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Is there a simple secret to truly great patient care? Medical science is able to alleviate more diseases and mitigate more suffering than ever before, but physicians are left feeling less respected, more criticized, more judged, and more burned out. Too many patients say we just do not care about them, regardless of the expertise we trained so hard to give to them. Generational truths and personal experiences from a rural, community-based surgical practice in Mississippi suggest that the art and the science of medicine are inseparable and interdependent. It is indeed possible for a highly trained, teaching surgeon to sit with his patients every Sunday in church, take care of the local football team, and speak at funerals of those he fought to save. This level of emotional agility is a requisite character trait in a rural setting, and one that can serve all surgeons well, no matter where they practice. Genuine compassion and a hand on the shoulder, supported by a foundation of scientific knowledge and clinical judgment, will almost guarantee a strong, trusting bond between doctor and patient. The secret of great patient care is simply caring for the patient

Rudolph Matas (1860-1957) was one of the foremost figures in the history of vascular surgery. He is considered the father of vascular surgery for his operations for arteriovenous fistula and peripheral artery aneurysm, all devised before the isolation of heparin and the wide adoption of techniques for vascular anastomosis. A medical and surgical prodigy, Matas received his medical degree from Tulane University at age 19 (1880) and was named its chair of surgery at 35 (1895), a position he would hold until 1927. A contemporary and friend of Halsted, Matas throughout his career was known as a leader in the field, holding the presidencies of the American College of Surgeons (1925-1926) and the American Surgical Association (1909). He maintained loyal relationships to those who trained in surgery with him at Touro Hospital in New Orleans, including the author’s grandfather, the first Richard J. Field. Matas was an honored guest at the dedication of the Centreville Clinic in 1928, the facility where three generations of Field surgeons have provided continuous service to its rural Mississippi community for nearly a century.

This historical review of the development of the Oregonator model of the Belousov–Zhabotinsky reaction is based on a lecture Dick Field presented during IrvFest2015—Celebrating a founding father of chaos!, a meeting in commemoration of Irving R. Epstein’s [Formula: see text] birthday. For Dick’s [Formula: see text] birthday festschrift, we focus here on the five papers in the series named “ Oscillations in chemical systems,” published in 1972 [Noyes et al., J. Am. Chem. Soc. 94, 1394–1395 (1972); Field et al., J. Am. Chem. Soc. 94, 8649–8664 (1972); Field and Noyes, Nature 237, 390–392 (1972)] and 1974 [Field and Noyes, J. Chem. Phys. 60, 1877–1884 (1974); Field and Noyes, J. Am. Chem. Soc. 96, 2001–2006 (1974)].

Recent work has introduced social dynamic models of people’s stress-related processes, some including amelioration of stress symptoms by support from others. The effects of support may be “direct”, depending only on the level of support, or “buffering”, depending on the product of the level of support and level of stress. We focus here on the nonlinear buffering term and use a model involving three variables (and 12 control parameters), including stress as perceived by the individual, physical and psychological symptoms, and currently active social support. This model is quantified by a set of three nonlinear differential equations governing its stationary-state stability, temporal evolution (sometimes oscillatory), and how each variable affects the others. Chaos may appear with periodic forcing of an environmental stress parameter. Here we explore this model carefully as the strength and amplitude of this forcing, and an important psychological parameter relating to self-kindling in the stress response, are varied. Three significant observations are made: 1. There exist many complex but orderly regions of periodicity and chaos, 2. there are nested regions of increasing number of peaks per cycle that may cascade to chaos, and 3. there are areas where more than one state, e.g., a period-2 oscillation and chaos, coexist for the same parameters; which one is reached depends on initial conditions.

The Belousov–Zhabotinsky (BZ) reaction is the prototype oscillatory chemical system. We investigate here a new scaling of the Oregonator model of BZ chemical kinetics and use this scaling to elucidate fundamental properties of BZ dynamics. In particular, the Showalter–Noyes criterion for oscillation, that the product [BrO3–][H+] exceeds a critical value, arises naturally as a subcritical Hopf bifurcation in this setting, as does the reduction to a two-variable model. We thus provide chemical explanations of the role of time scales in the BZ reaction.

The irreversible dehydration reaction of dihydroxyacetone (DHA) to methylglyoxal (MGO) in a honey model system has been examined to investigate the influence of added perturbant species on the reaction rate. The secondary amino acid proline, primary amino acids (alanine, lysine and serine), and iron, or combinations of these perturbants, were added to artificial honey with either DHA or MGO and stored at 20, 27 and 37°C. These systems were monitored over time. A 1:1 conversion of DHA to MGO was not observed in any system studied, including the control system with no added perturbants. Addition of proline to the matrix increased consumption of DHA but did not produce any more MGO than the control sample. Lysine and serine behaved similarly. Alanine enhanced the conversion of DHA to MGO and had the best efficiency of conversion of DHA to MGO for the amino acids studied. An iron II salt enhanced the conversion of DHA to MGO, even in the presence of proline.

During a study of the conversion of dihydroxyacetone (DHA) to methylglyoxal (MGO) in maturing New Zealand mānuka honey, the kinetics of formation of 5-(hydroxymethyl)furfural (HMF) was studied at temperatures from 4 to 37°C. Formation of HMF was first-order during an induction period and zero-order thereafter indicating that the mechanism includes the formation of certain critical intermediates and that these require time to build up; the duration of the induction period depended primarily upon temperature. The zero-order rate constant at 37°C was the same for mānuka honey and clover honey doped with 2000 or 10,000mg/kg DHA and for artificial honey with 2000mg/kg of DHA and either alanine or proline and alanine added. Zero-order rate constants for artificial honey with added amino acids were less than for a control without amino acids. A simulation was created to predict the formation of HMF over time at 37°C in mānuka honey.

The unstirred, ferroin (Fe(phen) 3 2+ ) catalyzed Belousov-Zhabotinsky (BZ) reaction is the prototype oscillatory chemical system. Reaction media with added Br - appear red (reduced, low [Fe(phen) 3 3+ ]) during an induction period of several minutes, followed by the "spontaneous" formation of "pacemaker" sites, which oscillate between a blue, oxidized state (high [Fe(phen) 3 3+ ]) and the red, reduced state and generate target patterns of concentric, outwardly moving waves of oxidation (blue). Auto-oscillatory behavior is also seen in the Oregonator model of Field, Koros and Noyes (FKN), a robust, reduced model that captures qualitative BZ kinetics in the auto-oscillatory regime. However, the Oregonator model predicts a blue (oxidized) induction phase. Here we develop a generalized Oregonator-like model with no explicit bifurcation parameter that yields the observed transition from a red initial state to oscillatory dynamics, and displays a new bifurcation mechanism not seen in the original Oregonator.

The aqueous solution equilibration of d‐glucaric acid with its lactone forms was studied by NMR with and without acid catalysis. The kinetics of the approach to equilibrium were simulated, and approximate equilibrium and rate constants were obtained.

The kinetics of conversion of dihydroxyacetone (DHA) to methylglyoxal (MGO) were investigated in mānuka honeys and DHA-doped clover honeys stored between 4 and 37°C. Both the disappearance of DHA and appearance of MGO were confirmed as overall, first order reactions, albeit probably composites of multiple reactions. Increasing the storage temperature accelerated the rate of DHA loss and the initial rate of formation of MGO, but better conversion efficiency was observed at lower temperature. At 37°C, more MGO was lost at later times in mānuka honey compared to DHA-doped-clover honey. Thirty-seven New Zealand mānuka honeys and four clover honeys were analysed for various chemical and physical properties; comparison of rate constants and these parameters identified some positive correlations.

A kinetic model for the conversion of dihydroxyacetone (DHA) to methylglyoxal (MGO) in honey is proposed; a building block approach was used to create the model. Artificial honeys doped with DHA and individual perturbants were fitted first, then multiple perturbants (alanine, proline and iron, and combinations of these) were fitted before comparing the simulation to real honey samples (doped clover and mānuka honey). The main responses in the prediction model were DHA, MGO, proline, primary amino acids, acidity, 3-phenyllactic acid and 4-methoxyphenyllactic acid. Three temperatures (20, 27 and 37°C) were studied and the conversion of DHA to MGO was monitored over at least 1year. Differences in the conversion between clover doped with DHA and mānuka honey were observed. The simulation fitted well for the honeys tested.

The kinetics of the reaction HBrO(2) + HBrO(2) --HOBr + BrO(3)(-) + H(+) is investigated in aqueous HClO(4) (0.04-0.9 M) and H(2)SO(4) (0.3-0.9 M) media and at temperatures in the range 15-38 degrees C. The reaction is found to be cleanly second order in [HBrO(2)], with the experimental rate constant having the form k(exp) = k + k'[H(+)]. The half-life of the reaction is on the order of a few tenths of a second in the range 0.01 M[HBrO(2)](0)0.02 M. The detailed mechanism of this reaction is discussed. The activation parameters for kare found to be E(double dagger) = 19.0 +/- 0.9 kJ/mol and DeltaS(double dagger) = -132 +/- 3 J/(K mol) in HClO(4), and E(double dagger) = 23.0 +/- 0.5 kJ/mol and DeltaS(double dagger) = -119 +/- 1 J/(K mol) in H(2)SO(4). The activation parameters for k' are found to be E(double dagger) = 25.8 +/- 0.5 kJ/mol and DeltaS(double dagger) = -106 +/- 1 J/(K mol) in HClO(4), and E(double dagger) = 18 +/- 3 kJ/mol and DeltaS(double dagger) = -130 +/- 11 J/(K mol) in H(2)SO(4). The values Delta(f)H(29)(8)(0)[BrO(2)(aq)] = 157 kJ/mol and Delta(f)H(29)(8)(0)[HBrO(2)(aq)] = -33 kJ/mol are estimated using a trend analysis (bond strengths) based on the assumption Delta(f)H(29)(8)(0)[HBrO(2)(aq)] lies between Delta(f)H(29)(8)(0)[HOBr(aq)] and Delta(f)H(29)(8)(0)[HBrO(3)(aq)] as Delta(f)H(29)(8)(0)[HClO(2)(aq)] lies between Delta(f)H(29)(8)(0)[HOCl(aq)] and Delta(f)H(29)(8)(0)[HClO(3)(aq)]. The estimated value of Delta(f)H(29)(8)(0)[BrO(2)(aq)] agrees well with calculated gas-phase values, but the estimated value of Delta(f)H(29)(8)(0)[HBrO(2)(aq)], as well as the tabulated value of Delta(f)H(29)(8)(0)[HClO(2)(aq)], is in substantial disagreement with calculated gas-phase values. Values of Delta(r)H(0) are estimated for various reactions involving BrO(2) or HBrO(2).

The spontaneous formation of ordered spatial concentration patterns in an unstirred chemical medium, supported by dissipation of chemical free energy, has been considered often since a pioneering suggestion by Turing and early work by Prigogine et al. and more recent work by Ross et al. involving nonequilibrium thermodynamics. The prototype experimental example is the oscillatory Belousov–Zhabotinsky reaction, in which target patterns of outward-moving concentric rings are readily observed. One widely-studied question is whether “microscopic” fluctuations can nucleate these target centers, or whether a catalytic, nucleating heterogeneous center is required. Vidal and Pagola observed spontaneous initiation with no nucleating particles visible at 6-micron resolution; however Zhang, Forster, and Ross argued theoretically that this is impossible in regimes far from Hopf bifurcations. We describe here an explicit mechanism in a “supercritical regime,” following and near to the low-f Hopf bifurcation in a generalized Oregonator model, by which microscopic fluctuations can nucleate activity, and reconcile these results with Zhang et al. Concentrations remain very close to the unstable steady-state values after the system slowly passes through the bifurcation point but before occurrence of the inevitable transition to large-amplitude limit cycle oscillations. Suitably timed small (even microscopic) fluctuations about this supercritical state can sharply accelerate the inevitable onset of large-amplitude limit cycle oscillations, potentially nucleating targets.

A high performance liquid chromatography (HPLC) method was developed to assay nitropropanoyl glucosides in the nuts of karaka (Corynocarpus laevigatus) a traditional food of New Zealand Māori. Levels of glucosides, measured as 3-nitropropanoic acid, ranged from 50.25 to 138.62 g kg−1 (5.0–13.9% w/w) and were highest in nuts from unripe drupes; these levels are higher than any previously reported. Other parts of the drupe also contained nitropropanoyl glucosides but at lower levels than the nut. Treatment procedures to remove the glucosides from the nuts varied in their efficacy with soxhlet extraction removing 98.7% and prolonged boiling and cold water extraction both removing 96%. These findings confirm the traditional methods for preparation of these nuts for consumption.

Dynamic equations describing photoxidation of tropospheric chemical pollutants are nonlinear, containing complex feedback loops. Such nonlinearity is known to give rise to various dynamical instabilities including multiple steady states, oscillation, and even chaos. A related type of instability, excitability, is demonstrated here using a two-variable (reduced from six) model of CH4 photoxidation in which perturbation of a stable but excitable steady state beyond a threshold is dramatically amplified before the steady state is reapproached. Such switching/amplification responses may have important implications for atmospheric/climatic modeling. A phase-plane analysis describes the origin of this excitability and suggests that it may be a relatively common phenomenon in environmental models.

Three components have been identified as being common to oscillation in five related but increasingly complex models of tropospheric chemistry. The first of these components is an NOx-empty/refill cycle in which [NOx] grows or declines, depending upon the relative source rates of NOx and HOx, the latter being generally proportional to the rate of photolysis of [O3]. The second component is a complex O3-production/loss cycle dependent upon [NOx], [HOx], [CO], and [O3]. The third component is nonlinear coupling (both direct and indirect) of the first two, which allows each of the two cycles to affect the other. This coupling also introduces a positive feedback that autocatalytically accelerates O3 production at high [CO] and [O3] when [NOx] and [NO]/[NO2] are simultaneously low, thus destabilizing the steady state. A schematic model is provided that illustrates the interaction of these three components and indicates that the positive feedback indeed is necessary for oscillation to occur. The major features ...

Oxygenated volatile organic species (oxygenates), including HCOOH, H 2 CO, CH 3 OH, HOCH 2 CHO (hydroxyacetaldehyde), CH 3 COOH, and C 6 H 5 OH, have recently been identified by Fourier transform infrared measurements as a significant component of the direct emissions from biomass combustion. These oxygenates have not generally been included in the hydrocarbon-based initial emission profiles used in previous photochemical simulations of biomass combustion smoke plumes. We explore the effects of oxygenates on this photochemistry by using an established initial emission hydrocarbon profile and comparing simulation results obtained both with and without addition of the above six oxygenates. Simulations are started at noon and carried out for 30 hours in an expanding Lagrangian plume. After an initial transient period during which [NO x ] falls rapidly, conditions within the oxygenated smoke plume are found to be strongly NO x -sensitive, and the simulated final species profile is thus strongly dependent upon the Δ[NO]/Δ[CO] initial emission profile. Oxygenate addition results in very significant and complex effects on net O 3 production, as well as on the relative amounts of long-lived HO, and NO, reservoir species (H 2 O 2 , organic hydroperoxides, HNO 3 , and peroxyacetyl nitrate (PAN)) that are mixed into the surrounding atmosphere. Oxygenates may either increase or decrease net O 3 production (depending upon the initial Δ[NO]/Δ[CO]). However, they always increase H 2 O 2 and organic hydroperoxide production as a result of increased rates of radical + radical reactions. These effects spring largely from accelerated removal of NO, from the smoke plume due to increased radical concentrations resulting both from photolysis of oxygenates (mainly CH 2 O) and from their relatively high reactivity. Predicted concentrations of H 2 O 2 , Δ[O 3 ]/Δ[CO], Δ[NH 3 ]/Δ[CO], and Δ[HCOOH]/Δ[CO] are compared with some available measured values.

A simplified box model extracted from tropospheric photochemistry is investigated as the influx of NO (FNO) is increased. A subcritical Hopf bifurcation is encountered as FNO is increased, beyond which the steady state is unstable, and the system evolves to an oscillatory state resulting from alternate dominance of two radical chain processes. The first is an O3-consuming process of net stoichiometry, CO + O3 → {CO2} + {O2}, occurring at high [CO] and [O3] and very low [NOx], but leading to increased [NOx] via FNO as CO and O3 are depleted. As [NOx] thus grows, passes through a maximum, and then declines, the second, an O3-producing process of net stoichiometry, CO + 2{O2} + hν → {CO2} + O3, is dominant. It remains so as O3 and CO accumulate (CO via its influx, FCO) until [NOx] again reaches very low values at high [O3] and [CO] as a result of the removal of NO2 by HO photochemically generated from the increasing [O3]. This alternation occurs because each process affects [NOx] and [HOx] so as to lead to dominance of the other. A period-doubling transition to chaotic oscillation occurs as FNO is increased further. The embedding dimension of the chaos is estimated to be four, and the original six-variable model can be reduced to a four-variable (CO, O3, [NO + NO2] and [HO + HO2]) system that behaves nearly identically to the full six-variable model. While the oscillatory and chaotic periods seem too long (at least weeks) to be observed in real atmospheres, the model displays the nonlinear nature and dynamic instability of tropospheric photochemistry and offers insight into the behavior of and transitions between higher and lower [NOx] states, which may be observable. The importance of the ratios [CO]/[NO2] and [O3]/[NO] to net O3 change is illustrated. The appearance of this instability suggests that predictions based upon the temporal evolution of this or even more complex models of tropospheric chemistry sometimes may be very sensitive to the exact initial conditions of [CO]/[NO2] and [O3]/[NO] prevailing.

We consider a simplified reaction mechanism from tropospheric chemistryconsisting ofsix chemical species involved in ten dynamic processes. The concentrations of all six speciesundergo temporal oscillation for some parameter values. An asymptoticapproach to reduction of the original six-variable model to a four-variable version is considered together with detailed explanation of the procedure as well as discussion of conditions under whichthe reduction is possible. The reduced system nearly quantitatively represents the oscillating behavior of thefull model and allows elucidation of its basic dynamical features. This approach also can be used to compare various small models of atmospheric chemistry, and to determine their underlying dynamic structure. The method can be systematically appliedto larger atmospheric models.

The kinetics of the Dushman reaction, 5I- + IO3- + 6H+ → 3I2 + 3H2O, is considerably more complex in aqueous, acidic media than is the behavior of the analogous reaction of Br- with BrO3-. The latter reaction is first order in both [Br-] and [BrO3-] and is believed to proceed via a series of simple oxygen-atom transfers, there being no evidence for the intermediacy of polybromine species such as H2Br2O3. In contrast, the [I-] order in the Dushman reaction is reported variously to be one or two, depending upon experimental conditions, especially [IO3-]0/[I-]0, and the kinetics of this reaction is generally very complex with the intermediacy of H2I2O3 having been suggested by several authors. Stopped-flow kinetic measurements of the Dushman reaction are reported here with excess [KIO3]0 ≈ 40[KI]0/5 and [HClO4]0 ≥ 140 × 6[KI]0/5 in which the observed [I-] order is cleanly two, but saturation kinetics is observed for the pseudo-second-order rate constant as [KIO3]0 and [HClO4]0 increase. This observation is r...

Thermal treatments of solid mixtures of inulin and citric acid result in the formation of di-d-fructose dianhydrides and oligomers derived therefrom. The kinetics of formation of these compounds have been investigated and simulated in computer studies. A mechanism is proposed. The conditions used in this study were analogous to the conditions pertaining to the roasting of chicory, during which similar compounds are formed. Keywords: Inulin; di-d-fructose dianhydrides; kinetics; chicory; roasting; thermolysis, prebiotics

We investigate the kinetics of bromination of malonic acid, bromomalonic acid, tartronic acid, and ethanetetracarboxylic acid in 1 M sulfuric acid with bromine and hypobromous acid as brominating agents. In all cases the reaction occurs via the enol form of the acid, and the reaction products are brominated species. The possibility of bromide production in the reaction of malonic acid or bromomalonic acid with hypobromous acid can be ruled out. These results are important for the negative feedback loop in the Belousov−Zhabotinsky reaction.

Earth-average temperature is investigated using a simple energy balance model of the Budyko-Sellers-Ghil type expressed as a delay-differential equation describing the absorption and reflection of incoming solar radiation and surface-reflected infrared radiation. Cloud albedos for both radiations and the surface albedo as affected by ice coverage are assumed to depend upon the temperature that existed some time ago, introducing a time delay into the model. A variety of steady and oscillatory states are possible for Earth-average temperature, assuming plausible functions for the albedos, blackbody cooling, and suitable delay times. Multiple true steady states and multiple transient pseudo steady states as well as periodic, chaotic, and square-wave relaxation-oscillations result, The bifurcation structure relating the appearance of these phenomena to system parameters is explored. This very simple climate model exhibits complex behavior in global temperature without solar variation or environmental perturbation. Bifurcations exist at which small changes in parameters lead to destabilization of steady states and dramatic changes in qualitative behavior.

The set of three reaction-diffusion equations describing the time-space behavior of the intermediate chemical species in the Oregonator model of the Belousov-Zhabotinsky reaction is investigated in an open, gel-disk reactor in one and two spatial dimensions. Numerical simulations using equal values of the three diffusion coefficients indicate the presence of solutions corresponding to large-amplitude, apparently stable, stationary concentration patterns. The requirement of differential transport rates of chemical activator and inhibitor species for the development of stable patterns is apparently met in this system by differential exchange rates with the reservoir(s) rather than by differential diffusion rates within the gel-reactor. The characteristics of these patterns as well as their stability and bifurcation properties are investigated and suggest that their appearance is dependent upon the existence of bistability in the homogeneous reaction kinetics. The patterns have an intrinsic wavelength, and one of a particular wave-number destabilizes via a Hopf bifurcation as the length of the gel-reactor is varied, giving rise to oscillatory breather-solutions past the bifurcation but before decomposition into a spatially homogeneous state occurs. The relationship of these results to experimental systems, as well as an analogy to the behavior of biological membranes, is discussed.

An overview of the role of kinetic deuterium isotope effects (KD1E) in understanding hydrogen transfer reactions in organometallic chemistry is presented. Recent kinetic studies on the reaction of Os 3 (CO) 10 (μ-H) 2 with CF 3 CN to form Os 3 (CO) 10 ( μ − η 1 -CF 3 C(H)=N)- (μ-H) ( 1 ) and Os 3 (CO) 10 ( μ - η 2 -CF 3 C=NH) (μ-H) ( 2 ) are reported The rate determining step in the reaction is formation of the initial adduct Os 3 (CO)(CF 3 CN)(μ-H)(H) which is present in insufficient concentration to observe directly. As a result, direct determination of rate constants for the hydrogen transfer step in the formation of 1 and 2 is not possible. However, variable temperature stems reveal that the ratio of 2:1 increases with decreasing temperature as does the KDIE for 2 , but not for 1 . These results, as well as the kinetic parameters calculated for the overall reaction, suggest that a significant tumteling component is associated with the formation of 2 but not 1 .

The unstirred, ferroin (Fe(phen)(3)2+)-catalyzed Belousov-Zhabotinsky (BZ) reaction1-4 is the prototype oscillatory chemical system. After an induction period of several minutes, one sees "spontaneous" formation of "pacemaker" sites, which oscillate between a blue, oxidized state (high [Fe(phen)3(3+)]) and a red, reduced state (low [Fe(phen)(3)3+]). The reaction medium appears red (reduced) during the induction phase, and the pacemaker sites generate target patterns of concentric, outwardly moving waves of oxidation (blue). Auto-oscillatory behavior is also seen in the Oregonator model of Field, Korös, and Noyes (FKN), a robust, reduced model which captures qualitative BZ kinetics in the auto-oscillatory regime. However, the Oregonator model predicts a blue (oxidized) induction phase. Here, we show that including reaction R8 of the FKN mechanism, not incorporated in the original Oregonator, accounts for bromide release during the induction phase, thus producing the observed red oxidation state.

The dynamics of reacting chemical systems is governed by typically polynomial differential equations that may contain nonlinear terms and/or embedded feedback loops. Thus the dynamics of such systems may exhibit features associated with nonlinear dynamical systems, including (among others): temporal oscillations, excitability, multistability, reaction-diffusion-driven formation of spatial patterns, and deterministic chaos. These behaviors are exhibited in the concentrations of intermediate chemical species. Bifurcations occur between particular dynamic behaviors as system parameters are varied. The governing differential equations of reacting chemical systems have as variables the concentrations of all chemical species involved, as well as controllable parameters, including temperature, the initial concentrations of all chemical species, and fixed reaction-rate constants. A discussion is presented of the kinetics of chemical reactions as well as some thermodynamic considerations important to the appearance of temporal oscillations and other nonlinear dynamic behaviors, e.g., deterministic chaos. The behavior, chemical details, and mechanism of the oscillatory Belousov–Zhabotinsky Reaction (BZR) are described. Furthermore, experimental and mathematical evidence is presented that the BZR does indeed exhibit deterministic chaos when run in a flow reactor. The origin of this chaos seems to be in toroidal dynamics in which flow-driven oscillations in the control species bromomalonic acid couple with the BZR limit cycle.

An 80-reaction, 26-species mechanistic model of the oscillatory Beloubov-Zhabotinbky (BZ) reaction recently introduced by Gyorgyi, Turanyi and Field (GTF model) is analyzed in this work. Major reaction interactions within the large mechanism are revealed, and by reaction rate sensitivity analysis redundant specie and reactions are identified. Removal of these results in a 42-reaction, 22-species mechanism that quantitatively agrees with the original model in three test simulations

Health psychology has studied the cross-sectional, stationary relationships linking stress, social support, and health. Levels of stress-related illness are generally modeled by including a nonlinear multiplicative or 'buffering' effect, corresponding to the interaction of stressor levels with social support from family and friends. The motivation of the present research is to extend an iterative, dynamic model of this well-investigated psychological process using a dynamical systems model expressed as a set of continuous, nonlinear differential equations similar to those of the 'Oregonator,' a model of a nonlinear dynamic chemical system. This model of the behavior of an individual is amenable to numerical investigation of its stationary-state stability properties, temporal evolution, and cause-effect relationships. The continuous variables in this new approach refer to varying states of an individual; they are Perceived stress (X), Symptoms (Y), and Social support (Z). It is expected that poor health in this model, represented by Symptoms (Y), is directly related to Perceived stress, as well as being tied in more complicated ways to Social support. A number of such models may be envisioned, some including a multiplicative, 'buffering' (- X x Z) effect of social support dependent on stress levels. We explore the behavior of this model over ranges of parameter values and initial conditions and relate these results to how an individual reacts to environmental challenges at various levels of stressors and social-support recruitment. Data generated by the model are in turn analyzed with a traditional cross-sectional statistical technique. Similarities and differences between chemical and psychological systems are discussed.

The fifth step of the Oregonator is modified to reflect more accurately the organic chemistry of the ferroin-catalyzed Belousov-Zhabotinsky reaction. This treatment leads to a model that supports much more robust spatial concentration patterns than does the unmodified Oregonator. Two-dimensional patterns are found numerically in solutions of the reaction-diffusion equations describing this new model. Reflective boundary conditions are examined in one and two dimensions. The two-dimensional solutions in a square reactor are related to one-dimensional solutions in wavelength and amplitude

The effect of imperfect mixing on bistability in the BrO 3 - -Ce(III)-Br - reaction (minimal BrO 3 - oscillator) in a continuous-flow stirred tank reactor (CSTR) is investigated as a function of flow rate using a phenomenological model of micromixing. There is a sift to higher flowrates and a broadening of the bistable region when mixing is less effficient, just as is found in experiments with nonpremixed feed streams

The reaction of BrO 3 - with SCN - in dilute HClO 4 is investigated in both batch and flow reactor modes. The stoichiometry of the reaction is BrO 3 - +SCN - +H 2 O→HSO 4 +HCN+Br - when SCN - is in excess and 7BrO 3 - +5SCN - +2H + →5BrCN+Br 2 +5SO 4 2+ +H 2 O when BrO 3 - is in excess

Past experiments and simulations on the Belousov-Zhabotinsky (BZ) reaction clearly demonstrated the existence of chaos in stirred flow reactors at low flow rates. However, the existence of chaos at high flow rates has remained the subject of controversy. The controversy is resolved by the present experiments at high flow rates, which accurately reproduce the complex sequence of periodic, complex periodic, and chaotic states observed by Hudson and co-workers (Hudson et al., 1979; Hudson and Mankin, 1981); the flow rates observed here for the different dynamical regimes agree with those of Hudson et al. within a few percent. This striking reproducibility of the complex periodic and chaotic dynamics is found to be insensitive to stirring rate, size of the reactor, purity of the reagents, temperature, and type of pumping (peristaltic or piston pumps, premixed or nonpremixed feeds). Moreover, the observed sequence is reproduced qualitatively by a four-variable model of the BZ reaction. Thus, this work provides definitive evidence for the existence of deterministic chaos in the BZ reaction at high flow rates. We conclude that past descriptions of aperiodic behavior at high flow rates in terms of various stochastic mechanisms, including incomplete mixing or switching between adjacent periodic states, are inappropriate for the conditions of the Hudson's experiments.

The evolution of concentration patterns from a local disturbance of an unstirred, homogeneously oscillating, chemical system subject to reaction and diffusion is investigated. A new pulse of concentration forms after each homogeneous oscillation until eventually the entire domain is filled. The theory of travelling fronts is used to develop a treatment which is useful in understanding the evolution of these patterns whenever the nullclines of the chemical dynamics have a certain, quite common form. The concepts developed are used to interpret the results of numerical simulation of the behavior of a modified Oregonator model of the Belousov-Zhabotinsky reaction.

We report a detailed numerical investigation of the relative abundance of periodic and chaotic oscillations in phase diagrams for the Belousov–Zhabotinsky (BZ) reaction as described by a nonpolynomial, autonomous, three-variable model suggested by Györgyi and Field [Nature (London) 355, 808 (1992)]. The model contains 14 parameters that may be tuned to produce rich dynamical scenarios. By computing the Lyapunov spectra, we find the structuring of periodic and chaotic phases of the BZ reaction to display unusual global patterns, very distinct from those recently found for gas and semiconductor lasers, for electric circuits, and for a few other familiar nonlinear oscillators. The unusual patterns found for the BZ reaction are surprisingly robust and independent of the parameter explored.

Oscillations may be observed in the concentrations of the colored form of methylene blue (MB + ) and oxygen during the methylene blue catalyzed oxidation of HS − by O 2 in a continuous-flow stirred tank reactor (CSTR). Oscillations have not been observed in a closed reactor. The major reactive intermediates are MB*, HS*, H 2 O 2 , and O 2 − . A mechanism for this chemical oscillator proposed by Resch, Field, Schneider, and Burger has been simplified from 14 chemical reactions involving seven variables to eight chemical reactions involving five variables. This simplification allows the dynamic structure of the mechanism to be understood. In contrast with all but one other proposed oscillatory mechanism in completely homogeneous solution, this mechanism does not involve autocatalysis, although it does contain nonlinearities

The reactions constituting the mechanism of the oscillatory Belousov-Zhabotinskii (BZ) reaction may be divided into an inorganic and an organic subset. The former is well established and generally accepted, but the latter remains under development. There has been considerable work on component reactions of the organic subset over the past few years, but little effort has been made to incorporate the results of this work into an improved BZ mechanism

A mechanism is discussed which reproduces in simulations the oscillations during the methylene-blue catalyzed reduction of O2 by HS− in a continuous-flow, strirred tank reactor (CSTR). It contains 14 reactions and is based on experiments and simulations of simpler reactions including the reduction of MB+ by HS− in the absence and presence of O2 and the reactions of H2O2 and O2 with HS−. All experiments on component reactions as well as the CSTR oscillations can be simulated by the same set of reactions and rate constants. The major dynamic feature of the mechanism is the competition for MB. by the oxidizing agents O2 and H2O2 and the reducing agents HS− and HS.. The species MB. is the radical intermediate between the colored (MB+) and colorless (MBH) forms of methylene blue.

The Noyes-Field-Thompson (NFT) mechanism of the oxidation of Ce(III) by BrO 3 − in ∼1 M H 2 SO 4 is an important part of the Field-Koros-Noyes (FKN) mechanism of the oscillatory Belousov-Zhabotinskii reaction. The details of the oxidation of Ce(III) by BrO 3 − and the NFT mechanism can be studied in isolation by using its complex behavior in a continuous-flow stirred tank reactor (CSTR). Both bistability and oscillations are observed in this system, which in a CSTR is referred to as the minimal BrO 3 − oscillator

In the last few years many new reaction routes and intermediates have been discovered in the mechanism of the Belousov-Zhabotinsky (BZ) reaction with the aid of high performance liquid chromatography (HPLC). These previous HPLC studies, however, were limited to the Ce(4+)-organic substrate (malonic or bromomalonic acid) systems only. Very recently some measurements were made on a cerium catalysed full BZ system but only in its induction period. The present work follows the evolution of the main chemical components in a cerium and in a ferroin catalysed full BZ system from the start until the end of the oscillatory regime in a batch reactor. While recording the potential oscillations of a bromide selective electrode we measured from time to time the concentration of the following components: malonic and bromomalonic acids and bromate as main components; malonyl malonate, ethanetetracarboxylic and bromoethenetricarboxylic acids which are recombination products of organic free radicals; oxidized intermediates: tartronic, oxalic (OA) and mesoxalic (MOA) acids, and brominated products: dibromoacetic and tribromoacetic acids. Recombination products are generated in the intervals when the autocatalytic reaction is "switched off". In the course of the autocatalytic periods, however, the organic radicals react with the inorganic bromine dioxide radical mainly which leads to the formation of MOA and OA. Due to a very fast Ce(4+)-MOA reaction, MOA can be detected in the ferroin catalysed BZ system only. Our model calculations deal exclusively with the cerium catalysed system. The suggested new Marburg-Budapest-Missoula (MBM) model includes both negative feedback loops (bromous acid-bromide ion Oregonator type and bromine dioxide-organic free radicals Radicalator type feedback) and the recently discovered radical-radical recombination reactions. Comparison of the experimental data with the model calculations shows a good qualitative agreement but some open problems still remain. To overcome these problems oxygen atom transfer and other redox reactions are proposed.