Quasi-linear Relations Research Articles

Growth mechanics of the viscoelastic membranes

Living membranes can grow as a response to their environment, and they are also known as viscoelastic materials. However, the growth phenomenon and the viscoelastic behavior of these membranes have been studied separately up to now. The main goal of this paper is to develop a general formulation that can account for growth and viscoelastic behaviors in membranes, simultaneously. Therefore, we propose a formulation for growing quasi-linear viscoelastic membranes. The growth model begins with a multiplicative decomposition of the gradient deformation tensor into elastic and growth tensor, where the growth of the membrane is considered as a single scalar-valued parameter. Furthermore, the quasi-linear viscoelasticity theory is utilized in the elastic configuration as additive decomposition of the second Piola–Kirchhoff stress tensor. To solve the evolution equations for both growth and quasi-linear viscoelastic relations, two implicit second order accuracy integration methods are employed. Moreover, strain-driven and stress-driven growth phenomena are accounted for based on a Total Lagrangian (TL) finite element formulation. The developed formulations can capture growth phenomena and viscoelastic properties of the membranes, individually, and it also enables to model co-existence of growth and viscoelasticity. Eventually, to evaluate the applicability of the developed formulation, several examples are investigated and compared to those available in the literature.

Relationships of the Seismicity at the Alaska Subduction Zone to Metamorphism and the Deep Fluid Regime

We examined the spatial distribution of intermediate-depth earthquakes in southern Alaska and the adjacent Aleutian Islands in relation to the deep fluid regime and volcanism. The distribution of earthquake hypocenters is studied in two variables, the depth of focus and the distance from the top of the slab. This approach shows that seismic activity is concentrated at 10–15 and 20–25 km from the top of the downgoing plate. Clusters of seismicity such as these cannot be due to slippage along the boundary between the continental block and the slab. In addition, extended structures of sharply increased seismic activity were found. Their location fits certain quasi-linear relations between pressure and temperature, and can mark metamorphic fronts in the subducted plate. Besides, the spatial earthquake distribution has a peak that appears to be related to active recent volcanism. It can be caused by active dehydration reactions in the subduction plate. These empirical findings testify in favor of the fluid-metamorphic model of earthquakes origin.

Abundances and Charge States of Heavy Ions in ICMEs Highly Related to Speed and Solar Activity

Abstract This statistical work studies the abundances and the charge states of the carbon, oxygen, and iron ions in 281 interplanetary coronal mass ejections (ICMEs) measured at 1 au by ACE spacecraft from 1998 to 2011. The Gaussian distribution test is applied, and the analysis of variance is used to quantify the similarity between two distributions of ionic charge states and abundances. The correlation coefficient is calculated to reveal the dependence of the abundances and the mean charge of heavy ions on the solar activity. The results show that the mean charge, the abundance, and the speed at 1 au are highly related to the sunspot number (SN). The O7+/O6+ shows statistical difference between the high speed and the low speed groups of ICMEs. Different from the cold materials inside ICMEs, the mean charge of carbon ions shows a positive relation to that of oxygen ions. The Mg/O in the studied ICMEs are much higher than that in the solar wind. Three types of charge distribution of C, O, and Fe ions are summarized. The fraction of each of the three types is related to the solar minimum or the solar maximum. The mean charge and the flux of oxygen ions show quasi-linear relations to the SN during solar minimum, and show fluctuations during maximum. The results reveal that the solar activity, which represents the solar magnetic field status by nature, controls the composition of heavy ions in ICMEs.

Quasilinear irreversible thermodynamics of a low-temperature-differential kinematic Stirling heat engine.

Low-temperature-differential (LTD) Stirling heat engines are able to operate with a small temperature difference between low-temperature heat reservoirs that exist in our daily lives, and thus they are considered to be an important sustainable energy technology. The author recently proposed a nonlinear dynamics model of an LTD kinematic Stirling heat engine to study the rotational mechanism of the engine [Y. Izumida, Europhys. Lett. 121, 50004 (2018)EULEEJ0295-507510.1209/0295-5075/121/50004]. This paper presents our study of the nonequilibrium thermodynamics analysis of this engine model, where a load torque against which the engine does work is introduced. We demonstrate that the engine's rotational state is in a quasilinear response regime where the thermodynamic fluxes show a linear dependence on the thermodynamic forces. Significantly, it is found that the response coefficients of the quasilinear relations are symmetric, which is similar to Onsager symmetry in linear irreversible thermodynamics. Based on these relations, we formulate the maximum efficiency of the engine. We also elucidate that the symmetry of the quasilinear response coefficients emerges by reflecting the (anti-)reciprocity of the Onsager kinetic coefficients identified for the relaxation dynamics of the engine in the vicinity of an equilibrium state. We expect that the present study will pave the way for developing nonequilibrium thermodynamics of autonomous heat engines described as a nonlinear dynamical system.

Generative well pattern design—principles, implementation, and test on OLYMPUS challenge field development problem

A novel generative (well pattern) design approach is proposed for a reservoir well pattern design, building upon the observation that automated methods are slow to beat human-designed patterns. The approach relies upon the construction of 3D well patterns as a function of geology in a mindset in which functional requirements derive from reservoir engineering heuristics. The concept of well patterns as graphs is leveraged and expanded. Nodes are well parts and geological features. Edges represent functional requirements driven by economical and physical considerations; they are expressed as 3D functions of geology. Diffusive time of flight and a novel measure are proposed to quantify the relative suitability of model cells to the positioning of wells. A small, but deemed complete, set of requirements is proposed relative to the reservoir engineering domain. The search space for inserting wells is limited to cells non-dominated from the joint perspective of requirements applicable to the considered well type. Tentatively, optimal patterns are built by balancing weights given to each requirement. The process is applied to a single and to multiple realizations enabling consideration of uncertainties. Weights are few and display quasi-linear and independent relations to common objective functions. The approach was tested on the OLYMPUS field development benchmark problem. Results illustrate the potential for initializing optimization with performing candidates while maintaining geographic coverage. The search space dimension was reduced by a factor of ~ 10100. A solution was found within the first 92 investigated settings that reaches a net present value (8% discount) of 643M$. Such performances are of a nature to ensure systemic superiority over purely human-driven optimization processes and, upon integration in iterative search processes, over competing global parameterization schemes whenever few calls are made to the objective function.

Zones of material separation in simulations of cutting

FEM simulations of orthogonal cutting are reported in which both the Johnson–Cook (JC) constitutive relation and the Johnson–Cook separation (fracture or damage) criterion are used. Results demonstrate that the damaged regions, in which separation of material occurs at the tool tip, form thin boundary layers on the top of the machined surface and on the underside of the chip. Damage was calculated in terms of the parameters of the Johnson–Cook fracture criterion appropriate for A2024-T351 aluminium alloy. The size of the damaged layers is some 35μm and appears to be independent of the uncut chip thickness t0 over the range investigated (50<t0<500μm). In most cases, the highly-damaged boundary layers make up only a very small proportion of the uncut chip thickness, so the deformation fields by which chips are formed are essentially the same as if the damage zone were absent. The result explains the success of variables-separable algebraic models of cutting with continuous chips in which the component works of chip plasticity, friction and separation are uncoupled.The FEM simulations predict quasi-linear relations between cutting force and uncut chip thickness, with an intercept on the force axis. This is exactly what is found experimentally and is predicted by algebraic models of continuous chip cutting under the assumption of sharp tool tip, where the slope of the plot relates to the yield stress of the workpiece and the intercept to its fracture toughness. The fracture toughness and the parameters of the JC damage relation, along with the size of the boundary layers of damage, are shown to be related.

Experimentally Based Estimates of Relations between X-Band Radar Signal Attenuation Characteristics and Differential Phase in Rain

AbstractCorrecting observed polarimetric radar variables for attenuation and differential attenuation effects in rain is important for meteorological applications involving measurements at attenuating frequencies such as those at X band. The results of estimating the coefficients in the correction-scheme relations from dual-wavelength polarimetric radar measurements of rainfall involving attenuating and nonattenuating frequencies are described. Such coefficients found directly from measurements are essentially free from different assumptions about drop shapes, drop size distributions, and/or relations between different radar variables that are typically used in many attenuation and differential attenuation correction schemes. Experimentally based estimates derived using dual-wavelength radar measurements conducted during a project in northern Colorado indicate values of the coefficients in the attenuation–differential phase quasi-linear relations at X band in the approximate range of 0.20–0.31 dB deg−1. The corresponding coefficients in the differential attenuation–differential phase relations are in the range of 0.052–0.065 dB deg−1.

Effects of Ions on the OH Stretching Band of Water as Revealed by ATR-IR Spectroscopy

The effects of various cations (Li+, Na+, K+, Rb+, Cs+, Mg2+, Ca2+, Sr2+, Ba2+, Mn2+, Co2+, and Ni2+) and anions (Cl−, Br−, I−, $$ {\text{NO}}_{3}^{ - } $$ , $$ {\text{ClO}}_{4}^{ - } $$ , $$ {\text{HCO}}_{3}^{ - } $$ , and $$ {\text{CO}}_{3}^{2 - } $$ ) on the molar absorptivity of water in the OH stretching band region (2,600–3,800 cm−1) were ascertained from attenuated total reflection infrared spectra of aqueous electrolyte solutions (22 in all). The OH stretching band mainly changes linearly with ion concentrations up to 2 mol·L−1, but several specific combinations of cations and anions (Cs2SO4, Li2SO4, and MgSO4) present different trends. That deviation is attributed to ion pair formation and cooperativity in ion hydration, which indicates that the extent of the ion–water interaction reflected by the OH stretching band of water is beyond the first solvation shell of water molecules directly surrounding the ion. The obtained dataset was then correlated with several quantitative parameters representing structural and dynamic properties of water molecules around ions: ΔG HB, the structural entropy (S str), the viscosity B-coefficient (B η ), and the ionic B-coefficient of NMR relaxation (B NMR). Results show that modification of the OH stretching band of water caused by ions has quasi-linear relations with all of these parameters. Vibrational spectroscopy can be a useful means for evaluating ion–water interaction in aqueous solutions.

Quasi-linear versus potential-based formulations of force–flux relations and the GENERIC for irreversible processes: comparisons and examples

An essential part in modeling out-of-equilibrium dynamics is the formulation of irreversible dynamics. In the latter, the major task consists in specifying the relations between thermodynamic forces and fluxes. In the literature, mainly two distinct approaches are used for the specification of force–flux relations. On the one hand, quasi-linear relations are employed, which are based on the physics of transport processes and fluctuation–dissipation theorems (de Groot and Mazur in Non-equilibrium thermodynamics, North Holland, Amsterdam, 1962, Lifshitz and Pitaevskii in Physical kinetics. Volume 10, Landau and Lifshitz series on theoretical physics, Pergamon Press, Oxford, 1981). On the other hand, force–flux relations are also often represented in potential form with the help of a dissipation potential (Silhavý in The mechanics and thermodynamics of continuous media, Springer, Berlin, 1997). We address the question of how these two approaches are related. The main result of this presentation states that the class of models formulated by quasi-linear relations is larger than what can be described in a potential-based formulation. While the relation between the two methods is shown in general terms, it is demonstrated also with the help of three examples. The finding that quasi-linear force–flux relations are more general than dissipation-based ones also has ramifications for the general equation for non-equilibrium reversible–irreversible coupling (GENERIC: e.g., Grmela and Ottinger in Phys Rev E 56:6620–6632, 6633–6655, 1997, Ottinger in Beyond equilibrium thermodynamics, Wiley Interscience Publishers, Hoboken, 2005). This framework has been formulated and used in two different forms, namely a quasi-linear (Ottinger and Grmela in Phys Rev E 56:6633–6655, 1997, Ottinger in Beyond equilibrium thermodynamics, Wiley Interscience Publishers, Hoboken, 2005) and a dissipation potential–based (Grmela in Adv Chem Eng 39:75–129, 2010, Grmela in J Non-Newton Fluid Mech 165:980–986, 2010, Mielke in Continuum Mech Therm 23:233–256, 2011) form, respectively, relating the irreversible evolution to the entropy gradient. It is found that also in the case of GENERIC, the quasi-linear representation encompasses a wider class of phenomena as compared to the dissipation-based formulation. Furthermore, it is found that a potential exists for the irreversible part of the GENERIC if and only if one does for the underlying force–flux relations.

GeV OBSERVATIONS OF STAR-FORMING GALAXIES WITH THEFERMILARGE AREA TELESCOPE

Recent detections of the starburst galaxies M82 and NGC 253 by gamma-ray telescopes suggest that galaxies rapidly forming massive stars are more luminous at gamma-ray energies compared to their quiescent relatives. Building upon those results, we examine a sample of 69 dwarf, spiral, and luminous and ultraluminous infrared galaxies at photon energies 0.1-100 GeV using 3 years of data collected by the Large Area Telescope (LAT) on the \textit{Fermi Gamma-ray Space Telescope} (\textit{Fermi}). Measured fluxes from significantly detected sources and flux upper limits for the remaining galaxies are used to explore the physics of cosmic rays in galaxies. We find further evidence for quasi-linear scaling relations between gamma-ray luminosity and both radio continuum luminosity and total infrared luminosity which apply both to quiescent galaxies of the Local Group and low-redshift starburst galaxies (conservative $P$-values $\lesssim0.05$ accounting for statistical and systematic uncertainties). The normalizations of these scaling relations correspond to luminosity ratios of $\log(L_{0.1-100 \rm{GeV}}/L_{1.4 \rm{GHz}}) = 1.7 \pm 0.1_{\rm (statistical)} \pm 0.2_{\rm (dispersion)}$ and $\log(L_{0.1-100 \rm{GeV}}/L_{8-1000 \mu\rm{m}}) = -4.3 \pm 0.1_{\rm (statistical)} \pm 0.2_{\rm (dispersion)}$ for a galaxy with a star formation rate of 1 $M_{\odot}$ yr$^{-1}$, assuming a Chabrier initial mass function. Using the relationship between infrared luminosity and gamma-ray luminosity, the collective intensity of unresolved star-forming galaxies at redshifts $0<z<2.5$ above 0.1 GeV is estimated to be 0.4-2.4 $\times 10^{-6}$ ph cm$^{-2}$ s$^{-1}$ sr$^{-1}$ (4-23% of the intensity of the isotropic diffuse component measured with the LAT). We anticipate that $\sim10$ galaxies could be detected by their cosmic-ray induced gamma-ray emission during a 10-year \textit{Fermi} mission.

Unusual Raman dispersion forDand2Dlines in high-curvature single-walled carbon nanotubes revealed byC13isotope substitution

The defect-induced $D$ line and its overtone are fundamental signatures in the Raman spectra of carbon nanomaterials. An analysis of these lines as a function of laser excitation energy is reported for double-walled carbon nanotubes where the inner tubes represent high-curvature nanotube species. From $^{13}\text{C}$ substituted inner tubes it is demonstrated that the quasilinear relations between laser energy and line position (Raman dispersion) cross over unexpectedly for low-energy excitation for the inner and outer tube shells. The result is quantitatively explained by a curvature-induced phonon softening and first-principles calculations of the optical transition energies.

FAULT DIAGNOSIS OF SENSORS IN AUTONOMOUS UNDERWATER VEHICLE: ADAPTIVE QUASI-LINEAR PARITY RELATIONS METHOD

The problem of sensors fault diagnosis in autonomous underwater vehicles is studied within the scope of model-based approach. Adaptive quasi-linear parity relations are considered for solving this problem in the presence of unknown add mass. Simulation results are given for the model of CR-01 autonomous underwater vehicle.

Constitutive Relations of Nonlinear Thermoelasticity of Anisotropic Bodies

Quasilinear relations for finite reversible deformation of anisotropic materials are obtained using a thermomechanical approach. Free energy is written as a function of temperature and compatible invariants of the logarithmic strain measure and basis tensors. Nonlinear thermomechanical effects including different types of material behavior in tension and compression and the temperature dependence of the elastic tensor are taken into account.

Quasi-Linear Parity Relations for Fault Detection in Nonlinear Uncertain Systems

The problem of robust residual generation for fault detection in nonlinear systems is studied within the scope of parity relation approach. The method is proposed for residual generation involving on-line construction of parity relations in quasi-linear form via solution of optimization and time-delay state estimation problems. A nonlinear forced-motion model of underwater vehicle is used to illustrate the robust residual generation and appropriate simulation results are given.

A model for the nonlinear elastic response of large arteries.

The nonlinear elastic response of large arteries subjected to finite deformations due to action of biaxial principal stresses, is described by simple constitutive equations. Generalized measures of strain and stress are introduced to account for material nonlinearity. This also ensures the existence of a strain energy density function. The orthotropic elastic response is described via quasi-linear relations between strains and stresses. One nonlinear parameter which defines the measures of strain and stress, and three elastic moduli are assumed to be constants. The lateral strain parameters (equivalent to Poisson's ratios in infinitesimal deformations) are deformation dependent. This dependence is defined by empirical relations developed via the incompressibility condition, and by the introduction of a fifth material parameter. The resulting constitutive model compares well with biaxial experimental data of canine carotid arteries.

The theoretical study of the heats of formation of organic compounds containing the substituents CH 3, CF 3, NH 2, NF 2, NO 2, OH and F

In this work, the heats of formation of some small molecules containing one or more of the following groups. CH 3, CF 3, NH 2, NHF, NF 2, NO 2, OH, F are studied. The calculations have been carried out theoretically, using the isodesmic procedure of Pople et al. In most cases, the thermal corrections were introduced using experimental (when available) or theoretical (at the SCF 6–31G level) vibrational frequencies. It was found that this correction is relatively negligible (compared to the accuracy of the heats of formation determined); nevertheless, the vibrational frequencies remain useful for determining the heat capacity and the entropy. We observe that the heats of formation, in families such as XCH 3- n F n , XNH 2- n F n , and CH 4- n X n , are related by quasilinear relations (Δ H f ≈ a + bn). Finally, the NF 2 and NO 2 substituents have large and comparable destabilization effects on the heat of formation. All the other substituents are stabilizing; the importance of the stabilization effect depends on the number of fluorine atoms.

Complete exceptionality, constitutive laws and symmetric form for a non-linear inelastic rod

In this paper we consider quasilinear constitutive laws characterizing ‘Maxwellian Materials’ in the case of a one-dimensional inelastic rod. By using the complete exceptionality condition, we are able to determine the most general class of quasilinear constitutive relations by which a weak discontinuity wave propagating along characteristics cannot evolve into a non- linear shock. The last part of the paper is devoted to point out some properties connected with the special class of constitutive relations where the material functions do not depend on the strain. In such a case by means of a field variables transformation, we are able to reduce the fundamental system of equations to a symmetric hyperbolic system where the coefficient of the field spatial derivative is a constant matrix. This special symmetric form is very useful to study shocks.

Quasilinear theory of viscoelasticity

By postulating equal contributions the number of kernels in the principal cubic theory of viscoelasticity and in the theory with regular kernels of two arguments is reduced to three. For certain quasilinear relations all the kernels and functions are determined from creep, relaxation, and simple loading and deformation tests. In the case of simple loading and deformation the problems for a viscoelastic incompressible material reduce to problems of the theory of small elastoplastic deformations of an incompressible material. Several problems relating to this case are considered.