Dynamics of a nonlinear microresonator based on resonantly interacting flexural-torsional modes

A novel microresonator operating on the principle of nonlinear modal interactions due to autoparametric 1:2 internal resonance is introduced. Specifically, an electrostatically actuated pedal-microresonator design, utilizing internal resonance between an out-of-plane torsional mode and a flexural in-plane vibrating mode is considered. The two modes have their natural frequencies in 1:2 ratio, and the design ensures that the higher frequency flexural mode excites the lower frequency torsional mode in an autoparametric way. A Lagrangian formulation is used to develop the dynamic model of the system. The dynamics of the system is modeled by a two degrees of freedom reduced-order model that retains the essential quadratic inertial nonlinearities coupling the two modes. Retention of higher-order model for electrostatic forces allows for the study of static equilibrium positions and static pull-in phenomenon as a function of the bias voltages. Then for the case when the higher frequency flexural mode is resonantly actuated by a harmonically varying AC voltage, a comprehensive study of the response of the microresonator is presented and the effects of damping, and mass and structural perturbations from nominal design specifications are considered. Results show that for excitation levels above a threshold, the torsional mode is activated and it oscillates at half the frequency of excitation. This unique feature of the microresonator makes it an excellent candidate for a filter as well as a mixer in RF MEMS devices.     

Some optimal path problems subject to improvements

In this paper, the functional equation technique of dynamic programming is applied to solve the problems of a) determining an optimal path from a given origin to a fixed destination when the path is subject to a given number of improvements, b) finding an optimal path from a given origin to an assigned destination by passing at least once through each node of a set of specified nodes when the path is subject to a given number of improvements, c) obtaining an optimal path from a given origin to a fixed destination by passing at least once through at least one node of each ofK sets of specified nodes when the path is subject to a given number of improvements.

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Zusammenfassung In dieser Arbeit wird die Funktionalgleichung des dynamischen Programmierens verwendet, um folgende drei Netzwerkprobleme zu lösen: a) Bestimmung eines optimalen Pfades von einem gegebenen Anfangs- zu einem gegebenen Endknoten, wenn längs einem Pfad eine gewisse Anzahl von Verbesserungen möglich sind. b) Wie a), wobei zusätzlich der Pfad mindestens einmal durch jeden Knoten einer spezifizierten Knotenmenge gehen soll. c) Wie a), wobei der Pfad durch mindestens einen Knoten in jeder vonK spezifizierten Knotenmenge gehen soll.

     

Observation of autoionization resonances in uranium by step-wise laser photoionization

A large number of autoionization resonances have been observed in uranium in the energy range 50,590–51,560cm^–1 by two-step three-photon ionization technique, using two copper vapor laser pumped dye lasers. A Rydberg series converging to the ionization limit of UII at 1749cm^–1 (⁶ L _13/2) has been identified. Some of these resonances are very narrow with a fwhm of 0.1cm^–1. Possible origins of these are discussed.     

Aromatic-aliphatic copolyesters—I. Synthesis and characterization

Copolyesters have been synthesized by interfacial polycondensation of 2,2-bis(4-hydroxyphenyl)-propane or phenolphthalein as aromatic diol and ethylene glycol or polyethylene glycol as aliphatic diol in various mole ratios with terephthaloyl or isophthaloyl chloride. Chemical compositions, dilute solution viscosities and solubility behaviours of these polymers have been investigated. The introduction of aliphatic diol in aromatic polyesters influences T_g, softening point, chemical resistance and thermal stability.     

Kinetics and mechanism of ligand substitution of mono(polyamine)-nickel(II) complexes with 4-(2-pyridylazo)resorcinol

Summary The kinetics and mechanism of ligand substitution reactions of tetraethylenepentamine nickel(II), Ni (Teren), and triethylenetetraamine nickel(II), Ni(Trien), with 4-(2-pyridylazo)resorcinol (parH₂) have been studied spectrophotometrically at I=0.1 M (NaClO₄) at 25°C. In both systems two distinct reaction steps are observed. The rapid first step follows the rate law d[Ni(Polyamine)(ParH₂)]/dt=k₁ [Ni(Polyamine)] [ParH₂]. The formation of ternary complexes of Ni (Polyamine) with ParH₂ has been investigated under second order equal concentration conditions. The values of second order rate constants for the Trien and Teren reactions are (2.1±0.2)×10⁴ M^–1s^–1 and (7.8±0.6)×10³ M^–1s^–1 respectively at pH=9.0, I=0.1 M and 25°C.The rate law for the second step may be written as d[Ni(Par)₂]/dt=k₂[Ni(Polyamine)(ParH₂)]. Values of k₂ for the Trien and Teren systems are (2.5±0.1)×10^–4 s^–1 and (4.76±0.3)×10^–5 s^–1 respectively.     

Detection of OH radical in laser induced photodissociation of tetrahydrofuran at 193 nm

On excitation at 193 nm, tetrahydrofuran (THF) generates OH as one of the photodissociation products. The nascent energy state distribution of the OH radical was measured employing laser induced fluorescence technique. It is observed that the OH radical is formed mostly in the ground vibrational level, with low rotational excitation (approximately 3%). The rotational distribution of OH (v"=0,J) is characterized by rotational temperature of 1250+/-140 K. Two spin-orbit states, 2Pi3/2 and 2Pi1/2 of OH are populated statistically. But, there is a preferential population in Lambda doublet levels. For all rotational numbers, the 2Pi+(A') levels are preferred to the 2Pi-(A") levels. The relative translational energy associated with the photoproducts in the OH channel is calculated to be 17.4+/-2.2 kcal mol-1, giving an fT value of approximately 36%, and the remaining 61% of the available energy is distributed in the internal modes of the other photofragment, i.e., C4H7. The observed distribution of the available energy agrees well with a hybrid model of energy partitioning, predicting an exit barrier of approximately 16 kcal mol-1. Based on both ab initio molecular orbital calculations and experimental results, a plausible mechanism for OH formation is proposed. The mechanism involves three steps, the C-O bond cleavage of the ring, H atom migration to the O atom, and the C-OH bond scission, in sequence, to generate OH from the ground electronic state of THF. Besides this high energy reaction channel, other photodissociation channels of THF have been identified by detecting the stable products, using Fourier transform infrared and gas chromatography.     

Dissociation dynamics of thiolactic acid at 193 nm: detection of the nascent OH product by laser-induced fluorescence

Electronically excited thiolactic acid (2-mercaptopropionic acid), H(3)C-CH(SH)-COOH, undergoes the C-OH bond cleavage on excitation to the S(2) state at 193 nm, generating the primary product OH (v,J), which is detected by laser-induced fluorescence technique in a collisionless condition of flow system. The partitioning of the available energy between vibrational, rotational, and translational degrees of freedom of nascent photofragments is obtained from relative intensities of ro-vibronic lines in laser-induced fluorescence spectrum of OH, and their Doppler profiles. The rotational population of OH (v(")=0) is characterized by rotational temperature of 408+/-25 K. OH is produced in a vibrationally cold state, i.e., mostly in v(")=0. The average translational energy of OH (v(")=0,J(")) is found to be 21.5+/-2.0 kcal/mol, which implies 25.6 kcal/mol of energy in relative translation of photoproducts corresponding to the f(t) value of approximately 0.6. The observed high translational energy is due to the presence of a barrier in the exit channel, implying that the C-OH bond scission takes place on an electronically excited potential energy surface. The observed partitioning of the available energy between various degrees of the photofragments is theoretically modeled, and the hybrid model, with 26.0 kcal/mol of barrier in the exit channel, is found to explain the measured data quite well. The experimental results are also supported with ab initio molecular orbital calculations for both the ground and the excited electronic states. Time-dependent density functional theory is used to understand the nature of various electronic transitions connecting the lower excited states. Potential energy curves as a function of the C-OH bond length of thiolactic acid suggest distinct exit barriers in the S(1), T(1), and T(2) states. But, we could locate the transition state structure for OH formation in the S(1) state alone. Thus, although thiolactic acid is excited to the S(2) state at 193 nm, it undergoes internal conversion to S(1) where it dissociates to yield OH. In addition to the OH channel from excited electronic states, we studied theoretically all probable dissociation channels occurring on the ground electronic state of thiolactic acid.