Oblique collisions of internal wave beams and associated resonances

2012 ◽  
Vol 711 ◽  
pp. 337-363 ◽  
Author(s):  
T. R. Akylas ◽  
H. H. Karimi
Keyword(s):  
Steady State ◽  
Internal Gravity Wave ◽  
Nonlinear Interactions ◽  
Resonant Response ◽  
Initial Value ◽  
Oblique Collision ◽  
The Difference ◽  
Forced Waves ◽  
Radiation Conditions ◽  
Steady State Amplitude

AbstractQuadratic nonlinear interactions between two colliding internal gravity wave beams in a uniformly stratified fluid, and the resulting radiation of secondary beams with frequencies equal to the sum and difference of those of the primary beams, are discussed. The analysis centres on oblique collisions, involving beams that propagate in different vertical planes. The propagation directions of generated secondary beams are deduced from kinematic considerations and the use of radiation conditions, thus extending to oblique collisions previously derived selection rules for plane collisions. Using small-amplitude expansions, radiated-beam profiles at steady state are also computed in terms of the characteristics of the colliding beams. It is pointed out that, for certain oblique collision configurations, radiated beams with frequency equal to the difference of the primary frequencies have unbounded steady-state amplitude. This resonance, which has no counterpart for plane collisions, is further analysed via the solution of an initial-value problem; ignoring dissipation, the transient resonant response grows in time like ${t}^{1/ 2} $, a behaviour akin to that of forced waves at cut-off frequencies.

Forsterite dissolution in superheated basaltic, andesitic and rhyolitic melts

1990 ◽  
Vol 54 (374) ◽  
pp. 67-74 ◽  
Author(s):  
C. H. Donaldson
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Dissolution Rate ◽  
Atmospheric Pressure ◽  
Initial Value ◽  
Steady State Condition ◽  
Rate Of Dissolution ◽  
Constant Rate ◽  
The Difference ◽  
Initial Dissolution Rate

AbstractDissolution rates of small forsterite spheres in superheated melts of basalt, andesite and rhyolite composition have been measured at 1300°C, atmospheric pressure. The rate is constant (83 µm hr−1) in the basalt, regardless of run duration. In the andesite the initial dissolution rate is 200µm hr−1, followed by a decrease to a constant value of 16µmhr−1 in 2–3 hours. Dissolution rate in the rhyolite decreases from an initial value of 1.7 to <0.1 µmhr−1 over 280 hours and never reaches a constant rate. Once the rate of dissolution has become constant, the film of contaminated melt that forms in melt about a crystal does not thicken with time, indicating attainment of a steady-state condition. Steady state is attributed to natural convection arising from the difference in density between the film of contaminated melt surrounding a crystal and that beyond. The density difference is approximately 2% of the density of the rock melt.

scholarly journals Effects of Genotypes and Treatment on Oxygenscan Parameters in Sickle Cell Disease

Cells ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 811
Author(s):  
Camille Boisson ◽  
Minke A. E. Rab ◽  
Elie Nader ◽  
Céline Renoux ◽  
Celeste Kanne ◽  
...  
Keyword(s):  
Steady State ◽  
Sickle Cell Disease ◽  
Blood Cell ◽  
Sickle Cell ◽  
Red Blood Cell ◽  
Cell Disease ◽  
Oxygen Gradient ◽  
Acute Complication ◽  
Adults And Children ◽  
The Difference

(1) Background: The aim of the present study was to compare oxygen gradient ektacytometry parameters between sickle cell patients of different genotypes (SS, SC, and S/β+) or under different treatments (hydroxyurea or chronic red blood cell exchange). (2) Methods: Oxygen gradient ektacytometry was performed in 167 adults and children at steady state. In addition, five SS patients had oxygenscan measurements at steady state and during an acute complication requiring hospitalization. (3) Results: Red blood cell (RBC) deformability upon deoxygenation (EImin) and in normoxia (EImax) was increased, and the susceptibility of RBC to sickle upon deoxygenation was decreased in SC patients when compared to untreated SS patients older than 5 years old. SS patients under chronic red blood cell exchange had higher EImin and EImax and lower susceptibility of RBC to sickle upon deoxygenation compared to untreated SS patients, SS patients younger than 5 years old, and hydroxyurea-treated SS and SC patients. The susceptibility of RBC to sickle upon deoxygenation was increased in the five SS patients during acute complication compared to steady state, although the difference between steady state and acute complication was variable from one patient to another. (4) Conclusions: The present study demonstrates that oxygen gradient ektacytometry parameters are affected by sickle cell disease (SCD) genotype and treatment.

On the steady-state solution of the M/G/2 queue

1979 ◽  
Vol 11 (01) ◽  
pp. 240-255 ◽  
Author(s):  
Per Hokstad
Keyword(s):  
Steady State ◽  
General Solution ◽  
Laplace Transform ◽  
Queue Length ◽  
Joint Distribution ◽  
Length Distribution ◽  
Steady State Solution ◽  
Queue Length Distribution ◽  
The Difference ◽  
Number Of Customers

The asymptotic behaviour of the M/G/2 queue is studied. The difference-differential equations for the joint distribution of the number of customers present and of the remaining holding times for services in progress were obtained in Hokstad (1978a) (for M/G/m). In the present paper it is found that the general solution of these equations involves an arbitrary function. In order to decide which of the possible solutions is the answer to the queueing problem one has to consider the singularities of the Laplace transforms involved. When the service time has a rational Laplace transform, a method of obtaining the queue length distribution is outlined. For a couple of examples the explicit form of the generating function of the queue length is obtained.

scholarly journals Inflammatory mediators in sickle cell anaemia highlight the difference between steady state and crisis in paediatric patients

2017 ◽  
Vol 182 (6) ◽  
pp. 933-936 ◽  
Author(s):  
Magda O. S. Carvalho ◽  
Théo Araujo-Santos ◽  
João H. O. Reis ◽  
Larissa C. Rocha ◽  
Bruno A. V. Cerqueira ◽  
...  
Keyword(s):  
Steady State ◽  
Sickle Cell ◽  
Inflammatory Mediators ◽  
Sickle Cell Anaemia ◽  
Paediatric Patients ◽  
The Difference

scholarly journals THE ACCUMULATION OF ELECTROLYTES

1932 ◽  
Vol 15 (6) ◽  
pp. 667-689 ◽  
Author(s):  
W. J. V. Osterhout ◽  
W. M. Stanley
Keyword(s):  
Steady State ◽  
Osmotic Pressure ◽  
Aqueous Phase ◽  
Thermodynamic Potential ◽  
Ph Value ◽  
Molecular Form ◽  
External Solution ◽  
Aqueous Layer ◽  
The Difference ◽  
Pass Through

Inasmuch as attempts to explain accumulation by the Donnan principle have failed in the case of Valonia, a hypothesis of the steady state has been formulated to explain what occurs. In order to see whether this hypothesis is in harmony with physico-chemical laws attempts have been made to imitate its chief features by means of a model. The model consists of a non-aqueous layer (representing the protoplasmic surface) placed between an alkaline aqueous phase (representing the external solution) and a more acid aqueous phase (representing the cell sap). The model reproduces most of the features of the hypothesis. Attention may be called to the following points. 1. The semipermeable surface is a continuous non-aqueous phase. 2. Potassium penetrates by combining with an acid HX in the non-aqueous layer to form KX which in turn reacts with an acid HA in the sap to form KA. Since KX is little dissociated in the non-aqueous layer potassium appears to pass through it chiefly in molecular form. 3. The internal composition depends on permeability, e.g., sodium penetrates less rapidly than potassium and in consequence potassium predominates over sodium in the "artificial sap." The order of penetration in the model is the same as in Valonia, i.e., K &gt; Na &gt; Ca &gt; Mg, and Cl &gt; SO4, but the quantitative resemblance is not close, e.g., the difference between potassium and sodium, and chloride and sulfate is much less in the model. 4. The formation of KA and NaA in the sap raises its osmotic pressure and water enters. 5. The concentration of potassium and sodium and the osmotic pressure become much greater inside than outside. For example, potassium may become 200 times as concentrated inside as outside. 6. No equilibrium occurs but a steady state is reached in which water and salt enter at the same rate so that the composition of the sap remains constant as its volume increases. 7. Since no equilibrium occurs there is a difference of thermodynamic potential between inside and outside. At the start the thermodynamic potential of KOH is much greater outside than inside. This difference gradually diminishes and in the steady state has about the same value as in Valonia. The difference in pH value between the internal and external solutions is also similar in both cases (about 2 pH units). 8. Accumulation does not depend on the presence of molecules or ions inside which are unable to pass out. One important feature of the hypothesis is not seen in the model: this is the exchange of HCO3 for Cl-. Experiments on this point are in progress.

Mitochondrial function in the presence of myoglobin

1982 ◽  
Vol 53 (5) ◽  
pp. 1116-1124 ◽  
Author(s):  
R. P. Cole ◽  
P. C. Sukanek ◽  
J. B. Wittenberg ◽  
B. A. Wittenberg
Keyword(s):  
Oxygen Consumption ◽  
Steady State ◽  
Liquid Phase ◽  
Gas Phase ◽  
Oxygen Pressure ◽  
Oxygen Electrode ◽  
Oxygen Binding ◽  
Atp Production ◽  
Skeletal Muscle Mitochondria ◽  
The Difference

The effect of myoglobin on oxygen consumption and ATP production by isolated rat skeletal muscle mitochondria was studied under steady-state conditions of oxygen supply. A method is presented for the determination of steady-state oxygen consumption in the presence of oxygen-binding proteins. Oxygen consumed in suspensions of mitochondria was replenished continuously by transfer from a flowing gas phase. Liquid-phase oxygen pressure was measured with an oxygen electrode; the gas-phase oxygen concentration was held constant at a series of fixed values. Oxygen consumption was determined from the characteristic response time of the system and the difference in the steady-state gas- and liquid-phase oxygen concentrations. ATP production was determined from the generation of glucose 6-phosphate in the presence of hexokinase. During steady-state mitochondrial oxygen consumption, the oxygen pressure in the liquid phase is enhanced when myoglobin is present. Functional myoglobin present in the solution had no effect on the relation of mitochondrial respiration and ATP production to liquid-phase oxygen pressure. Myoglobin functions in this system to enhance the flux of oxygen into the myoglobin-containing phase. Myoglobin may function in a similar fashion in muscle by increasing oxygen flux into myocytes.

scholarly journals A Study on the Effects of Model Structure and Demand Allocation on Water Network Modeling

2020 ◽  
Vol 42 (3) ◽  
pp. 110-120
Author(s):  
Seonghan Kim ◽  
Kwansue Jung ◽  
Sukmin Yoon ◽  
No-Suk Park
Keyword(s):  
Steady State ◽  
Network Modeling ◽  
Extended Period ◽  
Model Structure ◽  
Water Network ◽  
Detailed Model ◽  
Water Head ◽  
Models Comparison ◽  
The Difference ◽  
Steady State Simulation

Objectives:In order to reduce the uncertainty of the pipe network modeling, the model structure was basically included all distribution pipes and several models were proposed according to the location of the water meters.Methods:For models verification, first, a steady state simulation of each model was made by constructing a model including all water supply pipes (All-meters Model), which are the bases of 3 simplified models, and considering the location of all water meters. The network analysis was performed by dividing into the steady state and the extended period simulation.Results and Discussion:From the results of models comparison, ‘All-meters Model’ and ‘All-connections Model’ were found to obtain more accurate results for constructing a water network model for simulation of water quality events in distribution network. When constructing an ‘All-meters Model’ in all networks, the model becomes complicated and data management does difficult. Therefore this study suggests a hybrid model construction.Conclusions:It would be reasonable to construct a detailed model (All-meters or All-connections Model) in looped network in which the water flow path can be changed according to the difference of water head, and a skeletonized model (Street-meters aggregation or Reduced-meters Model) for a branch network that does not have a significant impact on demand allocations.

scholarly journals Calcium Exchange and Contraction Strength of Guinea Pig Atrium in Normal and Hypertonic Media

1969 ◽  
Vol 54 (4) ◽  
pp. 494-511 ◽  
Author(s):  
Gerald R. Little ◽  
William W. Sleator
Keyword(s):  
Steady State ◽  
Ion Exchange ◽  
Guinea Pig ◽  
Extracellular Space ◽  
Entry Rate ◽  
Steady State Condition ◽  
Peak Tension ◽  
Guinea Pig Atrium ◽  
Calcium Exchange ◽  
The Difference

A Krebs-Henseleit (KH) medium made hypertonic by adding nonpermeant molecules substantially increased the isometric peak tension at steady-state contractions below 3 per sec in guinea pig atrium at 27°C. Action potential durations were decreased. KH plus 100 mM raffinose or sucrose resulted in similar and nearly maximal changes which were essentially reversible upon return to normal KH. When one active contracting atrium was used to passively stretch a second atrium, the difference in Ca ion exchange (1 min exchange with the extracellular space) between active and stretched atria significantly increased at 1 per sec and at 2 per sec in going from normal to 100 mM hypertonic KH. The calculated mean Ca ion cellular exchange per beat per 100 g of cells (a) doubled in changing from normal to 100 mM hypertonic KH, and (b) decreased slightly in changing from contractions of 1 per sec to 2 per sec in normal KH. These data are consistent with the hypothesis (a) that Ca ion entry per beat from the extracellular space is proportional to membrane depolarized time with a constant medium and a steady-state condition, and the hypothesis (b) that 100 mM hypertonicity doubles the Ca ion entry rate during depolarization. These data enable rejection of the hypothesis that the peak tension is proportional to the Ca ion entry per beat from the extracellular space under steady-state conditions, and suggest that any additional Ca ion involved in the larger contractions at higher frequencies comes from an increase in Ca ion available from intracellular stores.

scholarly journals Ionized calcium concentrations in squid axons.

1976 ◽  
Vol 67 (4) ◽  
pp. 433-467 ◽  
Author(s):  
R Dipolo ◽  
J Requena ◽  
F J Brinley ◽  
L J Mullins ◽  
A Scarpa ◽  
...  
Keyword(s):  
Steady State ◽  
Light Emission ◽  
Mean Value ◽  
Ionized Calcium ◽  
Initial Value ◽  
Light Levels ◽  
Light Measurement ◽  
Ca 50 ◽  
Subsequent Introduction

Values for ionized [Ca] in squid axons were obtained by measuring the light emission from a 0.1-mul drop of aequorin confined to a plastic dialysis tube of 140-mum diameter located axially. Ionized Ca had a mean value of 20 x 10(-9) M as judged by the subsequent introduction of CaEGTA/EGTA buffer (ratio ca. 0.1) into the axoplasm, and light measurement on a second aequorin drop. Ionized Ca in axoplasma was also measured by introducing arsenazo dye into an axon by injection and measuring the Ca complex of such a dye by multichannel spectrophotometry. Values so obtained were ca. 50 x 10(-9) M as calibrated against CaEGTA/EGTA buffer mixtures. Wth a freshly isolated axon in 10 mM Ca seawater, the aequorin glow invariably increased with time; a seawater [Ca] of 2-3 mM allowed a steady state with respect to [Ca]. Replacement of Na+ in seawater with choline led to a large increase in light emission from aequorin. Li seawater partially reversed this change and the reintroduction of Na+ brought light levels back to their initial value. Stimulation at 60/s for 2-5 min produced an increase in aequorin glow about 0.1% of that represented by the known Ca influx, suggesting operationally the presence of substantial Ca buffering. Treatment of an axon with CN produced a very large increase in aequorin glow and in Ca arsenazo formation only if the external seawater contained Ca.

Moments of the Flow Variables, Part II : The Effective Conductivity

2003 ◽  
Author(s):  
Yoram Rubin
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Effective Conductivity ◽  
Effective Property ◽  
Flow Equation ◽  
Laplace’S Equation ◽  
Flow Conditions ◽  
Laplace's Equation ◽  
Head Gradient ◽  
The Difference

Many applications require primary information such as average fluxes as a prelude to more complex calculations. In water balance calculations one may be interested only in the average fluxes. For both cases the concept of effective conductivity is useful. The effective hydraulic conductivity is defined by where the angled brackets denote the expected value operator. The local flux fluctuation is defined by the difference qi(x) — (qi(x)). Its statistical properties as well as those of the velocity will be investigated in chapter 6. To qualify as an effective property in the strict physical sense, Kef must be a function of the aquifer’s material properties and not be influenced by flow conditions such as the head gradient and boundary conditions (Landauer, 1978). Our goal in this chapter is to explore the concept of the effective conductivity Kef and to relate it to the medium’s properties under as general conditions as possible. Additionally, we shall explore the conditions where this concept is irrelevant and applicable, the important issue being that Kef is defined in an ensemble sense, but for applications we need spatial averages. Several methods for deriving Kef will be described below. The general approach for defining Kef includes the following steps. First, H is defined as an SRF and is expressed with the aid of the flow equation in terms of the hydro-geological SRFs (conductivity, mostly) and the boundary conditions. The H SRF is then substituted in Darcy’s law and an expression in the form equivalent to (5.1) is sought. If and only if the coefficient in front of the mean head gradient is not a function of the flow conditions will it qualify as Kef. The derivation of the effective conductivity employs the flow equation. In steady-state incompressible flow, for example, Laplace’s equation is employed. Solutions derived under Laplace’s equation are applicable, under appropriate conditions, for other physical phenomena governed by the same mathematical model. For example, the electrical field in steady state is also described by Laplace’s equation.

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