Size Constant Research Articles

Determination of Pressure Jump Dependence and Time Constants of Hydraulic Pumps with Constant Pressure and Variable Flow

Simulations of the pump response time refer to the determination of the time constant of the transient process when the flow and pressure change. The changes mentioned in the standards are precisely defined and prescribed by the “MIL-P-19692E” norms. The simulation showed that the time constants are within the permissible limits prescribed by these norms. The diagram shows the responses for the considered pump and for the case when the flow changes from Qn to Qmin and changes from Qmin to Qn. The time constants t1 and t2 are defined on the diagrams, with the parameters that the pump has. In addition, the standards define the pressure jump that occurs during the transient process as well as time constants. From the flow change diagram, it can be seen that the flow change is also very fast and takes place in time intervals shorter than 0.1 s. By evaluating the size of the time constants, t1 and t2, it can be concluded that they have a value below 0.05 s, which meets the regulations in that area. Also, the size of the jump pressure meets the regulations because it is only 1.2 M Pa above the nominal pressure.

Growth of structure constants of free Lie algebras relative to Hall bases

We derive a priori bounds on the size of the structure constants of the free Lie algebra over a set of indeterminates, relative to its Hall bases. We investigate their asymptotic growth, especially as a function of the length of the involved Lie brackets.First, using the classical recursive decomposition algorithm, we obtain a rough upper bound valid for all Hall bases. We then introduce new notions (which we call alphabetic subsets and relative foldings) related to structural properties of the Lie brackets created by the algorithm, which allow us to prove a sharp upper bound for the general case. We also prove that the length of the relative folding provides a strictly decreasing indexation of the recursive rewriting algorithm. Moreover, we derive lower bounds on the structure constants proving that they grow at least geometrically in all Hall bases.Second, for the celebrated historical length-compatible Hall bases and the Lyndon basis, we prove tighter sharp upper bounds, which turn out to be geometric in the length of the brackets.Third, we construct two new Hall bases, illustrating two opposite behaviors in the two-indeterminates case. One is designed so that its structure constants have the minimal growth possible, matching exactly the general lower bound, linked with the Fibonacci sequence. The other one is designed so that its structure constants grow super-geometrically.Eventually, we investigate asymmetric growth bounds which isolate the role of one particular indeterminate. Despite the existence of super-geometric Hall bases, we prove that the asymmetric growth with respect to each fixed indeterminate is uniformly at most geometric in all Hall bases.

Iterative approaches to the self-consistent nuclear energy density functional problem

Large-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing solvers can become very slow, and their performance dependent on manual fine-tuning of numerical parameters. In addition, convergence can sensitively depend on particularities of the EDF's parametrisation under consideration. Using the widely-used Skyrme EDF as an example, we investigate the impact of the parametrisation of the EDF, both in terms of the operator structures present and the size of coupling constants, on the convergence of numerical solvers. We focus on two aspects of the self-consistency cycle, which are the diagonalisation of a fixed single-particle Hamiltonian on one hand and the evolution of the mean-field densities and potentials on the other. Throughout the article we use a coordinate-space representation, for which the behaviour of algorithms can be straightforwardly analysed. We propose two algorithmic improvements that are easily implementable in existing solvers, heavy-ball dynamics and potential preconditioning. We demonstrate that these methods can be made virtually parameter-free, requiring no manual fine-tuning to achieve near-optimal performance except for isolated cases. The combination of both methods decreases substantially the CPU time required to obtain converged results. The improvements are illustrated for the MOCCa code that solves the self-consistent HFB problem in a 3d coordinate space representation for parametrisations of the standard Skyrme EDF at next-to-leading order in gradients and its extension to next-to-next-to-leading order.

A NEW METHOD FOR CONSTANT ESTIMATE STABILITY OF COMPLEX WITH EDTA

The present work describes a new methodology in analytical chemistry, which makes it possible to calculate the stability constant (equilibrium or formation) of the coordination compounds generated between all metallic cations in the periodic table, except for alkali metals (group 1 ) together with the ethylene diamine tetraacetic acid binder. The system is simple to use, inexpensive, and allows the knowledge of the size of the conditional formation constants for all metals coordinated with the complexing agent to be investigated at any pH value investigated. In addition, the method is also extensive for other binders having the same chemical reaction property as ethylenediamine tetraacetic acid performs with metal ions in the same stoichiometric bonding ratio. For the execution of this study, solutions of copper (II) cation was employed, at a concentration of 1.0x10-2 mol L-1 and the complexing agent, also presenting the same concentration of metal. The assay was conducted in a buffering system consisting of ammonium hydroxide and ammonium chloride salt at a constant pH of 10.0. The method allows its use in experimental procedures developed both in a chemical laboratory and in a classroom, used during the theoretical activities. The chelating agent has a wide spectrum of application in the food product industries, also in the generation of cleaning materials in general, as well as in the photography industry, textile production, paper manufacture and the like, rubbers and the like, polymers and derivatives, among other production lines intended for its manufacture for human consumption.

NMR experiments for the rapid identification of P=O···H-X type hydrogen bonds in nucleic acids.

Hydrogen bonds involving the backbone phosphate groups occur with high frequency in functional RNA molecules. They are often found in well-characterized tertiary structural motifs presenting powerful probes for the rapid identification of these motifs for structure elucidation purposes. We have shown recently that stable hydrogen bonds to the phosphate backbone can in principle be detected by relatively simple NMR-experiments, providing the identity of both the donor hydrogen and the acceptor phosphorous within the same experiment (Duchardt-Ferner et al., Angew Chem Int Ed Engl 50:7927-7930, 2011). However, for imino and hydroxyl hydrogen bond donor groups rapidly exchanging with the solvent as well as amino groups broadened by conformational exchange experimental sensitivity is severely hampered by extensive line broadening. Here, we present improved methods for the rapid identification of hydrogen bonds to phosphate groups in nucleic acids by NMR. The introduction of the SOFAST technique into 1H,31P-correlation experiments as well as a BEST-HNP experiment exploiting 3hJN,P rather than 2hJH,P coupling constants enables the rapid and sensitive identification of these hydrogen bonds in RNA. The experiments are applicable for larger RNAs (up to ~ 100-nt), for donor groups influenced by conformational exchange processes such as amino groups and for hydrogen bonds with rather labile hydrogens such as 2'-OH groups as well as for moderate sample concentrations. Interestingly, the size of the through-hydrogen bond scalar coupling constants depends not only on the type of the donor group but also on the structural context. The largest coupling constants were measured for hydrogen bonds involving the imino groups of protonated cytosine nucleotides as donors.

Prediction of Extremely Strong Antiferromagnetic Superexchange in Silver(II) Fluorides: Challenging the Oxocuprates(II)

AbstractStrong magnetic coupling between the spins of unpaired electrons is an essential ingredient of many fascinating physical phenomena. Here we report calculations using the hybrid HSE06 functional of magnetic superexchange constants, J, for a series of low‐dimensional CuII and AgII binary and ternary systems with fluoride and oxide ligands. The calculations correctly reproduce the sign and size of the magnetic superexchange constants for prototypical antiferromagnetic (AFM) 1D (J1D) and 2D (J2D) systems, while overestimating the absolute values of J by about 11 %. We find that [AgF][BF4], a quasi‐1D system with linear infinite [AgIIF+] chains, is predicted to exhibit an unprecedented strong AFM superexchange via one atom (F), with J1D about −300 meV. Compression of [AgF][BF4] to 10 GPa should lead to a further increase in AFM interactions with J1D reaching −360 meV at 10 GPa.

Prediction of Extremely Strong Antiferromagnetic Superexchange in Silver(II) Fluorides: Challenging the Oxocuprates(II).

Strong magnetic coupling between the spins of unpaired electrons is an essential ingredient of many fascinating physical phenomena. Here we report calculations using the hybrid HSE06 functional of magnetic superexchange constants, J, for a series of low-dimensional CuII and AgII binary and ternary systems with fluoride and oxide ligands. The calculations correctly reproduce the sign and size of the magnetic superexchange constants for prototypical antiferromagnetic (AFM) 1D (J1D ) and 2D (J2D ) systems, while overestimating the absolute values of J by about 11 %. We find that [AgF][BF4 ], a quasi-1D system with linear infinite [AgII F+ ] chains, is predicted to exhibit an unprecedented strong AFM superexchange via one atom (F), with J1D about -300 meV. Compression of [AgF][BF4 ] to 10 GPa should lead to a further increase in AFM interactions with J1D reaching -360 meV at 10 GPa.

QCD in Stars

We discuss cold dense QCD by examining constraints from neutron stars, nuclear experiments, and QCD calculations at low and high baryon density. The two solar mass constraint and suggestive small radii (10~13 km) of neutron stars constrain the strength of hadron-quark matter phase transitions. Assuming the adiabatic continuity from hadronic to quark matter, we use a schematic quark model for hadron physics and examine the size of medium coupling constants. We find that to baryon density nB ~ 10n0 (n0: nuclear saturation density), the model coupling constants should be as large as in the vacuum, indicating that gluons remain non- perturbative even after the quark matter formation.

Hindered magnetic dipole transitions between P -wave bottomonia and coupled-channel effects

In the hindered magnetic dipole transitions of heavy quarkonia, the coupled-channel effects originating from the coupling of quarkonia to a pair of heavy and anti-heavy mesons can play a dominant role. Here, we study the hindered magnetic dipole transitions between two $P$-wave bottomonia, $\chi_b(n P)$ and $h_b(n^\prime P)$, with $n\neq n^\prime$. In these processes the coupled-channel effects are expected to lead to partial widths much larger than the quark model predictions. We estimate these partial widths which, however, are very sensitive to unknown coupling constants related to the vertices $\chi_{b0}(nP)B\bar B$. A measurement of the hindered M1 transitions can shed light on the coupled-channel dynamics in these transitions and hence on the size of the coupling constants. We also suggest to check the coupled-channel effects by comparing results from quenched and fully dynamical lattice QCD calculations.

DC Grid Control Through the Pilot Voltage Droop Concept—Methodology for Establishing Droop Constants

Converter control is an important aspect of voltage-source-converter high-voltage dc (VSC-HVDC) based multi-terminal dc grids. Variants of power drooped against dc voltage control have previously been proposed for this purpose. However, there is at this time no clear methodology available on how to select the size of the droop constants for distributing a power mismatch, following, e.g., a converter trip, on several converters. This paper proposes a methodology for establishing droop constants for a variant of power drooped against dc voltage called pilot voltage droop control. The methodology is derived from the basic control laws in a straight forward fashion and the accuracy is exemplified by time domain simulations in Digsilent's Powerfactory platform.

Variation in Pharmacognostic Characters and Polyphenolic Contents among Four Species of Medicinal Plants from the Genus Spermacoce (Rubiaceae).

Spermacoce hispida L. is one of the important medicinal plants used in traditional systems of medicine. It is observed that, several times it is difficult to differentiate the plant from the other allied species from the same genus, Spermacoce, especially, when they are in drug form. Therefore, the present study aims to document the differences in the pharmacognostic characters, preliminary phytochemical analysis and polyphenolic contents from the leaves of four species belonging to the genus Spermacoce, viz. S. hispida L., S. mauritiana O. Gideon, S. stricta L. and S. ocymoides Burm. Transverse section passing through the midrib with lamina on either sides, epidermal characters, leaf constants, organoleptic characters, physicochemical analysis, extractive values and preliminary phytochemical analysis were carried out for all these species. Total phenolic content by Folin-Ciocalteu method and total flavonoids by AlCl3 method were also estimated from the leaves of all these species. The results indicated that S. hispida can be clearly differentiated from the other selected species on the basis of size and number of epidermal cells, size of trichomes, leaf constants, physicochemical analysis and extractive values. However, it is also found that S. hispida possess total phenolic content at 6.88±0.34 mg CAE/g and 9.17±0.46 mg TAE/g. Total flavonoids was at 5.98±0.30 mg QE/g. The study will provide information with respect to identification and differentiation amongst selected species of genus Spermacoce.

Convergence of local atomistic stress based on periodic lattice

Local stress in an atomic system, which provides an average stress measurement within a spatial volume containing a collection of atoms, is essential for determining the mechanical properties of a nanoscale structure as well as developing a proper multiscale modeling technique. Theoretically, the smaller averaging volume where a local stress can converge, the closer this atomistic stress definition can approach the ideal continuum stress. As a result, the more accurate stress concentration can be evaluated for the inhomogeneous case. With reference to the previous studies focusing on the spherical averaging volume, dependent on the type of crystals, the convergent radius of the virial stress or Hardy stress usually spans the size of several lattice constants. In this paper, we find that, once the averaging volume is periodic, the convergence of the virial stress and Hardy stress can be accomplished within one single lattice, which is much smaller than what is required by other non-periodic volumes such as a sphere. In the final section, a cracked sodium chloride crystal is considered to demonstrate that the crack opening stress described by the periodic lattices captures the stress concentration near the crack tip.

Analysis and stability of bent-core liquid crystal fibers

In this paper we analyze a free-boundary modelfor free-standing fibers made from smectic layers of kinked(bent-core) liquid crystal molecules. In [1] a radial modelwas proposed to explain how fibers form (assuming radially symmetricconfigurations) based on the distinctive packing and ferroelectricproperties of bent--core molecules. We develop this model further toinclude smectic energy terms so as to allow for non--circularcross--sections with non--radial configurations and fields. We showthat the relative size of the energy's elasticity constants can beused to determine the stability (instability) of radially symmetricfibers with respect to non--radial perturbations.

Determination of size and sign of hetero-nuclear coupling constants from 2D 19F–13C correlation spectra

Fluorinated organic compounds have become increasingly important within the polymer and the pharmaceutical industry as well as for clinical applications. For the structural elucidation of such compounds, NMR experiments with fluorine detection are of great value due to the favorable NMR properties of the fluorine nucleus. For the investigation of three fluorinated compounds, triple resonance 2D HSQC and HMBC experiments were adopted to fluorine detection with carbon and/or proton decoupling to yield F–C, F–C{H}, F–C{Cacq} and F–C{H,Cacq} variants. Analysis of E.COSY type cross-peak patterns in the F–C correlation spectra led, apart from the chemical shift assignments, to determination of size and signs of the JCH, JCF, and JHF coupling constants. In addition, the fully coupled F–C HMQC spectrum of steroid 1 was interpreted in terms of E.COSY type patterns. This example shows how coupling constants due to different nuclei can be determined together with their relative signs from a single spectrum. The analysis of cross-peak patterns, as presented here, not only provides relatively straightforward routes to the determination of size and sign of hetero-nuclear J-couplings in fluorinated compounds, it also provides new and easy ways for the determination of residual dipolar couplings and thus for structure elucidation. The examples and results presented in this study may contribute to a better interpretation and understanding of various F–C correlation experiments and thereby stimulate their utilization.

Stability of B 7 Fibers

Recent experimental studies have found that fluid smectic phases of bent core liquid crystals form stable free standing fibers with extremely high slenderness ratios. In [1] a model was proposed to explain their formation based on the distinctive packing properties of bent core molecules in the SmCG phase. Here we develop this model further to include smectic energy terms so as to allow more general configurations and fields. We show that the relative size of the energy's elasticity constants can be used to determine the stability (instability) of circular fibers.

Characterization of the complexation of tauro- and glyco-conjugated bile salts with γ-cyclodextrin and 2-hydroxypropyl-γ-cyclodextrin using affinity capillary electrophoresis

The complexation of seven bile salts, present in the small intestine of rat, dog and man, (taurocholate, tauro-β-muricholate, taurodeoxycholate, taurochenodeoxycholate, glycocholate, glycodeoxycholate and glycochenodeoxycholate) with γ-cyclodextrin and the chemically modified 2-hydroxypropyl-γ-cyclodextrin, was studied using affinity capillary electrophoresis (ACE). The cyclodextrins (CDs) were investigated due to their use in drug formulation as excipients for solubilisation of poorly soluble drugs and drug candidates. Using mobility shift ACE, the bile salt cyclodextrin interactions were characterized demonstrating 1:1 binding stoichiometry with stability constants ranging from 2 × 103 to 8 × 104 M−1. The binding constants showed a systematic dependence on the number and position of hydroxyl groups on the steroid skeleton and the stability constants were in general higher for complexation with the native cyclodextrin than with the modified cyclodextrin. Based upon the size of the complexation constants, it was suggested that the interaction between the CDs and the bile salts takes place at the C and D ring of the steroid skeleton. The complexation of bile salts with the γ-cyclodextrins may compete with drug-γ-cyclodextrin complex formation and, thus, potentially affect drug absorption and efficacy.

Occurrence of Subharmonic Tones in a Beam Supported Elastically

The occurrence of subharmonic tones in a beam supported by springs and dampers at both ends, and subjected to a nonsymmetric excitation having two components, one independent of, and the other harmonically varying with, time is considered. The beam can form a system with internal resonance due to the size of spring constants of support ends. To analyze the problem, the method of multiple scales is used. The analysis shows that in the system with internal resonance considered here, subharmonic tones of orders 1/2 and 1/3 can occur in a multi mode. The validity of the theoretical analysis is confirmed by numerical simulation.

Mutually Exclusive Spiky Pattern and Segmentation Modeled by the Five-Component Meinhardt–Gierer System

We consider the five-component Meinhardt–Gierer model for mutually exclusive patterns and segmentation, which was proposed in [H. Meinhardt and A. Gierer, J. Theoret. Biol., 85 (1980), pp. 429–450]. We prove rigorous results on the existence and stability of mutually exclusive spikes which are located in different positions for the two activators. Sufficient conditions for existence and stability are derived, which depend in particular on the relative size of the various diffusion constants. Our main analytical methods are the Liapunov–Schmidt reduction and nonlocal eigenvalue problems. The analytical results are confirmed by numerical simulations.

Folk theorems on the determinization and minimization of timed automata

Timed automata are known not to be complementable or determinizable. Natural questions are, then, could we check whether a given TA enjoys these properties? These problems are not algorithmically solvable. Minimizing the “resources” of a TA (number of clocks or size of constants) are also unsolvable problems. In this paper we provide simple undecidability proofs using a “constructive” version of the problems where we require not just a yes/no answer, but also a “witness”. Proofs are then simple reductions from the universality problem. Recent work of Finkel shows that the corresponding decision problems are also undecidable [O. Finkel, On decision problems for timed automata, Bulletin of the European Association for Theoretical Computer Science 87 (2005) 185–190].

Coherent 2D Resonance Raman Spectroscopy as a tool for studying molecular structure

Coherent 2D Resonance Raman Spectroscopy (C2DRRS) is a new spectroscopic technique that can sort normally congested Resonance Raman peaks into predictable patterns. This paper discusses evidence that connects the location, shape and spacing of these patterns to the relative size of specific spectroscopic constants. Simulations and experimental results for the Δ v = 0 and Δ v = 1 transitions of the C 2 Swan band reveal a relatively simple relationship between spectroscopic constants and the resulting 2D pattern.