Pivot–slide model of the motion of a curling rock

2016 ◽  
Vol 94 (12) ◽  
pp. 1305-1309 ◽  
Author(s):  
Mark R.A. Shegelski ◽  
Edward Lozowski
Keyword(s):  
Mathematical Model ◽  
Weak Dependence ◽  
Physical Processes ◽  
Physical Mechanisms ◽  
Model Predictions

We present the framework of a new mathematical model to account for the curl of a curling rock. The model is based upon two physical processes: a brief pivot of the rock around a point directly beneath the contact annulus, followed by a longer slide. The model predictions agree with observed curl distances on pebbled ice. The model also gives a weak dependence of the curl distance on the rate of rotation of the rock, in agreement with observations. We suggest possible physical mechanisms to initiate these two processes.

Modeling the Conditions for Microdroplets Formation and their Detachment from the Molten Metal on the Electrode

2021 ◽  
Vol 313 ◽  
pp. 1-7
Author(s):  
V.D. Sarychev ◽  
S.A. Solodsky ◽  
Sergey A. Nevskii ◽  
M.A. Kuznetsov ◽  
D.P. Ilyaschenko ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Molten Metal ◽  
High Frequency ◽  
Plasma Discharge ◽  
Pulse Action ◽  
Materials Processing ◽  
Physical Processes ◽  
Micro Scale ◽  
Physical Mechanisms ◽  
Frequency Pulse

Formation of nanostructure states on the surface of materials exposed to concentrated flows of energy is one of the relevant problems of modern materials processing. In the paper the authors describe the mechanism of the micro-scale droplets formation based on the study and modeling of the physical processes and technological aspects of the interaction between the heterogenic plasma flows and the molten substance at the electrode tip. The authors show new physical mechanisms and criteria for micro-and nanoparticles origination, develop a physical-mathematical model of the interaction between the molten metal and the plasma discharge with imposed high-frequency pulse action.

Physical Mechanisms Responsible for Track Changes and Rainfall Distributions Associated with Tropical Cyclone Landfall

2017 ◽  
Author(s):  
Johnny C.L. Chan
Keyword(s):  
Surface Roughness ◽  
Tropical Cyclone ◽  
Land Surface ◽  
Disaster Preparedness ◽  
Physical Processes ◽  
Physical Mechanisms ◽  
Model Predictions ◽  
Forecast Models ◽  
Landfall Location ◽  
Tropical Cyclone Landfall

As a tropical cyclone approaches land, its interaction with the characteristics of the land (surface roughness, topography, moisture availability, etc.) will lead to changes in its track as well as the rainfall and wind distributions near its landfall location. Accurate predictions of such changes are important in issuing warnings and disaster preparedness. In this chapter, the basic physical mechanisms that cause changes in the track and rainfall distributions when a tropical cyclone is about to make landfall are presented. These mechanisms are derived based on studies from both observations and idealized simulations. While the latter are relatively simple, they can isolate the fundamental and underlying physical processes that are inherent when an interaction between the land and the tropical cyclone circulation takes place. These processes are important in assessing the performance of the forecast models, and hence could help improve the model predictions and subsequently disaster preparedness.

Physical Mechanisms Responsible for Track Changes and Rainfall Distributions Associated with Tropical Cyclone Landfall

2017 ◽  
Author(s):  
Johnny C.L. Chan
Keyword(s):  
Surface Roughness ◽  
Tropical Cyclone ◽  
Land Surface ◽  
Disaster Preparedness ◽  
Physical Processes ◽  
Physical Mechanisms ◽  
Model Predictions ◽  
Forecast Models ◽  
Landfall Location ◽  
Tropical Cyclone Landfall

As a tropical cyclone approaches land, its interaction with the characteristics of the land (surface roughness, topography, moisture availability, etc.) will lead to changes in its track as well as the rainfall and wind distributions near its landfall location. Accurate predictions of such changes are important in issuing warnings and disaster preparedness. In this chapter, the basic physical mechanisms that cause changes in the track and rainfall distributions when a tropical cyclone is about to make landfall are presented. These mechanisms are derived based on studies from both observations and idealized simulations. While the latter are relatively simple, they can isolate the fundamental and underlying physical processes that are inherent when an interaction between the land and the tropical cyclone circulation takes place. These processes are important in assessing the performance of the forecast models, and hence could help improve the model predictions and subsequently disaster preparedness.

CH4 Direct Reduction of In-Flight Fe3O4 Concentrate Particles

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Bahador Abolpour ◽  
M. Mehdi Afsahi ◽  
Ataallah Soltani Goharrizi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Fine Particles ◽  
Direct Reduction ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Dynamic Motion ◽  
Magnetite Ore ◽  
Model Predictions ◽  
Kinetics Of

Abstract In this study, reduction of in-flight fine particles of magnetite ore concentrate by methane at a constant heat flux has been investigated both experimentally and numerically. A 3D turbulent mathematical model was developed to simulate the dynamic motion of these particles in a methane content reactor and experiments were conducted to evaluate the model. The kinetics of the reaction were obtained using an optimizing method as: [-Ln(1-X)]1/2.91 = 1.02 × 10−2dP−2.07CCH40.16exp(−1.78 × 105/RT)t. The model predictions were compared with the experimental data and the data had an excellent agreement.

A mathematical model of rat collecting duct II. Effect of buffer delivery on urinary acidification

2002 ◽  
Vol 283 (6) ◽  
pp. F1252-F1266 ◽  
Author(s):  
Alan M. Weinstein
Keyword(s):  
Mathematical Model ◽  
Carbonic Anhydrase ◽  
Collecting Duct ◽  
Phosphate Concentration ◽  
Rate Coefficients ◽  
Urinary Flow ◽  
Urinary Acidification ◽  
Model Predictions ◽  
Disequilibrium Ph ◽  
Urinary Acid

A mathematical model of the rat collecting duct (CD) is used to examine the effect of delivered load of bicarbonate and nonbicarbonate buffer on urinary acidification. Increasing the delivered load of HCO[Formula: see text] produces bicarbonaturia, and, with luminal carbonic anhydrase absent, induces a disequilibrium luminal pH and a postequilibration increase in urinary Pco 2. At baseline flows, this disequilibrium disappears when luminal carbonic anhydrase rate coefficients reach 1% of full catalysis. The magnitude of the equilibration Pco 2 depends on the product of urinary acid phosphate concentration and the disequilibrium pH. Thus, although increasing phosphate delivery to the CD decreases the disequilibrium pH, the increase in urinary phosphate concentration yields an overall increase in postequilibration Pco 2. In simulations of experimental HCO[Formula: see text] loading in the rat, model predictions of urinary Pco 2 exceed the measured Pco 2 of bladder urine. In part, the higher model predictions for urinary Pco 2 may reflect higher urinary flow rates and lower urinary phosphate concentrations in the experimental preparations. However, when simulation of CD function during HCO[Formula: see text] loading acknowledges the high ambient renal medullary Pco 2 (5), the predicted urinary Pco 2 of the model CD is yet that much greater. This discrepancy cannot be resolved within the model but requires additional experimental data, namely, concomitant determination of urinary buffer concentrations within the tubule fluid sampled for Pco 2 and pH. This model should provide a means for simulating formal testing of urinary acidification and thus for examining hypotheses regarding transport defects underlying distal renal tubular acidosis.

scholarly journals Modelling Macrophage Infiltration into Avascular Tumours

2002 ◽  
Vol 4 (1) ◽  
pp. 21-38 ◽  
Author(s):  
C. E. Kelly ◽  
R. D. Leek ◽  
H. M. Byrne ◽  
S. M. Cox ◽  
A. L. Harris ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Spatial Structure ◽  
Random Motion ◽  
Numerical Results ◽  
Macrophage Infiltration ◽  
Numerical Techniques ◽  
Model Predictions ◽  
Independent Experimental Data

In this paper a mathematical model that describes macrophage infiltration into avascular tumours is presented. The qualitative accuracy of the model is assessed by comparing numerical results with independent experimental data that describe the infiltration of macrophages into two types of spheroids: chemoattractant-producing (hepa-1) and chemoattractant-deficient (or C4) spheroids. A combination of analytical and numerical techniques are used to show how the infiltration pattern depends on the motility mechanisms involved (i.e. random motion and chemotaxis) and to explain the observed differences in macrophage infiltration into the hepa-1 and C4 spheroids. Model predictions are generated to show how the spheroid's size and spatial structure and the ability of its constituent cells influence macrophage infiltration. For example, chemoattractant-producing spheroids are shown to recruit larger numbers of macrophages than chemoattractant-deficient spheroids of the same size and spatial structure. The biological implications of these results are also discussed briefly.

scholarly journals Mathematical model and simulations of MERS outbreak: Predictions and implications for control measures

BIOMATH ◽  
2017 ◽  
Vol 5 (2) ◽  
pp. 1612141 ◽  
Author(s):  
Nofe Al-Asuoad ◽  
Libin Rong ◽  
Sadoof Alaswad ◽  
Meir Shillor
Keyword(s):  
Mathematical Model ◽  
Middle East ◽  
Coupled System ◽  
Control Measures ◽  
Nonlinear Ordinary Differential Equations ◽  
Contact Rate ◽  
Isolation Rate ◽  
Model Predictions ◽  
The World ◽  
The City

The Middle East Respiratory Syndrome (MERS) has been identified in 2012 and since then outbreaks have been reported in various localities in the Middle East and in other parts of the world. To help predict the possible dynamics of MERS, as well as ways to contain it, this paper develops a mathematical model for the disease. It has a compartmental structure similar to SARS models and is in the form of a coupled system of nonlinear ordinary differential equations (ODEs). The model predictions are fitted to data from the outbreaks in Riyadh (Saudi Arabia) during 2013-2016. The results reveal that MERS will eventually be contained in the city. However, the containment time and the severity of the outbreaks depend crucially on the contact coefficients and the isolation rate constant. When randomness is added to the model coefficients, the simulations show that the model is sensitive to the scaled contact rate among people and to the isolation rate. The model is analyzed using stability theory for ODEs and indicates that when using only isolation, the endemic steady state is locally stable and attracting. Numerical simulations with parameters estimated from the city of Riyadh illustrate the analytical results and the model behavior, which may have important implications for the disease containment in the city. Indeed, the model highlights the importance of isolation of infected individuals and may be used to assess other control measures. The model is general and may be used to analyze outbreaks in other parts of the Middle East and other areas.

scholarly journals A MODEL FOR BREACH GROWTH IN A DIKE-BURST

1988 ◽  
Vol 1 (21) ◽  
pp. 140 ◽  
Author(s):  
Paul J. Visser
Keyword(s):  
Mathematical Model ◽  
The Netherlands ◽  
Laboratory Experiments ◽  
Suspended Load ◽  
Experimental Results ◽  
Sand Transport ◽  
Model Predictions ◽  
Pumped Storage

A mathematical model for sand-dike breach erosion is presented. The heart of the model is a modified Bagnold (1963) energetics—based sand transport conception combined with a simplified Galappatti and Vreugdenhil (1985) pick up mechanism for the suspended load. The model has been tested to three laboratory experiments. The agreement between model predictions and experimental results is surprisingly good. Prototype calculations are presented for the 73 m high sand—dike of a proposed pumped—storage plant in the Netherlands.

Pretreatment of Textile Industry Wastewaters with Ozone

1994 ◽  
Vol 29 (9) ◽  
pp. 151-160 ◽  
Author(s):  
M. Tzitzi ◽  
D. V. Vayenas ◽  
G. Lyberatos
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Textile Industry ◽  
Batch Studies ◽  
Cod Reduction ◽  
Industrial Wastewaters ◽  
Model Predictions ◽  
Textile Wastewaters

Ozonation of textile industrial wastewaters was examined in CSTR and batch studies. Experiments were done for various types of textile wastewaters and for different reaction and retention times. Much better results were obtained using ozonation after the coagulation-precipitation stage. Also a mathematical model was developed, able to describe wastewater decolonization and COD reduction. In all cases the comparison between the model predictions and the experimental data was satisfactory.

scholarly journals The circumstellar discs of Be stars

2010 ◽  
Vol 6 (S272) ◽  
pp. 325-336 ◽  
Author(s):  
Alex C. Carciofi
Keyword(s):  
Angular Resolution ◽  
Central Star ◽  
High Angular Resolution ◽  
Be Stars ◽  
Keplerian Orbit ◽  
Physical Processes ◽  
Simple Description ◽  
Model Predictions ◽  
Mass Ejection ◽  
Very High

AbstractCircumstellar discs of Be stars are thought to be formed from material ejected from a fast-spinning central star. This material possesses large amounts of angular momentum and settles in a quasi-Keplerian orbit around the star. This simple description outlines the basic issues that a successful disc theory must address: 1) What is the mechanism responsible for the mass ejection? 2) What is the final configuration of the material? 3) How the disc grows? With the very high angular resolution that can be achieved with modern interferometers operating in the optical and infrared we can now resolve the photosphere and immediate vicinity of nearby Be stars. Those observations are able to provide very stringent tests for our ideas about the physical processes operating in those objects. This paper discusses the basic hydrodynamics of viscous decretion discs around Be stars. The model predictions are quantitatively compared to observations, demonstrating that the viscous decretion scenario is currently the most viable theory to explain the discs around Be stars.

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