Number Of Constants Research Articles

On the relationship between control theory and nonholonomic mechanics

This paper concerns transitions of a mechanical system, in a given time, from one state, in which the generalized coordinates and velocities are given, into another one, in which the system should have the required coordinates and velocities. It is assumed that such a transition may be effected using a single control force. It is shown that if one determines the force using the Pontryagin maximum principle (from the minimality condition of the time integral of the force squared during the time of motion), then a nonholonomic high-order constraint occurs in the defined process of motion of the system. As a result, this problem can be attacked by the theory of motion of nonholonomic systems with high-order constraints. According to this theory, in the set of different motions with a constraint of the same order, the optimal motion is the one for which the generalized Gauss principle is fulfilled. Thus, a control force that is chosen from the set of forces that provide the transition of a mechanical system from one state to another during a given time can be specified both on the basis of the Pontryagin maximum principle and on the basis of the generalized Gauss principle. Particular attention is paid to the comparison of the results that are obtained by these two principles. This is illustrated using the example of a horizontal motion of a pendula cart system to which a required force is applied. To obtain the control force without jumps at the beginning and the end of the motion, an extended boundary problem is formulated in which not only the coordinates and velocities are given at these times, but also the derivatives of the coordinates with respect to time up to the order n ≥ 2. This extended boundary-value problem cannot be solved via the Pontryagin maximum principle, because in this case the number of arbitrary constants will be smaller than the total number of the boundary-value conditions. At the same time, the generalized Gauss principle is capable of solving the problem, because in this case it is only required to increase the order of the principle to a value that agrees with the number of given boundary-value conditions. The results of numerical calculations are presented.

A Modified Johnson-Cook Constitutive Equation to Predict Hot Deformation Behavior of Ti-6Al-4V Alloy

A modified Johnson-Cook constitutive equation of Ti-6Al-4V alloy is proposed based on hot compression tests performed in the temperature range of 1073-1323 K and strain rate 0.001-1 s−1. The experimental stress-strain data were employed to develop the modified Johnson-Cook constitutive equation of different phase regimes (α + β and β phase). The predicted flow stresses using the developed equation were compared with experimental data. Correlation coefficient (R) and average absolute relative error (AARE) were introduced to verify the validity of the constitutive equation. The values of R and AARE for α + β phase were 0.990 and 7.81%, respectively. And in β phase region, the values of R and AARE were 0.985 and 10.36%, respectively. Meanwhile, the accuracy, the number of material constants involved, and the computational time required of the constitutive equation were evaluated by comparing with a strain-compensated Arrhenius-type constitutive equation. The results indicate that accuracy of modified Johnson-Cook constitutive equation is higher than that of compensated Arrhenius-type model at α + β phase, while lower at single β phase region. Meanwhile, the time required for evaluating the material constants of modified Johnson-Cook constitutive equation is much shorter than that of the strain-compensated Arrhenius type ones.

Measurements of elastic constants in anisotropic media

Simulation of elastic-wave propagation in rock requires knowledge of the elastic constants of the medium. The number of elastic constants required to describe a rock depends on the symmetry class. For example, isotropic symmetry requires only two elastic constants, whereas transversely isotropic symmetry requires five unique elastic constants. The off-diagonal elastic constant depends on a wave velocity measured along a nonsymmetry axis. The most difficult barrier when measuring these elastic constants is the ambiguity between the phase and group velocity in experimental measurements. Several methods to eliminate this difficulty have been previously proposed, but they typically require several samples, difficult machining, or complicated computational analysis. Another approach is to use the surface (Rayleigh) wave velocity to obtain the off-diagonal elastic constant. Rayleigh waves propagated along symmetry axes have phase and group velocities that are equal for materials with no frequency dispersion, thereby eliminating the ambiguity. Using a theoretical secular equation that relates the Rayleigh velocity to the elastic constants enable determination of the off-diagonal elastic constant. Laboratory measurements of the elastic constants in isotropic and anisotropic materials were made using ultrasonic transducers (central frequency of 1 MHz) for the Rayleigh-wave method and a wavefront-imaging method. The two methods indicated agreement within 1% and 3% for isotropic and transversely isotropic samples, respectively, demonstrating the ability of the Rayleigh-wave method to measure the off-diagonal elastic constant. The surface-wave approach eliminates the need for multiple samples, expensive computational calculations, and most importantly, it removes the ambiguity between the phase and group velocity in the measured data for materials with no frequency dispersion because all measurements are made along symmetry axes.

Free energy of a Lovelock holographic superconductor

We study thermodynamics of black hole solutions in Lanczos-Lovelock AdS gravity in d+1 dimensions coupled to nonlinear electrodynamics and a Stueckelberg scalar field. This class of theories is used in the context of gauge/gravity duality to describe a high-temperature superconductor in d dimensions. Larger number of coupling constants in the gravitational side is necessary to widen a domain of validity of physical quantities in a dual QFT. We regularize the gravitational action and find the finite conserved quantities for a planar black hole with scalar hair. Then we derive the quantum statistical relation in the Euclidean sector of the theory, and obtain the exact formula for the free energy of the superconductor in the holographic quantum field theory. Our result is analytic and it includes the effects of backreaction of the gravitational field. We further discuss on how this formula could be used to analyze second order phase transitions through the discontinuities of the free energy, in order to classify holographic superconductors in terms of the parameters in the theory.

Chiral effective field theory analysis of hadronic parity violation in few-nucleon systems

We reconsider the derivation of the nucleon-nucleon parity-violating (PV) potential within a chiral effective field theory framework. We construct the potential up to next-to-next-to-leading order by including one-pion-exchange, two-pion-exchange, contact, and 1/M (M being the nucleon mass) terms, and use dimensional regularization to renormalize the pion-loop corrections. A detailed analysis of the number of independent low-energy constants (LEC's) entering the potential is carried out. We find that it depends on six LEC's: the pion-nucleon PV coupling constant $h^1_\pi$ and five parameters multiplying contact interactions. We investigate PV effects induced by this potential on several few-nucleon observables, including the $\vec{p}$-$p$ longitudinal asymmetry, the neutron spin rotation in $\vec{n}$-$p$ and $\vec{n}$-$d$ scattering, and the longitudinal asymmetry in the $^3$He$(\vec{n},p)^3$H charge-exchange reaction. An estimate for the range of values of the various LEC's is provided by using available experimental data.

Surface complexation of the phototrophic anoxygenic non-sulfur bacterium Rhodopseudomonas palustris

This work extends our knowledge of anoxygenic phototrophic bacteria (APB) interactions and contributes to the database of aquatic microorganism trace element adsorption parameters, such as heavy metal pollutants and limiting micronutrients. The surface properties of a phototrophic anaerobic non-sulfur bacterium (Rhodopseudomonas palustris KR-95p), which is often considered a model microorganism for Precambrian anoxygenic primary producers, were studied using potentiometric acid-base titration at various ionic strengths. The electrophoretic mobility of viable cells was measured as a function of pH and ionic strength, as well as cation (Zn, Cd, and Pb) and anion (Mo, W, and Cr) concentration. Zn, Cd, Sr, Pb, Cu, Cs, Al, Ga, Sb, As, Ge, Tl, W, and Mo adsorption was studied as a function of pH at a constant initial element concentration, yielding the pH-dependent adsorption edge. Zn, Cd, Sr, Cu and Pb adsorption was also studied as a function of metal concentration in solution at a constant pH, producing a “Langmuirian” adsorption isotherm. The non-electrostatic linear programming method (LPM) was used to fit the experimental data and assess the number of surface sites and adsorption reaction constants involved in heavy metal and anion binding to the cyanobacteria surface.The total H/OH binding site number (80–480μmol/gwet) for Rps. palustris encompasses the values reported for other APB (60–120μmol/gwet) and cyanobacteria (50–200μmol/gwet) examined using the same technique. For the cations, the adsorption edge follows the order Pb2+>Cu2+≫Cd2+≈Zn2+>Sr2+>Tl+>Cs+, which is similar to the element hydrolysis order. Trivalent hydrolysates (Al3+ and Ga3+) demonstrated increased adsorption with a pH increase at 2≤pH≤4 followed by desorption from the bacterial surface at pH>5–6 as negatively charged Al(OH)4− and Ga(OH)4−, similar to anions, such as MoO42− and WO42−. This behavior directly reflects the level of trace element complexation with two primary binding sites at the surface, carboxylate and phosphorylate, and certain electrostatic-like interactions between negatively charged anions and positive amine groups in acidic solutions. The main results of the present study are that the Rps. palustris exhibit trace element binding properties through their pH-dependence and overall adsorption capacity, which are similar to properties described earlier for other phototrophic bacteria, both anoxygenic bacteria and cyanobacteria. The absolute adsorption capacities for metal cations follow the order Rps. palustris<APB Rdb. blasticus<cyanobacteria Gloeocapsa sp, which presumably reflects a greater concentration of free metal cations in the external milieu for this species. Correspondingly, the adsorbed anion concentration is greatest for Rps. palustris, which therefore yields a higher proportion of positively charged amine groups or fewer negative charges overall due to a lower fraction of carboxylates and phosphorylates.

Grüneisen analysis of thermodynamic properties of δ-phase Pu–Ga alloys

We present a Grüneisen analysis of the intriguing temperature dependence of the thermal expansion and bulk modulus of delta phase plutonium alloys. This analysis exploits the thermodynamic relationship between these quantities and the heat capacity and reduces the description of complicated behaviour to the determination of a manageable number of numerical constants. We conclude from the analysis (1) that there is a small Schottky-like heat capacity anomaly at high temperatures and (2) that the size of this anomaly depends strongly on alloy concentration. Grüneisen analysis provides an economical description of the thermal expansion and bulk modulus of δ-Pu.

A multi-objective optimization approach to the parameter determination of constitutive plasticity models for the simulation of multi-phase load histories

This work develops a multi-objective optimization approach to determine the material constants of constitutive plasticity models. The process is implemented using an actual set of experimental results in the form of multi-phase cyclic-monotonic load histories. With the result of a multi-objective approach being a set of solutions (a set of calibrated models), the characteristics of these solutions are examined individually and within the framework of the entire set. Two elements of parameter determination are considered to address the characteristics of the calibrated models in a multi-objective space: the number of material constants, and the load history used to calibrate the models.

Damage prediction for un-coated and coated aluminum alloys under thermal and mechanical fatigue loadings based on a modified plastic strain energy approach

Abstract In this article, a novel energy-based lifetime prediction model has been presented for uncoated and coated aluminum alloys, subjected to thermal and mechanical fatigue loadings. For this objective, isothermal and thermo-mechanical fatigue tests were performed on the A356.0 alloy, with and without thermal barrier coating systems. This model, which was based on the plastic strain energy, had three correction factors including temperature, strain and mean stress effects. The predicted lifetime showed a proper agreement with experimental data. By the present model, higher accuracy was obtained in comparison to other existed approaches. Besides, the present model had lower number of material constants.

Implications of conformal invariance in momentum space

We present a comprehensive analysis of the implications of conformal invariance for 3-point functions of the stress-energy tensor, conserved currents and scalar operators in general dimension and in momentum space. Our starting point is a novel and very effective decomposition of tensor correlators which reduces their computation to that of a number of scalar form factors. For example, the most general 3-point function of a conserved and traceless stress-energy tensor is determined by only five form factors. Dilatations and special conformal Ward identities then impose additional conditions on these form factors. The special conformal Ward identities become a set of first and second order differential equations, whose general solution is given in terms of integrals involving a product of three Bessel functions (`triple-K integrals'). All in all, the correlators are completely determined up to a number of constants, in agreement with well-known position space results. We develop systematic methods for explicitly evaluating the triple-K integrals. In odd dimensions they are given in terms of elementary functions while in even dimensions the results involve dilogarithms. In some cases, the triple-K integrals diverge and subtractions are necessary and we show how such subtractions are related to conformal anomalies. This paper contains two parts that can be read independently of each other. In the first part, we explain the method that leads to the solution for the correlators in terms of triple-K integrals and how to evaluate these integrals, while the second part contains a self-contained presentation of all results. Readers interested only in results may directly consult the second part of the paper.

The changing nature of advertisements inThe Freeman's Journal: a case study, 1763-1924

Purpose– The aim of this paper is to examine the nature of newspaper advertisements published in the Irish newspaperThe Freeman's Journal. This is approached by examining the construction of a selection of printed advertisements, including the strategies used in each, which appeared inThe Freeman's Journalbetween 1763 and 1924.Design/methodology/approach– The central primary source used isThe Freeman's Journaland the selected advertisements. A number of primary and secondary sources are employed in the analysis of the featured advertisements in respect to the format, language and marketing strategies used in each.Findings– The case study finds that there were a number of constants in the advertisements examined, as well as a number of advertising strategies employed from the eighteenth century onward, that have more commonly been associated with the 1918 to 1939 interwar period. It also found that the use of illustrations did not solely depend on twentieth century printing advances, but that printing developments did much to expand and progress advertising in Ireland.Originality/value– This case study explores a little researched area in Irish advertising history.

Determination of Flow Stress Using Parametric Linearity Relationship of Arrhenius Power Law

AbstractIn this study, hot workability aspect for modeling the flow stress at specified deformation level is investigated. The proposed model contains the basic parametric relationship of Arrhenius power law. The developed mathematical model is validated on Al 2024 alloy to check its feasibility over a wide range of strain rate, strain, and temperature. When compared with Johnson-Cook (JC) model, it is found to give a more perceptible experimental output by limited evaluation of arbitrary constants. The proposed model uses the input from hot compression test without the necessacity to go to torsion experiment. This proves its supremacy over JC model which require both the inputs. It also limits the number of constants, so produces a forwarding mark to N.S. Babu Model which needs 48 numbers of constants to define the constitutive aspect of deformation.

Complementary Measurement of Thermal Architecture of NbSi TES with Alpha Particle and Complex Impedance

As shown by the Planck mission (Planck Collaboration. Astronomy and astrophysics. arXiv1303.5071P, 2013), background limited bolometers in a space environment are very sensitive to high energy particles. In order to not degrade their sensitivity, it is necessary to reduce this unwanted signal. To achieve this goal, a good understanding of the detector’s thermal architecture is mandatory. To investigate this question, we used an \(\alpha \) particle source in front of our niobium silicon (NbSi) alloy Transition edge sensors (TES). The number of time constants required to fit the data and the way these time constants behave as we change the bias power gave us a good insight on the TES thermal architecture. Indeed we expect a decrease of the detector time constant due to the electro-thermal feedback properties. We will first present some standard characterizations of NbSi TES using a simple thermal model and how they indicate the presence of multiple thermal decouplings. Then we will show the results of the \(\alpha \) particles measurements and how we used them to build our thermal model for Complex Impedance fitting. All this work has been done for the QUBIC experiment, a B-modes instrument.

Suppressing one‐bond homonuclear 13C,13C scalar couplings in the J‐HMBC NMR experiment: application to 13C site‐specifically labeled oligosaccharides

Site-specific (13)C isotope labeling is a useful approach that allows for the measurement of homonuclear (13)C,(13)C coupling constants. For three site-specifically labeled oligosaccharides, it is demonstrated that using the J-HMBC experiment for measuring heteronuclear long-range coupling constants is problematical for the carbons adjacent to the spin label. By incorporating either a selective inversion pulse or a constant-time element in the pulse sequence, the interference from one-bond (13)C,(13)C scalar couplings is suppressed, allowing the coupling constants of interest to be measured without complications. Experimental spectra are compared with spectra of a nonlabeled compound as well as with simulated spectra. The work extends the use of the J-HMBC experiments to site-specifically labeled molecules, thereby increasing the number of coupling constants that can be obtained from a single preparation of a molecule.

NMR spectroscopy on flavins and flavoproteins.

(1)H-, (11)B-, (13)C-, (15)N-, (17)O-, (19)F-, and (31)P-NMR chemical shifts of flavocoenzymes and derivatives of it, as well as of alloxazines and isoalloxazinium salts, from NMR experiments performed under various experimental conditions (e.g., dependence of the chemical shifts on temperature, concentration, solvent polarity, and pH) are reported. Also solid-state (13)C- and (15)N-NMR experiments are described revealing the anisotropic values of corresponding chemical shifts. These data, in combination with a number of coupling constants, led to a detailed description of the electronic structure of oxidized and reduced flavins. The data also demonstrate that the structure of oxidized flavin can assume a configuration deviating from coplanarity, depending on substitutions in the isoalloxazine ring, while that of reduced flavin exhibits several configurations, from almost planar to quite bended. The complexes formed between oxidized flavin and metal ions or organic molecules revealed three coordination sites with metal ions (depending on the chemical nature of the ion), and specific interactions between the pyrimidine moiety of flavin and organic molecules, mimicking specific interactions between apoflavoproteins and their coenzymes. Most NMR studies on flavoproteins were performed using (13)C- and (15)N-substituted coenzymes, either specifically enriched in the pterin moiety of flavin or uniformly labeled flavins. The chemical shifts of free flavins are used as a guide in the interpretation of the chemical shifts observed in flavoproteins. Although the hydrogen-bonding pattern in oxidized and reduced flavoproteins varies considerably, no correlation is obvious between these patterns and the corresponding redox potentials. In all reduced flavoproteins the N(1)H group of the flavocoenzyme is deprotonated, an exception is thioredoxin reductase. Three-dimensional structures of only a few flavoproteins, mostly belonging to the family of flavodoxins, have been solved. Also the kinetics of unfolding and refolding of flavodoxins has been investigated by NMR techniques. In addition, (31)P-NMR data of all so far studied flavoproteins and some (19)F-NMR spectra are discussed.

Stator resistance estimator for direct torque control of permanent magnet synchronous motor drive systems using multi-resolution analysis wavelet

This paper presents an innovative technique for stator resistance estimation of direct torque control permanent magnet synchronous motor based on multi-resolution analysis wavelet PI controller. The online stator resistance estimation employed adjusts precisely the stator resistance value relatively to the evolution of the stator current estimation error gradient to avoid the drive instability and ensure the tracking of the actual value of the stator resistance. The multi-resolution wavelet PI controller implemented for the three level wavelet decomposition is computationally far simpler as compared to the multi-resolution technique with separate computations for high and low pass filtering at each level of decomposition. Also it is prominent by less number of tuning constants and less tuning effort as compared to a standard multi-resolution wavelet controller. The simulation results show that the proposed method can reduce the torque ripple and current ripple, superior to track the actual value of the stator resistance for different operating conditions.

Analysis of Tool Life during Turning Operation by Determining Optimal Process Parameters

In any metal cutting operation the features of tools, input work materials, machine parameter settings will influence the process efficiency and output quality characteristics. A significant improvement in process efficiency may be obtained by process parameter optimization that identifies and determines the regions of critical process control factors leading to desired outputs or responses with acceptable variations ensuring a lower cost of manufacturing. For turning process, the cutting conditions i.e. Speed, Feed and Depth of cut plays an important role in the efficient use of a machine tool.In order to determine the optimum cutting conditions, one has to estimate the tool life and cutting forces with a reasonable degree of accuracy since many of the constraints those are applying on a process are influenced by these parameters. For a practical machining situation, since no adequate machining theory is available to predict the tool life and cutting forces, one is compelled to rely on empirical equations to predict these parameters. However, these empirical equations involve a number of constants which are not readily available. Hence this Paper proposes an alternative approach to determine the optimal process parameters used to predict cutting forces, tool life and surface finish

A modified Zerilli–Armstrong constitutive model to predict hot deformation behavior of 20CrMo alloy steel

True stress and true strain values were obtained from isothermal hot compression tests conducted on a Gleeble thermal simulation machine, in a wide range of temperatures (1173–1373K) and strain rates (1.5×10−3–1.5×10−2s−1). The experimental data were used to develop a modified Zerilli–Armstrong constitutive model. The predicted flow stresses using the developed model were compared with experimental values. A correlation coefficient (R) of 0.989 and an average absolute relative error (AARE) of 7.71% between the measured and calculated flow stresses have been obtained. Comparing with a modified Johnson–Cook model developed in the authors’ previous study, the accuracy, the number of material constants involved and the computational time required of the model were evaluated.

Uncertainty analysis of multi-rate kinetics of uranium desorption from sediments

Multi-rate surface complexation models have been proposed to describe the kinetics of uranyl (U(VI)) surface complexation reactions (SCR) rate-limited by diffusive mass transfer to and from intragranular sorption sites in subsurface sediments. In this study, a Bayesian-based, Differential Evolution Markov Chain method was used to assess the uncertainty and to identify factors controlling the uncertainties of the multi-rate SCR model. The rate constants in the multi-rate SCR were estimated with and without assumption of a specified lognormal distribution to test the lognormal assumption typically used to minimize the number of the rate constants in the multi-rate model. U(VI) desorption under variable chemical conditions from a contaminated sediment at US Hanford 300 Area, Washington was used as an example. The results indicated that the estimated rate constants without a specified lognormal assumption approximately followed a lognormal distribution, indicating that the lognormal is an effective assumption for the rate constants in the multi-rate SCR model. However, those rate constants with their corresponding half-lives longer than the experimental durations for model characterization had larger uncertainties and could not be reliably estimated. The uncertainty analysis revealed that the time-scale of the experiments for calibrating the multi-rate SCR model, the assumption for the rate constant distribution, the geochemical conditions involved in predicting U(VI) desorption, and equilibrium U(VI) speciation reaction constants were the major factors contributing to the extrapolation uncertainties of the multi-rate SCR model. Overall, the results from this study demonstrated that the multi-rate SCR model with a lognormal distribution of its rate constants is an effective approach for describing rate-limited U(VI) desorption; however, the model contains uncertainties, especially for those smaller rate constants, that require careful consideration for predicting U(VI) sorption and desorption.

Steady Modeling of a Turbocharger Turbine for Automotive Engines

Nowadays the turbocharging technique is playing a fundamental role in improving automotive engine performance and reducing fuel consumption and the exhaust emissions, in spark-ignition and compression ignition engines, as well. To this end, one-dimensional (1D) modeling is usually employed to compute the engine-turbocharger matching, to select the boost level in different operating conditions, and to estimate the low-end torque level and the transient response. However, 1D modeling of a turbocharged engine requires the availability of the turbine and compressor characteristic maps. This leads to some typical drawbacks: (1)Performance maps of the turbocharger device are usually limited to a reduced number of rotational speeds, pressure ratios, and mass flow rates because of turbine/compressor matching limits; (2) as a consequence of previous issue, unphysical extrapolation of maps' data is commonly required; and (3) heat transfer conditions may strongly differ between test bench measurements and actual operation, where turbocharger is coupled to an internal combustion engine. To overcome the above problems, in the present paper a numerical procedure is introduced: It solves 1D steady flow equations inside the turbine components with the aim of accurately reproducing the experimentally derived characteristic maps. The steady procedure describes the main phenomena and losses arising within the stationary and rotating channels constituting the turbine. It is utilized to directly compute the related steady maps, starting from the specification of a reduced set of geometrical data. An optimization process is employed to identify a number of tuning constants included in the various loss correlations. The procedure is applied to the simulation of five different turbines: three waste-gated turbines, a twin-entry turbine, and a variable geometry turbine. The numerical results show good agreement with the experimentally derived maps for all the tested devices. The model is, hence, used to evaluate the turbine performance in the whole operating domain.