Single Inflection Research Articles

Non-classical global solutions for a class of scalar conservation laws

We consider the Cauchy problem for a class of scalar conservation laws with flux having a single inflection point. We prove existence of global weak solutions satisfying a single entropy inequality together with a kinetic relation, in a class of bounded variation functions. The kinetic relation is obtained by the travelling-wave criterion for a regularization consisting of balanced diffusive and dispersive terms. The result is applied to the one-dimensional Buckley-Leverett equation.

NONCONVEX CONSERVATION LAWS AND ORDINARY DIFFERENTIAL EQUATIONS

The paper deals with the well posedness of a class of ordinary differential equations. The vector field depends on the solution to a scalar conservation law, whose flux function is assumed to have a single inflection point (from whence ‘nonconvex’ is derived). Filippov solutions to the ordinary differential equations are considered, and Hölder continuous dependence on the initial data is proved. The motivation for the problem is a model of traffic flow.

Alveolar inflation during generation of a quasi-static pressure/volume curve in the acutely injured lung.

Lower and upper inflection points on the quasi-static curve representing a composite of pressure/volume from the whole lung are hypothesized to represent initial alveolar recruitment and overdistension, respectively, and are currently utilized to adjust mechanical ventilation in patients with acute respiratory distress syndrome. However, alveoli have never been directly observed during the generation of a pressure/volume curve to confirm this hypothesis. In this study, we visualized the inflation of individual alveoli during the generation of a pressure/volume curve by direct visualization using in vivo microscopy in a surfactant deactivation model of lung injury in pigs. Prospective, observational, controlled study. University research laboratory. Eight adult pigs. Pigs were anesthetized and administered mechanical ventilation, underwent a left thoracotomy, and were separated into two groups: control pigs (n = 3) were subjected to surgical intervention, and Tween lavage pigs (n = 5) were subjected to surgical intervention plus surfactant deactivation by Tween lavage (1.5 mL/kg 5% solution of Tween in saline). The microscope was then attached to the lung, and the size of each was alveolus quantified by measuring the alveolar area by computer image analysis. Each alveolus in the microscopic field was assigned to one of three types, based on alveolar mechanics: type I, no visible change in alveolar size during ventilation; type II, alveoli visibly change size during ventilation but do not totally collapse at end expiration; and type III, alveoli visibly change size during tidal ventilation and completely collapse at end expiration. After alveolar classification, the animals were disconnected from the ventilator and attached to a super syringe filled with 100% oxygen. The lung was inflated from 0 to 220 mL in 20-mL increments with a 10-sec pause between increments for airway pressure and alveolar confirmation to stabilize. These data were utilized to generate both quasi-static pressure/volume curves and individual alveolar pressure/area curves. The normal lung quasi-static pressure/volume curve has a single lower inflection point, whereas the curve after Tween has an inflection point at 8 mm Hg and a second at 24 mm Hg. Normal alveoli in the control group are all type I and do not change size appreciably during generation of the quasi-static pressure/volume curve. Surfactant deactivation causes a heterogenous injury, with all three alveolar types present in the same microscopic field. The inflation pattern of each alveolar type after surfactant deactivation by Tween was notably different. Type I alveoli in either the control or Tween group demonstrated minimal change in alveolar area with lung inflation. Type I alveolar area was significantly (p <.05) larger in the control as compared with the Tween group. In the Tween group, type II alveoli increased significantly in area, with lung inflation from 0 mL (9666 +/- 1340 microm2) to 40 mL (12,935 +/- 1725 microm2) but did not increase further (220 mL, 14,058 +/- 1740 microm2) with lung inflation. Type III alveoli initially recruited with a relatively small area (20 mL lung volume, 798 +/- 797 microm2) and progressively increased in area throughout lung inflation (120 mL, 7302 +/- 1405 microm2; 220 mL, 11,460 +/- 1078 microm2) The normal lung does not increase in volume by simple isotropic (balloon-like) expansion of alveoli, as evidenced by the horizontal (no change in alveolar area with increases in airway pressure) pressure/area curve. After surfactant deactivation, the alveolar inflation pattern becomes very complex, with each alveolar type (I, II, and III) displaying a distinct pattern. None of the alveolar pressure/area curves directly parallel the quasi-static lung pressure/volume curve. Of the 16, only one type III atelectatic alveolus recruited at the first inflection point and only five recruited concomitant with the second inflation point, suggesting that neither inflection point was due to inflection point was due to massive alveolar recruitment. Thus, the components responsible for the shape of the pressure/volume curve include all of the individual alveolar pressure/area curves, plus changes in alveolar duct and airway size, and the elastic forces in the pulmonary parenchyma and the chest wall.

G^2 Two-Point Hermite Rational Cubic Interpolation

We consider the problem of G^2 two-point Hermite interpolation by a rational cubic. Given two points with tangent vectors and curvatures, the necessary and sufficient conditions are placed on the weights of the rational cubic curve which ensures that (i) if the data suggest a C -shaped curve, the rational cubic interpolates a C -shaped curve without loops, cusps, or inflections, and (ii) if the data suggest an S -shaped curve, the rational cubic interpolates an S -shaped curve with a single inflection, no loops and no cusps.

Osculatory interpolation

We consider the problem of G 2 two-point Hermite interpolation by rational cubics. Given two points with unit tangent vectors and consistent signed curvatures, the necessary and sufficient conditions are placed on the weights of the rational cubic curve which ensures that (i) if the data (control polygon) suggest a C-shaped curve, the the rational cubic interpolates a C-shaped curve without loops, cusps, or inflections, and (ii) if the data suggest an S-shaped curve, the the rational cubic interpolates an S-shaped curve with a single inflection, no loops and no cusps.

Quantum Yields of the Photocatalytic Oxidation of Formate in Aqueous TiO2 Suspensions under Continuous and Periodic Illumination

Quantum yields φF for the oxidation of formate in periodically illuminated TiO2 suspensions are always smaller than, but approach, at sufficiently high intermittence, the φF's measured under continuous exposure at equivalent average photon absorption rates 〈Ia〉. We find that φF,cont = (0.031 ± 0.003)×Ia-0.39±0.03 in the range 0.089 ≤ Ia/μeinstein L-1 s-1 ≤ 2.02. Under periodic illumination, φF begins to rise from its minimum value: φF,long τ = φF,cont(Ia,max) = 0.021, for light periods τL ≤ 1 s, regardless of the duty cycle γ. Thereafter, φF climbs to its upper limit: φF,short τ = φF,cont (〈Ia〉 = γIa,max), after a single inflection at τL ∼ 200 ms for γ = 0.35, but only after a second inflection at τL ∼ 10 ms for γ = 0.05. Thus, the photocatalytic oxidation of formate in ∼10 nm TiO2 nanoparticle suspensions under periodic illumination behaves kinetically as a homogeneous photochemical system; i.e., φF's are not limited by mass diffusion, or by adsorption/desorption, but by carrier recombination. The latter has a characteristic time of about 0.1 s under present conditions. Sparse carriers, such as those present in γ = 0.05 experiments at short τL's, are deactivated within ∼6 ms. Therefore, photocatalytic quantum yields on nanoparticle surfaces are actually insensitive to events in the sub-milliseconds domain.

Variation of the viscoelastic properties of wood as a surface finishes substrate

The variation of the viscoelastic properties of wood during exposure to sunlight-type radiation of thin specimens of Abies grandis as a model of the thin surface film of solid timber was followed by thermomechanical analysis (TMA) tests in compression and in tension. For all the types of tests carried out, the TMA traces obtained present only a single inflexion point, which has been assigned to lignin softening. Sunlight radiation was found to have a degrading effect on lignin while the cellulose to hemicelluloses interactions do not appear to be worsened during exposure to the same. The softening temperature variation as a function of sunlight radiation exposure appears to be a parameter which can be used both to observe wood degradation as well as to control the effectiveness and durability of wood stabilization treatments.

Conformational Polymorphism of High MrGlutenin Subunits Detected by Transverse Urea Gradient Gel Electrophoresis

Unfolding behaviour of different allelic variants of high Mrglutenin subunits has been studied by transverse urea gradient gel electrophoresis, a system in which a gradient of urea (from 0 to 8 M) is generated perpendicularly to the direction of migration. A different unfolding pattern is observed between x- and y-type subunits. The former type of subunits generally present a broad unfolding pattern without any clear transition, as urea concentration increases, suggesting the existence of several conformational intermediates. On the contrary most of the y-type subunits present an unfolding pattern showing an abrupt decrease in mobility, with a single inflection point at the midpoint of the transition indicative of a protein unfolding in a single, cooperative, two-state transition. Native and bacterial expressed subunits, differing for the size of the repetitive domain, were used to assess the role of variation in size of such region on unfolding behaviour. Free energy values associated to unfolding process were calculated for most of the y-type subunits presenting a two state transition. In particular, different values were found for subunit Dy10 and Dy12, with the former being larger than the latter, suggesting a different stability of the two subunits. Possible implications for qualitative differences associated to allelic subunits are also discussed.

Shock waves in nonuniform gas

Shock waves propagating through a stratified gas are investigated numerically and analytically. A shock wave is produced by a piston that begins to move from rest abruptly at some constant velocity in a two-dimensional horizontal duct. Initially the gas in the duct has a temperature or density distribution only along the vertical axis at a constant pressure. The initial density distribution, which is assumed to change monotonically, has a zero spatial gradient at the upper and lower walls and then has a single inflection point. It is confirmed that at least three types of shock patterns can be realized asymptotically. The first is a single curved shock, the second is a shock with a Mach stem (Mach reflection), and the last is a shock with a reflected branch (regular reflection). The first is substantially steady but the latter two are essentially unsteady. The time evolution of the induced flow field is investigated in detail. Based on this information, an analytical solution for the substantially steady curved shock is obtained in the coordinate system fixed on the shock. The shock profile as well as the induced flow field is investigated in detail with this solution. It is shown that the analytical results can predict quite well the numerical results. Finally, the flow instability of this shock-induced flow is investigated, because the induced flow has a nonuniform horizontal velocity distribution along the vertical axis at a constant pressure.

Proton Binding Is Part of Protein Relaxation of Flash‐Excited Reaction Center from Photosynthetic Bacteria Rhodobacter sphaeroides

AbstractIn the first part of this work, a brief review is presented of the recent knowledge of charge stabilization processes in flash‐excited reaction center protein from photosynthetic bacteria Rhodobacter sphaeroides. The adaptation of the protein to charge separation is comprised of different manifestations of protein relaxation including proton binding at the late phase. In the second part, a unique method, comparative measurement of prompt and millisecond‐delayed fluorescence of the bacteriochlorophyll dimer of the reaction center protein is used to determine the free energy levels of the charge‐separated states with respect to that of the excited singlet state of the dimer: −910 ± 20 meV and −970 ± 20 meV were measured at pH 8.0 for reaction centers in the absence and presence of secondary quinone, respectively. The pH‐dependence of the energetics of charge stabilization due to light‐induced proton binding is described in reaction centers with and without secondary quinone activity. The range of free‐energy change between pH 11 and pH 5 was −65 meV with a single (alkaline) inflection point (no active secondary quinone) and −175 meV with an additional (acidic) inflection point (active secondary quinone). The conclusions from fluorescence data agreed well with pH‐dependence of integrated proton uptake (a model‐independent method) and with calculations based on interaction of quinones with four key amino acid residues. The enthalpy and entropy parts of the free‐energy changes were determined from van't Hoff analysis of the delayed fluorescence and compared with data of other methods. It is concluded that the charge stabilization including proton binding is a highly enthalpy‐driven process.

Undercompressive shocks and Riemann problems for scalar conservation laws with non-convex fluxes

The Riemann initial value problem is studied for scalar conservation laws whose fluxes have a single inflection point. For a regularization consisting of balanced diffusive and dispersive terms, the travelling wave criterion is used to select admissible shocks. In some cases, the Riemann problem solution contains an undercompressive shock. The analysis is illustrated by exploring parameter space for the Buckley–Leverett flux. The boundary of the set of parameters for which there is a physical solution of the Riemann problem for all data is computed. Within the region of acceptable parameters, the solution hasseveral different forms, depending on the initial data; the different forms are illustrated by numerical computations. Qualitatively similar behaviour is observed in Lax–Wendroff approximations of solutions of the Buckley–Leverett equation with no dissipation or dispersion.

Richard J. Smith lecture in defense of common sense

When a person's name is attached to an event, an invention, or an award, it runs the risk of becoming depersonalized. The name itself becomes gradually devoid of the essence of the character of the individual for whom the trophy, award, or lectureship was named. It becomes a noun, said rapidly, in a single breath, without punctuation, spacing, or inflexion: thecyyoungaward, thenobelprize, therichardjsmithlecture. Nobody reflects anymore on Cy Young, the pitcher or Alfred Bernhard Nobel, the scientist. I would not want this fate to befall the memory of Richard J. Smith. Dick Smith passed away in 1987, only 11 years ago. He was 57 years old, and had been one of the brightest in our profession; the owner of an intellect that simply dazed those with whom he came in contact. He was also a true scholar, thoughtful, eminently witty, and, most appropriately, commonsensical. He trained in the field of orthopedics at the Hospital for Joint Diseases, New York, NY. It was there that he first became aware of hand surgery as a subspecialty, influenced by the gentle giant of hand surgery, Emmanuel Kaplan. He took a year to train in hand surgery, with Guy Pulvertaft in Derby, England, and with Joe Boyes, in Los Angeles, CA. He eventually returned to the Hospital for Joint Diseases, where he succeeded Dr Kaplan in 1968, 1 year

Characterization of pharmacodynamic recession slopes for direct and indirect response models.

Direct pharmacologic effects are known to recede over time with largely linear slopes (Levy's k.m product, J. Pharm. Sci. 53:342, 1964) and indirect responses have similar behavior. Pharmacodynamic slope properties were examined mathematically for the Hill function with monoexponential drug disposition and simulations were carried out for other pharmacokinetic functions. Both types of pharmacodynamic profiles exhibit a single terminal inflection point (fp) when drug concentrations exceed the EC50 (that concentration causing one-half maximum effect, Emax). For direct effects it was found that Cfp (the drug concentration at fp) = EC50, the determinants of inflection time were identified, and Slopefp = -lambda z gamma Emax/4 where lambda z is the terminal disposition slope and gamma is the Hill coefficient. These characteristics were explored for the four basic indirect response models which also exhibit recession profiles with slight sigmoidity and a single terminal inflection point at higher doses. The drug concentration at inflection Cfp is < or = IC50 or SC50 (drug concentrations causing half-maximal inhibition or stimulation), while the inflection response (Rfp) attains constant values at larger doses. Indirect Response Models I, III, and IV have nearly linear return slopes for a wide range of doses which are governed by the disposition slope lambda z of the drug, loss constant kout of the response, maximum inhibition (Imax) or stimulation (Smax) factors, and a unique fractional constant (0 < G < or = 1). Model II exhibits more complex behavior with recession slopes which are less likely to be parallel for various doses. Most indirect responses are expected to show nearly linear recession slopes which are parallel for moderate to large doses and mainly governed by an identical combination of pharmacokinetic (lambda z), system (kout), and dynamic capacity factors (Imax or Smax).

Physico-chemical studies on BELGARD EV and BELGARD EV 2000 solutions. Part II. Potentiometric and conductometric acid-base titrations

The two anti-scale agents BELGARD EV (BELEV) and BELGARD EV 2000 (BELEV 2) are titrated against standard NaOH solution. Both the potentiometric (pH metric) and the conductometric titration techniques are used. For the sake of comparison the reaction of the monomer (maleic acid, H 2M) is also investigated. The two titration techniques reveal that H 2M neutralizes along two equal steps. The pK 1 and pK 2 of the acid are calculated as 2.9 and 6.1, in good agreement with the values quoted in the literature. The potentiometric titration curves of BELEV and BELEV 2 solutions are similar and show a single drawn-out inflexion. Computer analysis of the curves reveal four acid species in case of BELEV and two in case of BELEV 2. The pK values, the percentage composition and the mean average molecular weights of all species are computed. The consumption of NaOH till any one and the same pH value varies linearly with the additives content in solution. This offers a simple method for analysis of BELEV and BELEV 2 preparations. The conductometric titration curves of the two agents indicate the presence of three acid species. Correlation with the pH curves is made in every case. Not all the inflexions in conductometric curves have correspondence in pH curves. The effect of addition of increasing concentrations of H 2M to BELEV (BELEV 2) solutions and of increasing BELEV (BELEV 2) concentrations to H 2M on the pH-metric curves is examined in detail. The two materials affect the neutralization pattern of one another. The results suggest the masking of the free-acid protons through hydrogen bonding with the polymers.

Monocular Diplopia Caused by Ocular Aberrations and Hyperopic Defocus

As a single aperture, approximately monofocal optical system, the human eye generally creates a single image on the retina. However, the literature contains many reports of perceptual monocular diplopia. While it is easy to understand how distortion may produce monocular diplopia, its reported high incidence in normal eyes is less easily understood. We examine a model which ascribes monocular diplopia to an interaction between defocus and ocular spherical aberration. Using a psychophysical hyperacuity-based alignment procedure we measured the transverse aberration function in 0.5 mm steps horizontally across the pupil in the eyes of three cyclopleged subjects. Ocular transverse aberration functions were derived with best refraction and with simulated myopia and hyperopia. Monocular diplopia was also measured under the same conditions. All three subjects showed significant, but different, degrees of positive spherical aberration. The measured ocular transverse aberration functions were predictably modified by the hyperopic and myopic defocus. Hyperopic defocus combined with positive (myopic) spherical aberration changes a monotonic transverse aberration function with a single inflection point into a biphasic function with two inflection points. The locations of the inflections predict the presence and magnitude of the perceived diplopia. These experimental results confirm Verhoeff's (1900) hypothesis for the ocular cause of monocular diplopia. Copyright © 1996 Published by Elsevier Science Ltd.

A planar cubic Bézier spiral

A planar cubic Bézier curve segment that is a spiral, i.e., its curvature varies monotonically with arc-length, is discussed. Since this curve segment does not have cusps, loops, and inflection points (except for a single inflection point at its beginning), it is suitable for applications such as highway design, in which the clothoid has been traditionally used. Since it is polynomial, it can be conveniently incorporated in CAD systems that are based on B-splines, Bézier curves, or NURBS (nonuniform rational B-splines) and is thus suitable for general curve design applications in which fair curves are important.

O-chloranil initiated polymerization of pyrrole in presence of N-vinylcarbazole and some properties of the polymer

The polymerization of a mixture of N-vinylcarbazole (NVC) and pyrrole (PY) by O-chloranil in toluene yields an insoluble black polymer P(PY-NVC) which exhibits properties distinct from PPY or PNVC. The inclusion of either monomer moieties in P(PY-NVC) has been endorsed by IR spectroscopy. Kinetics of PPY-OCA homopolymerization and of PY-NVC-OCA copolymerization have been elucidated. TGA reveals the stability order as PNVC > P(PY-NVC) > PPY. DSC analyses reveal a single inflection for P(PY-NVC) around (198–202 °C) and for PPY and PNVC around 180 and 228 °C respectively. PPY exhibits a high dielectric constant (~ 350) at 10 Hz while P(PY-NVC) or PNVC exhibit values (~ 11) and (~5) respectively—the dielectric constant falling consistently with increasing frequency as does the dielectric loss parameter also—suggesting interfacial polarization. P(PY-NVC) shows maximum d.c. conductivity of 3.5 x 10 −6ohm −1cm −1depending on [PY]/[NVC] mole ratio. For PPY, the conductivity is in the range (10 −3–10 −5)ohm −1cm −1 and the conductivity in all these polymers is dependent on the concentrations of the monomers, O-CA and runs parallel to the trend in conversion.

Self-assembly of DNA oligomers into high molecular weight species.

Thermal denaturation, gel electrophoresis, and circular dichroism methods were used to characterize DNA oligomers possessing one or two segments of four contiguous G bases in order to investigate their environmentally dependent conformational properties. The sequences of the oligomers studied were the following: HP1-T series, C4T4G4T5-8; HP1-TG series, C4T4G4T1-4G4. In NaCl at concentrations up to 200 mM, the melting profiles of these oligomers are characterized by single inflection points whose Tm values are independent of DNA concentration. In addition, these oligomers run as single bands in polyacrylamide gels under those same conditions as well as in 100 mM K+ or 20 mM Mg2+. These data suggest that these oligomers exist as intramolecular hairpins comprised of four G:C base pairs in the stems, loops of four T bases, and 3'-overhangs of T5-8 or T1-4G4. In the presence of 100 mM K+ plus 20 mM Mg2+, however, gel electrophoresis indicates that oligomers of the HP1-T series exist as equilibria between parent hairpins and four-stranded structures (i.e., quadraplexes). Quadraplex formation for any member of the HP1-T series requires unfolding of the hairpin, exposing the G4 segment prior to quadraplexation. Members of the HP1-TG series self-assemble into multistranded species of high molecular weight in the presence of 100 mM K+ plus 20 mM Mg2+. For this series of oligomers, the data suggest that these higher order species arise from successive additions of parent oligomer to an initially formed quadraplex.(ABSTRACT TRUNCATED AT 250 WORDS)

Autocatalytic continuous reactions in a stirred tank: I. Multiplicity of steady states

The multiplicity of steady states in a stirred tank was considered, in which a continuum of autocatalytic reactions of the type A + 2 B → 3 B, B → C is taking place by letting A( x) be the “species” of a continuous mixture. The distribution of A( x) in the feed can be quite general (though it was found to be convenient to do calculations with gamma distributions) and a method is given for determining the region of parameter space coorresponding to qualitatively different behaviors in the case where the overall conversion curve has a single inflection point. As with the single component, there is a region in which there are three steady states, outside of which the steady state is unique. It was found that the size of the region of multiplicity only slightly as the variance of the feed distribution increases.

The Mono- and Multi-Layer Behaviors of 2,4-HDDA Doped with Stearic Acid Includingin situPolymerization

Abstract The properties of the mono- and multi-layer of 2,4-HDDA doped with stearic acid including in-situ UV-polymerization were investigated by studying surface pressures(i.e., film miscibility in mixed monolayers) and its transferability onto the substrate(i.e., interactions and film depositions in mixed monolayers). The collapse pressure of monolayers increased in proportion to the amount of SA. For the polymerized monolayer, the isotherms showed only a single inflection point of the surface pressure. For the undoped case it was hard to prepare multilayer, but the transferability was much enhanced by doping SA.