Number Of Constants Research Articles

Selection platforms for directed evolution in synthetic biology.

Life on Earth is incredibly diverse. Yet, underneath that diversity, there are a number of constants and highly conserved processes: all life is based on DNA and RNA; the genetic code is universal; biology is limited to a small subset of potential chemistries. A vast amount of knowledge has been accrued through describing and characterizing enzymes, biological processes and organisms. Nevertheless, much remains to be understood about the natural world. One of the goals in Synthetic Biology is to recapitulate biological complexity from simple systems made from biological molecules–gaining a deeper understanding of life in the process. Directed evolution is a powerful tool in Synthetic Biology, able to bypass gaps in knowledge and capable of engineering even the most highly conserved biological processes. It encompasses a range of methodologies to create variation in a population and to select individual variants with the desired function–be it a ligand, enzyme, pathway or even whole organisms. Here, we present some of the basic frameworks that underpin all evolution platforms and review some of the recent contributions from directed evolution to synthetic biology, in particular methods that have been used to engineer the Central Dogma and the genetic code.

Connection between Petri nets and Polish notation

We propose Petri nets that produce languages of Polish notation and reverse Polish notation for propositional formulas and mathematical expressions. Propositional formulas can contain a given number of variables and mathematical expressions. Arithmetic expressions can contain a given number of variables and constants. We also propose inhibitor nets that produce the fixed-point binary numbers in mathematical expressions for above-mentioned languages. The technique of the nets construction allows to use arbitrary functions with a given arity. We also propose a coloured Petri net for calculating values of propositional formulas in reverse Polish notation. The technique of the net construction allows to use arbitrary functions with a given arity using a truth table of a corresponding function.

Peridynamical Modelling of Nanoindentation in Ceramic Composites

Indentation in brittle solids involves many complex phenomena related to cleavage and contact, as well as intrinsic stress singularities, which are almost impossible to capture with traditional continuum approach and FEA at mesoscale. In case of a two-phase ceramic composite [1–3] the number of unknown material and interfacial constants, that have to be calibrated experimentally, increases rapidly [4, 5]. In this paper, nanoindentation in zirconia-toughened alumina (ZTA) is modelled using discrete (peridynamical) approach

Extreme conditions of elastic constants and principal axes of anisotropy

This paper describes the derivation of extreme conditions of each elasticity coefficient (Young’s modulus, shear modulus, et al.,) for the general case of linear-elastic anisotropic materials. The stationarity conditions are obtained, and they determine the orthogonal coordinate systems being the principal axes of anisotropy, where the number of independent elasticity constants decreases from 21 to 18 and, in some cases of anisotropy, to 15 or lower. The example of a material with cubic symmetry is given.

Experimental investigations and numerical modeling of 2D temperature fields in flow boiling in minichannels

The experimental purpose of the study was to simultaneously measure and record two-dimensional temperature distributions on the heating surface and the images of the corresponding two-phase flow structures. The study was conducted for FC-72 flow boiling in rectangular, vertical and asymmetrically heated minichannels with a high aspect ratio of 40, 20 and 13.3 (0.5, 1.0, 1.5mm deep, 20mm wide and 360mm long), for heat fluxes ranging from 58 to 132kWm−2, absolute pressure from 1.16 to 1.84bar and the mass flux from 185 to 1139kgm−2s−1. The flat heating surface was made of a thin rolled plate. The inlet temperature of the liquid was kept constant at 288K. The CCD camera, mounted on the heated side of the channel, produced color images of liquid crystals. High-speed camera images, taken through the glass window on the opposite side of the channel, were used to measure void fraction for selected cross-sections as a function of variable thermal and flow parameters. The ranges of characteristic two-phase flow structures were determined relative to the hydraulic diameter dh and local void fraction φ(x). The best-agree correlation was found for the relationship between the local void fraction and the local vapor quality in high aspect ratio minichannels.The theoretical part of the study focused on the development of flow boiling heat transfer model based on the Trefftz method. It was formulated to include the minimum number of experimental constants and to numerically solve the manifold inverse problems. The numerical procedure included solving two sequential inverse problems (in the heating foil and in the flowing liquid) and the accompanying direct problem (in the protecting glass pane). To obtain two-dimensional temperature distributions in the boiling liquid for bubbly and bubbly–slug flows, a triple coupled inverse problem was solved using the Trefftz method. The numerical solution was compared with the simplified one, assuming that the entire heat generated in the foil was transferred to the flowing refrigerant. Both solutions gave similar results.

Chemical Equilibria in Methanol Synthesis Including the Water–Gas Shift Reaction: A Critical Reassessment

A large number of experimental equilibrium constants for the reactions involved in methanol synthesis were collected or calculated from several literature sources. Equilibrium relationships were derived from basic thermochemical data and subsequently fitted to the experimental results by adapting only the Gibbs energy of formation values for CH3OH and CO. Very small changes of these parameters as compared to the original literature values were sufficient to obtain accurate relationships that adequately describe the experimental results.

A simplified cyclic plasticity model for calculating stress-strain response under multiaxial non-proportional loadings

Abstract Given the dependence of many fatigue damage parameters on both stress and strain values, being able to produce accurate stress-strain estimations is an essential first step when performing a fatigue life analysis. However, more advanced cyclic plasticity models, capable of capturing complex material behavior under multiaxial non-proportional loadings, often require the determination of a large number of material constants from experimental data that are not always available to the analyst. Therefore, in this study, a simplified Armstrong-Frederick-Chaboche style plasticity model, based on the assumption of Masing material behavior and a newly proposed transient hardening formulation, was evaluated in terms of its ability to predict stress-strain response under complex multiaxial loading conditions. To do this, experimental stress-strain data were generated for 2024-T3 aluminum alloy using both constant and variable amplitude multiaxial block loading histories designed to reflect a wide variety of stress states that might be encountered in any given service loading history. Stress-strain predictions were performed both with and without the consideration of non-proportional hardening effects in order to provide a baseline for evaluating the results. Although all stress-strain predictions were found to agree well with the experimental data, both quantitatively and qualitatively, it was shown that, in general, predictions for axial stress amplitudes and mean axial stresses were consistently better than those for shear stress.

A Comparative Investigation on the Capability of Modified Zerilli-Armstrong and Arrhenius-Type Constitutive Models to Describe Flow Behavior of BFe10-1-2 Cupronickel Alloy at Elevated Temperature

True stress and true strain data obtained from isothermal compression tests on a Gleeble-3800 thermo-mechanical simulator, in a wide range of temperatures (1073-1323 K) and strain rates (0.001-10 s−1), has been used to evaluate the material constants of two constitutive models: the modified Zerilli-Armstrong and the strain compensation Arrhenius-type models. Furthermore, a comparative study was conducted on the capabilities of the two models in order to represent the elevated temperature flow behavior of BFe10-1-2 cupronickel alloy. The suitability levels of these two models were evaluated by comparing the accuracy of their predictions of deformation behavior, correlation coefficient (R), average absolute relative error (AARE), relative errors of prediction, and the number of material constants. The results show that the predicted values of these two models agree well with the experimental values of BFe10-1-2 cupronickel alloy except at the temperature of 1123 K and the strain rate of 1 s−1. Meanwhile, the strain compensated Arrhenius-type model can track the deformation behavior of BFe10-1-2 cupronickel alloy more accurately throughout the entire temperature and strain rate range, while fewer material constants are involved in the modified Zerilli-Armstrong model.

Flavour symmetries in a renormalizable SO(10) model

In the context of a renormalizable supersymmetric SO(10) Grand Unified Theory, we consider the fermion mass matrices generated by the Yukawa couplings to a 10⊕120⊕126‾ representation of scalars. We perform a complete investigation of the possibilities of imposing flavour symmetries in this scenario; the purpose is to reduce the number of Yukawa coupling constants in order to identify potentially predictive models. We have found that there are only 14 inequivalent cases of Yukawa coupling matrices, out of which 13 cases are generated by Zn symmetries, with suitable n, and one case is generated by a Z2×Z2 symmetry. A numerical analysis of the 14 cases reveals that only two of them—dubbed A and B in the present paper—allow good fits to the experimentally known fermion masses and mixings.

Graphical analysis of electrochemical impedance spectroscopy data in Bode and Nyquist representations

Though it becomes a routine to fit impedance data to an equivalent electric circuit model (EECM) using complex nonlinear least square (CNLS) to extract physical parameters from impedance data, two formidable challenges still remain: to build a physically meaningful EECM and to find good initial estimates for model parameters. In this study, combining graphical analysis of impedance data in both Bode and Nyquist plots, a two-step procedure is proposed to address the challenges: (1) a frequency derivative phase angle method is developed in Bode plot to identify the number of time constants (or electrochemical processes); (2) graphical analysis of impedance data in Nyquist plot is used sequentially for initial parameter determination. Major graphical analysis methods are compared in terms of frequency resolution, accuracy and complexity using synthetic data. The superiority of the proposed procedure is illustrated using the experimental data of a three-electrode lithium-ion cell.

Constraining condensed-phase formation kinetics of secondary organic aerosol components from isoprene epoxydiols

Abstract. Isomeric epoxydiols from isoprene photooxidation (IEPOX) have been shown to produce substantial amounts of secondary organic aerosol (SOA) mass and are therefore considered a major isoprene-derived SOA precursor. Heterogeneous reactions of IEPOX on atmospheric aerosols form various aerosol-phase components or "tracers" that contribute to the SOA mass burden. A limited number of the reaction rate constants for these acid-catalyzed aqueous-phase tracer formation reactions have been constrained through bulk laboratory measurements. We have designed a chemical box model with multiple experimental constraints to explicitly simulate gas- and aqueous-phase reactions during chamber experiments of SOA growth from IEPOX uptake onto acidic sulfate aerosol. The model is constrained by measurements of the IEPOX reactive uptake coefficient, IEPOX and aerosol chamber wall losses, chamber-measured aerosol mass and surface area concentrations, aerosol thermodynamic model calculations, and offline filter-based measurements of SOA tracers. By requiring the model output to match the SOA growth and offline filter measurements collected during the chamber experiments, we derive estimates of the tracer formation reaction rate constants that have not yet been measured or estimated for bulk solutions.

Assembly Mechanism and Nanomechanics of Aβ in Alzheimer's Disease

Alzheimer's disease (AD) is characterized by progressive dementia and eventual loss of bodily functions that, historically, is associated with the formation of plaques composed of amyloid beta (Aβ), a 36-43 amino acid peptide. A much more complex picture is now emerging that involves many different species of Aβ oliogomers along the assembly pathway. We have used atomic force microscopy (AFM) to investigate Aβ assembly dynamics in order to observe fibril morphology and to characterize fibril elongation and nanomechanics in physiologically relevant buffers on mica as well as on supported lipid bilayers. We have especially focused on resolving small oligomers that is currently thought to initiate deterioration of brain function in AD and its drug intervention and on defining early stage oligomer to fibril growth by integrations between optical spectroscopy determination of protein conformation and AFM observations. We aim to apply quantitative kinetic schemes to identify the number of steps and kinetic constants using time-resolved AFM, thioflavin T fluorescence and circular dichroism data to define the transition from lag to log phase and the broader assembly mechanism.

Stroboscopic prethermalization in weakly interacting periodically driven systems.

Time-periodic driving provides a promising route toward engineering nontrivial states in quantum many-body systems. However, while it has been shown that the dynamics of integrable, noninteracting systems can synchronize with the driving into a nontrivial periodic motion, generic nonintegrable systems are expected to heat up until they display a trivial infinite-temperature behavior. In this paper we show that a quasiperiodic time evolution over many periods can also emerge in weakly interacting systems, with a clear separation of the timescales for synchronization and the eventual approach of the infinite-temperature state. This behavior is the analog of prethermalization in quenched systems. The synchronized state can be described using a macroscopic number of approximate constants of motion. We corroborate these findings with numerical simulations for the driven Hubbard model.

Analysis of Quarter Rounds of Salsa and Chacha Core and Proposal of an Alternative Design to Maximize Diffusion

Background/Objectives: Salsa and ChaCha are commonly used encryption primitives. Both Salsa and ChaCha core use Quarter round as its core function. The objective of the paper is to analyze the diffusion property of Quarter round of both these algorithms and propose an alternative design named Modified ChaCha Core (MCC). Methods: The Quarter round functions of all these three algorithms are compared using the diffusion matrices that reflect change in output words with a small change in input words. For each algorithm we generated more than a million diffusion matrices depending on the possible permutations of rotations constants used in Quarter round. Findings: Results of our experiment reflected that for Salsa and ChaCha core, there are high number of alternative rotation constants that generate more diffusion than the rotation constants prescribed by the authors. The comparison of diffusion matrices of all three competing structures also concluded that quarter round of MCC exhibits more diffusion than Quarter round of Salsa and ChaCha and it does so in lesser operations. Applications: MCC core; the design proposed in this paper, may be used to generate stream ciphers or may be used to generate collision resistant compression function for a cryptographic hash algorithm. Keywords: ChaCha, Diffusion, Modified ChaCha, MCC, Salsa, Stream Ciphers

Second-Order Convergence of Monotone Schemes for Conservation Laws

We prove that a class of monotone, \emph{$W_1$-contractive} schemes for scalar conservation laws converge at a rate of $\Delta x^2$ in the Wasserstein distance ($W_1$-distance), whenever the initial data is decreasing and consists of a finite number of piecewise constants. It is shown that the Lax--Friedrichs, Enquist--Osher and Godunov schemes are $W_1$-contractive. Numerical experiments are presented to illustrate the main result. To the best of our knowledge, this is the first proof of second-order convergence of any numerical method for discontinuous solutions of nonlinear conservation laws.

Modeling of Nonlinear Propagation in Space-Division Multiplexed Fiber-Optic Transmission

In recent years, space-division multiplexed (SDM) transmission in multimode and multicore fiber structures has been attracting growing interest as a mean of scaling the capacity of the optical transport network. As in the case of standard systems based on the single-mode fibers, the ultimate limit to the achievable transmission rate is set by the nonlinearity of the fiber, and hence, the accurate modeling of nonlinear propagation in SDM fibers is a critical task. A key feature of long multimode fiber structures that are relevant for communications is the existence of random coupling between modes. This coupling has a major effect on the properties of nonlinear propagation, and in its presence, the coupled nonlinear Schrodinger equations, which are characterized by a very large number of propagation constants, reduce to the much simpler form of the coupled generalized Manakov equations. These equations shed light on the relevant aspects of signal propagation dynamics, and facilitate the establishment of an intuitive physical picture. Another key feature of SDM fibers is the existence of modal dispersion that introduces frequency dependence into the mode mixing process and modifies the effects of nonlinear propagation. In this paper, we review all of the above mentioned phenomena, and in addition, we assess the way in which the information capacity of SDM fibers is expected to scale with the number of propagation modes. Finally, we extend the Manakov formalism so as to account for the noninstantaneous Raman contribution to the nonlinear response of silica.

Classical Definitions of Gravitation, Electricity and Magnetism

<p class="1Body">In further demonstration of simultaneous existence of the atom as wave and particle, we reproduce values of a number of physical constants using the classical mass equation hϑ = mc<sup>2</sup>. Most, possibly all, physical constants are coefficients of linear correlations of parameters of the intrinsic electromagnetic (e-m) oscillation that defines the atom; for example: (i) angular frequency per unit radius ω/r correlates with rotational strain τ to produce the effect identified with atomic mass; (ii) the atomic waveform’s e-m flux density ρ<sub>w</sub> correlates with its radius r<sub>w</sub> and with the field modulus ϵ<sub>w</sub> to produce the effect associated with Newtonian Gravitation G; (iii) universal (Galilean) gravitational acceleration g arises from correlations of (a) the particulate atom’s centripetal force F<sub>p</sub> with its mass m<sub>p</sub>, (b) the material density ρ<sub>p</sub> with radius r<sub>p</sub> and (c) the field (i.e., waveform) modulus ϵ<sub>w</sub> with stress σ<sub>w</sub>; (iv) the particulate atom’s modulus correlates with its stress field to define the electric constant or permittivity; (v) the waveform (i.e., field) centripetal force F<sub>w</sub> correlates with strain τ<sub>w</sub> to give electron magnetic moment μ<sub>e</sub> and τ<sub>w</sub> correlates with ω/r to define electrostatic atomic mass unit amu/eV; (vi) the particulate atom’s mass m<sub>p</sub> correlates with density ρ<sub>p</sub> to produce the effect associated with magnetic flux density B and (vii) a universal invariant waveform gravitational (centripetal) acceleration g = 7.9433 x 10<sup>59</sup> m s<sup>-2</sup> kg<sup>-1</sup> binds matter together on atomic, stellar, galactic and cosmic scales, it is identifiable with the strong nuclear force (SNF) suggesting that the SNF is not electromagnetic but mechanical. The investigation identifies centripetal force as the only causality of gravitation raising valid questions regarding possibility for quantum gravitation.</p>

A reformulation of constitutive relations in the strain gradient elasticity theory for isotropic materials

• The Abstract and the Conclusion parts have been rewritten and polished. • The use of the English language has been improved with the help of the language editing service. • The research objectives and procedures are presented more clearly in the revised manuscript. The general isotropic strain gradient elasticity theory with five higher-order elastic constants is reformulated by introducing two different orthogonal decompositions of the strain gradient tensor. Just applying the mathematical reformulations, no extra conditions needed, the constitutive relations, equilibrium equation and boundary conditions are reformulated. In the reformulated theory, the number of independent higher-order elastic constants is proved to be three for isotropic materials, which indicates that the five higher-order elastic constants in the general isotropic strain gradient elasticity theory are dependent with each other. Therefore, the general strain gradient elasticity theory contains only three independent material length-scale parameters for isotropic materials in addition to the Lame constants. The new theory is different from the existed strain gradient elasticity theory with one or three material length-scale parameters, which introduces extra conditions during deriving process. Moreover, the reformulated theory can be directly reduced to that of incompressible materials by assuming the terms associated with hydrostatic strains to be zero. Some examples, such as torsion of cylindrical bars, shearing of fixed-end layers, and pure bending of thin beams, are performed to reveal the necessity of including multi-length-scale parameters in the strain gradient elasticity theory to predict size effects at micron scale.

미분탄 보일러 연소 해석에서 석탄 반응 모델 및 난류 혼합 속도의 영향 평가

ABSTRACTInvestigating coal combustion in a large-scale boiler using computational fluid dynamics (CFD) requires a combination of flow and reaction models. These models include a number of rate constants which are often difficult to determine or validate for particular coals or furnaces. Nonetheless, CFD plays an important role in developing new combustion technologies and improving the operation. In this study, the model selection and rate constants for coal devolatilization, char conversion, and turbulent reaction were evaluated for a commercial wall-firing boiler. The influence of devolatilization and char reaction models was found not significant on the overall temperature distribution and heat transfer rate. However, the difference in the flame shapes near the burners were noticeable. Compared to the coal conversion models, the rate constant used for the eddy dissipation rate of gaseous reactions had a larger influence on the temperature and heat transfer rate. Based on the operation data, a value for the rate constant was recommended.

On the independence of strain invariants of two preferred direction nonlinear elasticity

It is often assumed in the literature that the nine classical strain invariants, which are used to characterize the strain energy of a compressible anisotropic elastic solid with two preferred non-orthogonal directions are independent. In this paper, it is shown that only six of the classical strain invariants are independent, and syzygies exist between the classical invariants. Alternatively, using principal axis techniques, it is simply proven that, only six of the classical strain invariants are independent and syzygies exist between the principal axis strain invariants. Consequently, all other sets of strain invariants, proposed in the literature, which are uniquely related to the set of principal axis strain invariants, have only six independent invariants. Due to syzygies, it is shown that the number of ground state constants required to fully describe the quadratic linear strain energy function of two-fibre solids is fourteen, not thirteen, as assumed in the literature.