto network under the effects of damping and inertia. These conditions are derived via an energy function method, which are related to the natural frequencies, damping and inertial constants of oscillators, and intra- and inter-cluster couplings among them. We show that each cluster can achieve exponential synchronization in the phase cohesive region when the inter-cluster coupling is sufficiently weak or strong. The effectiveness of presented conditions is validated on numerical examples.

Adaptive Control With Unknown System Dynamics Estimator for Quadrotor Attitude Tracking

This paper presents an adaptive control scheme via combining with an unknown system dynamics estimator (USDE) for attitude control of quadrotors subject to both parametric uncertainties and external disturbances. The presented controller is designed by effectively merging an adaptive control with an USDE via backstepping, where the extraneous uncertainties are addressed by USDE, and the adaptive law driven by tracking errors accounts for identifying unknown inertial moment constants. The unique characteristic is that a reinforced attitude controlling can be realized benefiting from the separate handling of parametric uncertainties and disturbances via an adaptive updating and a concise disturbance observation, significantly releasing the learning load of USDE and a high gain can be avoided in feedback loops. Meanwhile, Lyapunov analysis demonstrates that all error variables are uniformly ultimately bounded in the closed-loop system. Eventually, simulations substantiate the utility of suggested control strategy.

Study on Flow Behavior of Parallel Lumped-Model under Constant Flow for Bronchial Tree

Redistribution of flow in the bronchial tree is an important factor that enhances gas exchange in the lungs, especially, in diseased lungs. The bifurcated bronchial tree is like an electric network in series and parallel. A lumped-model of parallel system for constant flow rate is solved analytically to demonstrate the intrinsic characteristics and the dynamic behavior of the system. Inertial and capacitive time constants are calculated for 19th generation airways of human lung to control the solution. The investigation revealed that (i) higher inertial force takes more time to maximize the inertial flow to steady state and more time to minimize the resistive flow to steady state and (ii) the compliant effect is negligible for a relatively higher inertial time constant, on the same experimental conditions. GANIT J. Bangladesh Math. Soc. 40.2 (2020) 86–94

Influences of interface properties on the wave propagation in the dipolar gradient elastic solid

The present work mainly focuses on the influence of interface material parameters, namely the interface mass density, the interface elastic rigidity, and the interface inertial interaction constants, on the reflection and transmission behavior of elastic wave propagating through dipolar gradient elastic solids. First, the interface kinetic energy density and interface deformation energy density are taken into account. By application of Hamilton’s variation principle, the governing equations and the boundary conditions of the dipolar gradient elastic solid are obtained. Due to the consideration of microstructure effects of the material, the interface conditions can be proposed in different forms. These interfacial conditions which include the microstructure effects and interface energy effects are then used to determine the amplitude ratio of reflection and transmission waves. A numerical example is provided for the generalized internal roller interface. The influence of the interface material parameters upon the reflection and transmission coefficients in terms of energy fluxes ratio is discussed based on the numerical results. It is revealed that the reflection and transmission behavior can be manipulated by the elaborated design of the interface at both the macroscale and the microscale.

Experimental Study on Pressure Drop and Flow Dispersion in Packed Bed of Natural Zeolite

The use of conventional correlation for pressure drop and dispersion coefficient calculation may result in inaccurate values for zeolite packed bed as the correlations are generally developed for regularly shaped and uniformly sized particles. To support the research on the application of modified natural zeolite as tar cracking catalyst, the research on the hydrodynamic behaviour of zeolite packed bed has been conducted. Experiments were carried out using a glass column with diameter of 37.8 mm. Natural zeolite with particle size of about 2.91 to 6.4 mm was applied as packing material in the column, and the bed height was varied at 9, 19 and 29 cm. Air was used as the fluid that flows through the bed and nitrogen was used as a tracer for residence time distribution determination. Air flow rates were in the range of 20 to 100 mL/s which correspond to the laminar-transitional flow regime. The pressure drops through the bed were in the range of 1.7 to 95.6 Pa, depending on the air flow rate and bed height. From these values, the parameters in the Ergun equation were estimated, taking into account the contribution by wall effect when the ratio of column to particle diameter is low. The viscous and inertial term constants in the Ergun equation calculated ranges from 179 to 199 and 1.41 to 1.47 respectively while the particle sphericity ranges from 0.56 to 0.59. The reactor Peclet number were determined to range from 5.2 to 5.5, which indicated significant deviation from a plug flow condition.

LEVEL: A computer program for solving the radial Schrödinger equation for bound and quasibound levels

This paper describes program LEVEL, which can solve the radial or one-dimensional Schrödinger equation and automatically locate either all of, or a selected number of, the bound and/or quasibound levels of any smooth single- or double-minimum potential, and calculate inertial rotation and centrifugal distortion constants and various expectation values for those levels. It can also calculate Franck–Condon factors and other off-diagonal matrix elements, either between levels of a single potential or between levels of two different potentials. The potential energy function may be defined by any one of a number of analytic functions, or by a set of input potential function values which the code will interpolate over and extrapolate beyond to span the desired range.

RKR1: A computer program implementing the first-order RKR method for determining diatomic molecule potential energy functions

This paper describes computer program RKR1, which implements the first-order semiclassical Rydberg–Klein–Rees procedure for determining the potential energy function for a diatomic molecule from a knowledge of the dependence of the molecular vibrational energies Gv and inertial rotation constants Bv on the vibrational quantum number v. RKR1 allows the vibrational energies and rotational constants to be defined in terms of: (i) conventional Dunham polynomial expansions, (ii) near-dissociation expansions (NDE׳s), or (iii) the mixed Dunham/NDE “MXR” functions introduced by Tellinghuisen [J Chem Phys 2003; 118: 3532]. Internal convergence tests ascertain and report on the precision of the resulting turning points. For cases in which only vibrational data are available, RKR1 also allows an overall potential to be constructed by combining directly-calculated well widths with inner turning points generated from a Morse function. It can also automatically smooth over irregular or unphysical behavior of the steep inner wall of the potential.

Potential energy curves and spectroscopic properties of GeS molecules: in ground states and low-lying excited states

The potential energy curves (PECs) for ground state (X1+) and five low-lying electronic states (11-, 11, A1, 15+, 25+) of the GeS molecule have been studied by multi-reference configuration interaction (MRCI) plus Davidson correction (+Q) with all-electron basis set aug-cc-pv5Z. Results show that the 25+ state is an unstable repulsive state, and the others are bound states, and the six electronic states are dissociated along the same channel, Ge(3P)+S(3P). The adiabatic transition energy Te equilibrium bond length Re, dissociation energy De, harmonic frequency e, anharmonic constant exe, and equilibrium dipole moments are obtained by fitting the PECs for the X1+, 11-, 11, A1 and 15+ states. While Re is 2.034 , De 5.728 eV, e 571.73 cm-1, exe 1.6816 cm-1, the equilibrium dipole moment is 1.9593 Debye for the ground state. The values of Te are 25904.81, 26209.22, 32601.19, 43770.26 cm-1 for 11, 11, A1 and 15+ states, respectively; the values of Re are 2.313, 2.322, 2.188, 2.8790 for 11, 11, A1 and 15+ states, respectively; the values of De are 2.524, 2.487, 1.694, 0.3036 eV for 11-, 11, A1 and 15+ states, respectively; the values of e are 358.90, 353.08, 376.32, 134.96 cm-1 for 11-, 11, A1 and 15+ states, respectively; the values of exe are 1.2421, 1.2151, 1.6608, 1.9095 cm-1 for 11, 11, A1 and 15+ states, respectively, and the values of equilibrium dipole moments are 1.3178, 1.4719, 1.5917, -1.9785 Debye for 11-, 11, A1 and 15+ states, respectively. By solving the radial Schrdinger equation of nuclear motion, the 30 vibration levels and 30 inertial rotation constants (J=0) for X1+, 11-, 11, A1 and 15+ states are also obtained, and all of are in good agreement with the available experimental and other theoretical values.

Control of cyclic fluctuations in an independent microgrid by an SOFC triple combined cycle inertia system

Abstract Technology was investigated to control cyclic fluctuations in an independent microgrid powered with unstable renewable energy by use of a solid oxide fuel cell (SOFC, 1 MW) in a triple combined cycle (SOFC-TCC) that included a gas turbine (G/T, 0.8 MW) and a steam turbine (S/T, 0.2 MW). A large-scale solar power system (0.8 MW) and a wind farm (0.8 MW) were interconnected with the electrical power network through an inverter. The cyclic fluctuations ingredient of the network was controlled by a suitably designed inertia system and by governor-free control of the G/T and S/T. The SOFC-TCC’s control block diagram was submitted to MATLAB/Simulink R 2013a, and the deviation of electrical power and frequency in the independent microgrid caused by the SOFC-TCC and renewable energy interconnection was clarified. As a result, a range of suitable inertial constants for G/T and S/T and the electrical output characteristics were determined. Selecting a small inertial constant for the simulation resulted in a large frequency deviation of G/T and S/T, with frequency stabilized for a short time. On the other hand, selecting a large inertial constant resulted in a controlled frequency deviation, although the unstable frequency of the power grid continued for a long time.

Dynamic model of micropolar elastic thin plates with independent fields of displacements and rotations

A general model of dynamic bending of isotropic micropolar elastic thin plates with independent fields of displacements and rotations is presented. The model has been justified asymptotically based on the solutions for special cases subject to simplifying assumptions. The model incorporates transverse shear deformations. Neglecting transverse shear, a model of the dynamics of micropolar elastic thin plates is also constructed. Then, we study free and forced oscillations and derive the natural frequencies, the amplitudes of the forced oscillations and the resonance conditions for micropolar elastic hinge-supported rectangular and circular plates. Finally, the basic characteristic features of micropolar plates are numerically analysed for different values of various elastic and inertial constants of the micropolar material.

Spectroscopic properties of BCl (X1Σ+, a3Π, A1Π) molecule

The X1Σ+, a3Π and A1Π states of BCl molecule are studied using the highly accurate valence internally contracted multireference configuration interaction approach including the Davidson modification. The Dunning's correlation-consistent basis sets, aug-cc-pV6Z and aug-cc-pV5Z, are used in the study. To obtain more reliable results, the potential energy curves (PECs) of three electronic states are extrapolated to the complete basis set limit by the two-point total-energy extrapolation scheme. The effects of the core-valence correlation and relativistic corrections on the PECs are taken into account. By fitting these PECs, the spectroscopic parameters (Te, Re, ωe, ωexe, Be, αe and De) of the X1Σ+, a3Π and A1Π states of BCl are determined. These parameter values coincide with the experimental results. In addition, the whole vibrational states for X1Σ+, a3Π and A1Π states at J =0 (J is the rotational quantum number) are determined by numerically solving the radical Schrödinger equation of the nuclear motion of diatomic molecules. For each vibrational state, the vibrational level and inertial rotation constants are obtained, which are in excellent accordance with the experimental results. With the potential energy curves obtained at MRCI+Q/56+CV+DK level and the MRCI wave functions, the Franck-Condon factors, radiative lifetime of transition from a3Π and A1Π to the ground state are computed.

Second-gradient homogenized model for wave propagation in heterogeneous periodic media

The paper is focused on a homogenization procedure for the analysis of wave propagation in materials with periodic microstructure. By a reformulation of the variational-asymptotic homogenization technique recently proposed by Bacigalupo and Gambarotta (2012a), a second-gradient continuum model is derived, which provides a sufficiently accurate approximation of the lowest (acoustic) branch of the dispersion curves obtained by the Floquet–Bloch theory and may be a useful tool for the wave propagation analysis in bounded domains. The multi-scale kinematics is described through micro-fluctuation functions of the displacement field, which are derived by the solution of a recurrent sequence of cell BVPs and obtained as the superposition of a static and dynamic contribution. The latters are proportional to the even powers of the phase velocity and consequently the micro-fluctuation functions also depend on the direction of propagation. Therefore, both the higher order elastic moduli and the inertial terms result to depend by the dynamic correctors. This approach is applied to the study of wave propagation in layered bi-materials with orthotropic phases, having an axis of orthotropy parallel to the direction of layering, in which case, the overall elastic and inertial constants can be determined analytically. The reliability of the proposed procedure is analysed by comparing the obtained dispersion functions with those derived by the Floquet–Bloch theory.

Further investigations of the low-lying electronic states of AsO+ radical

The high level quantum chemistry ab inito multi-reference configuration interaction (MRCI) method with large V5Z basis set is used to calculate the spectroscopic properties of the 15 Λ—S electronic states (X1Σ+, A1Π, 1Δ, 1Σ−, 3Σ+, 3Π, 3Δ, 3Σ−, 5Σ+, 5Π, 5Δ, 1Π (II), 5Σ+ (II), 1Π (III), and 1Π (IV)) of AsO+ radical correlated to the dissociation limit As+(3Pg) + O(3Pg) and As+(1Dg) + O(1Dg). In order to obtain better potential curves and more accurate spectroscopic properties, the Davidson modification is taken into account. With the potential energy curves (PECs) determined here, vibrational levels G(v) and inertial rotation constants Bu are computed for all the bound electronic states when the rotational quantum number J equals zero (J = 0). Except for the states X1Σ+, A1Π, it is the first time that the multi-reference configuration calculation has been used on the 13 Λ—S electronic states of the AsO+ radical. The potential energy curves of all the Λ—S electronic states are depicted according to the avoided crossing rule of the same symmetry. Spin—orbit coupling effect (SOC) is introduced into the states X1Σ+, A1Π, 3Π to consider its effects on the spectroscopic properties. Transition dipole moments (TDMs) from A1Π1, 3Π1 states to the ground state X1Σ+0 + are predicted as well.

Lowest triplet (n, π*) electronic state of acrolein: Determination of structural parameters by cavity ringdown spectroscopy and quantum-chemical methods

The cavity ringdown absorption spectrum of acrolein (propenal, CH(2)=CH-CH=O) was recorded near 412 nm, under bulk-gas conditions at room temperature and in a free-jet expansion. The measured spectral region includes the 0(0)(0) band of the T(1)(n, π*) ← S(0) system. We analyzed the 0(0)(0) rotational contour by using the STROTA computer program [R. H. Judge et al., J. Chem. Phys. 103, 5343 (1995)], which incorporates an asymmetric rotor Hamiltonian for simulating and fitting singlet-triplet spectra. We used the program to fit T(1)(n, π*) inertial constants to the room-temperature contour. The determined values (cm(-1)), with 2σ confidence intervals, are A = 1.662 ± 0.003, B = 0.1485 ± 0.0006, C = 0.1363 ± 0.0004. Linewidth analysis of the jet-cooled spectrum yielded a value of 14 ± 2 ps for the lifetime of isolated acrolein molecules in the T(1)(n, π*), v = 0 state. We discuss the observed lifetime in the context of previous computational work on acrolein photochemistry. The spectroscopically derived inertial constants for the T(1)(n, π*) state were used to benchmark a variety of computational methods. One focus was on complete active space methods, such as complete active space self-consistent field (CASSCF) and second-order perturbation theory with a CASSCF reference function (CASPT2), which are applicable to excited states. We also examined the equation-of-motion coupled-cluster and time-dependent density function theory excited-state methods, and finally unrestricted ground-state techniques, including unrestricted density functional theory and unrestricted coupled-cluster theory with single and double and perturbative triple excitations. For each of the above methods, we or others [O. S. Bokareva et al., Int. J. Quantum Chem. 108, 2719 (2008)] used a triple zeta-quality basis set to optimize the T(1)(n, π*) geometry of acrolein. We find that the multiconfigurational methods provide the best agreement with fitted inertial constants, while the economical unrestricted Perdew-Burke-Ernzerhof exchange-correlation hybrid functional (UPBE0) technique performs nearly as well.

Potential energy curves, spectroscopic constants and spin-orbit coupling: A theoretical study on twelve triplet Λ-S states of Ge2 molecule

The potential energy curves (PECs) of twelve triplet Λ-S states and fourteen Ω states generated from five triplet Λ-S states of Ge2 molecule are calculated by an ab initio quantum chemical method. The PEC calculations are made for internuclear separations from 0.15 to 1.10 nm using the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson modification (MRCI + Q). The basis set used here is the aug-cc-pV5Z-pp. Convergent behavior is discussed and excellent convergence is observed with respect to the basis sets and level of theory. The PECs are extrapolated to the complete basis set limit by the total-energy extrapolation scheme. The spin-orbit coupling effect is accounted for by the Breit- Pauli Hamiltonian in combination with the aug-cc-pVTZ-pp basis set. With the PECs, the spectroscopic parameters are evaluated by fitting the first ten vibrational levels, which are obtained by solving the ro-vibrational Schrodinger equation using Numerov’s method. The spectroscopic results are compared with those reported in the literature. Excellent agreement with available measurements is found. The vibrational levels and inertial rotation constants are calculated for each Λ-S state and those of the first ten vibrational states are reported for the non-rotation Ge2 molecule. The spectroscopic parameters of the 13Σ + , 13Δ u , 23Σ + , 13Π g , 23Π g , 33Π g , 13Σ − , 23Σ − , 23Π u and 23Σ − Λ-S states and the vibrational levels and inertial rotation constants of all the Λ-S states determined by the MRCI + Q/Q5 calculations are expected to be reliable predicted ones.

Study on spectroscopic properties and molecular constants of the ground and excited states of AsCl free-radical

The dissociation limit of AsCl free-radical is correctly determined based on group theory and atomic and molecular statics. Potential energy curves (PECs) for the ground state and several low-lying electronic excited states of AsCl free-radical are calculated using the multi-reference configuration interaction method with the basis set of aug-cc-pV5Z where the Davidson correction is considered as an approximation to full CI. Separation parameters (Re, e, ee, D0, De, Be and e) are evaluated using the PEC of AsCl. Spectroscopic parameters are compared with those reported in the literature, and excellent agreement is found between them. With the PEC of AsCl free-radical, forty vibrational states of AsCl free-radical are predicted when J=0 by numerically solving the radial Schrdinger equation of nuclear notion. For each vibrational state, the vibrational levels and inertial rotation constants are reported.

Spectroscopic properties of AlC (X4∑-, B4∑-) molecule

The potential energy curves (PECs) of X4∑- and B4∑- states of the AlC molecule have been studied using highly accurate internally contracted multireference configuration interaction approach with the Davidson modification. The Dunning's correlation-consistent basis sets, aug-cc-pVnZ (n=D,T,Q,5,6) are used for the present study. To improve the quality of PECs, core-valence correlation and scalar relativistic corrections are considered. Core-valence correlation corrections are calculated with an aug-cc- pCVTZ basis set. Scalar relativistic correction calcualtions are made using the third-order Douglas-Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. Obvious effect on the PECs by the core-valence correlation and relativistic corrections has been observed. All the PECs are extrapolated to the complete basis set limit. The convergence observations of present calculations are made and the convergent behavior is discussed with respect to the basis set. Using these PECs, the spectroscopic parameters (TeReωeωexeωeyeBe and αe) of the X4∑- and B4∑- states are determined and compared with those reported in the literature. The vibration manifolds are evaluated for each state of non-rotation AlC molecule by numerically solving the radial Schrödinger equation of nuclear motion. For each vibrational state, the vibrational level and inertial rotation constants are obtained, which are in excellent accordance with the experimental findings.

Spectroscopic properties and molecular constants of the ground and excited states of SF molecule

The potential energy curves (PEC) for the ground state (X2∏) and three excited states (4∑-, 2∑-, 2Δ) of SF molecule are computed using the multireference configuration interaction method and the basis sets aug-cc-pV6Z where the Davidson correction is considered as an approximation to full CI. The separation parameters (Re, ωe, ωeχe, D0, De, Be and αe) are evaluated using the PEC of SF. The spectroscopic parameters are compared with those reported in the literature, and excellent agreement is found between them. With the PEC of SF, some vibrational states of SF are predicted when J=0 by numerically solving the radical Schrödinger equation of nuclear motion. For each vibrational state, the vibrational levels and inertial rotation constants are reported.

Potential energy curves and vibrational levels of ground and excited states of LiAl

The potential energy curves (PECs) for ground electronic state (X1∑+) and seven excited electronic states (a3∏, A1∏, b3∑+, c3∑+, B1∏, C1∑+, d3∏) of LiAl are obtained using the multi-configuration reference single and double excited configuration interaction method. Equilibrium bond length Re, adiabatic excited energy Te and vertical excited energy Tv are obtained. It is shown that c3∑+ is an unstable repulsive state, A1∏ is a weak bound state and the others are all bound states. Predissociation can be found between b3∑+ and c3∑+ states. Eight electronic states are dissociated along two channels, Li(2S)+Al(2P0) and Li(2P0)+Al(2P0). And then PECs are fitted to analytical Murrell-Sorbie (MS) potential function to deduce the spectroscopic parameters:the Re is 0.2863 nm, ωe is 316 cm-1 and De is 1.03 eV for the ground state; the values of Tv of excited states are 0.27, 0.83, 1.18, 1.14, 1.62, 1.81 and 2.00 eV; the values of De are 1.03, 0.82 and 0.26, repulsive state, 1.54, 1.10, 0.93 eV, and the values of corresponding frequency ωe are 339, 237, 394, repulsive state, 429, 192, 178 cm-1. By solving the radial Schrödinger equation of nuclear motion, the vibration levels, inertial rotation constants (J=0) are reported for the first time.