Numerical procedures in defining entropy solutions for conservation laws

 U okviru ove doktorske disertacije posmatrani su zakoni održanja sa funkcijom fluksa koja ima prekid u x = 0, pri čemu delovi fluksa levo i desno od x = 0 imaju smo po jedan ekstrem. U prvoj glavi se može naći pregled osnovnih pojmova, definicija i teorema. U drugoj  glavi su opisani hiperbolični sistemi zakona održanja, slaba rešenja, kao  i numerički postupci za njihovo rešavanje. U trećoj glavi su predstavljeni  diskretni profili darnih talasa. U četvrtoj glavi su opisani zakoni održanja  sa prekidnom funkcijom fluksa i ukratko su predstvaljeni rezultati drugih autora iz ove oblasti. U petoj glavi je najpre analizirana tzv. jednačina sa dva fluksa u slučaju kada oba dela fluksa levo i desno od  x = 0 imaju minimum, a pri tome se seku u najviše jednoj tačci unutar intervala. Primenom regularizacije na intervalu [−ε, ε], za ε > 0 dovoljno malo, dokazano je postojanje diskretnih udarnih profila za postupak Godunova za zakone održanja sa promenljivom funkcijom fluksa. Definisan je i odgovarajući diskretan uslov entropije, a postojanje entropijskog diskretnog  udarnog profila je postavljen kao kriterijum za dopustivost udarnih talasa. Potom je analizirana ista jednačina u slucaju kada deo fluksa levo  od x = 0 ima maksimum, a deo fluksa desno od x = 0 minimum, dok se oba dela fluksa seku na  krajevima posmatranog intervala. U ovom slučaju, uopšten je uslov entropije. U okviru ove glave je prikazano nekoliko numeričkih primera za oba opisana slučaja. Numerički rezultati  su dobijeni korišcenjem softvera razvijenog za potrebe ove teze u pro gramskom paketu Mathematica.We consider conservation laws with a flux discontinuity at x = 0, where the flux parts from both left and right hand side of x = 0 have at most one extreme on the  observed  domain. The first chapter provides elementary definitions and theorems..The second chapter refers to hyperbolic systems of conservation laws, their solutions, and  numerical procedures. The third chapter is devoted to discrete  shock profiles. The fourth chapter describes conservation laws with discontinuous flux functions and provides basic information upon known results in this field. In the  fifth chapter, we first  analyse the two-flux equation when both flux parts have a minimum and cross at most    at one point in the interior of the domain. Using a flux regularization on the interval [−ε,   ε], for ε > 0 small enough, we show the existence of discrete shock profiles for Godunov’s scheme for conservation laws with discontinuous flux functions. We also define a discrete entropy condition accordingly, and use the existence of an entropy discrete shock profile as an entropy criterion for shocks. Then we analyse the same problem in the case when the flux part on the left of x = 0 has a maximum and the part on the right of x = 0 has a minimum, whereas the fluxes cross at the edges of the interval. We derive a more general discrete entropy condition in this case. We provide several numerical examples in both of the above mentioned flux cases. All the  presented numerical results are obtained using a program written in Mathematica. Finally, in chapter six, we prove the existence of  singular shock waves in the case when the graph of one of the flux parts is above the graph of the other one on the entire domain. For that purpose, we use the shadow wave technique. At the end of this chapter, we provide a numerical verification of the obtained singular solution

Numerical verification of delta shock waves for pressureless gas dynamics

AbstractThe subject of this paper is theoretical analysis and numerical verification of delta shock wave existence for pressureless gas dynamic system. The existence of overcompressive delta shock wave solution in the framework of Colombeau generalized functions is proved. This result is verified numerically by specially designed procedure that is based on wave propagation method implemented in CLAWPACK. The method is coupled with dynamic refinement mesh. We also consider a strictly hyperbolic system obtained from the original one by perturbation and change of variables. The same numerical procedure is applied to the perturbed problem. The obtained numerical results in both cases confirm theoretical expectations

Numerical procedures in defining entropy solutions for conservation laws

 U okviru ove doktorske disertacije posmatrani su zakoni održanja sa funkcijom fluksa koja ima prekid u x = 0, pri čemu delovi fluksa levo i desno od x = 0 imaju smo po jedan ekstrem. U prvoj glavi se može naći pregled osnovnih pojmova, definicija i teorema. U drugoj  glavi su opisani hiperbolični sistemi zakona održanja, slaba rešenja, kao  i numerički postupci za njihovo rešavanje. U trećoj glavi su predstavljeni  diskretni profili darnih talasa. U četvrtoj glavi su opisani zakoni održanja  sa prekidnom funkcijom fluksa i ukratko su predstvaljeni rezultati drugih autora iz ove oblasti. U petoj glavi je najpre analizirana tzv. jednačina sa dva fluksa u slučaju kada oba dela fluksa levo i desno od  x = 0 imaju minimum, a pri tome se seku u najviše jednoj tačci unutar intervala. Primenom regularizacije na intervalu [−ε, ε], za ε > 0 dovoljno malo, dokazano je postojanje diskretnih udarnih profila za postupak Godunova za zakone održanja sa promenljivom funkcijom fluksa. Definisan je i odgovarajući diskretan uslov entropije, a postojanje entropijskog diskretnog  udarnog profila je postavljen kao kriterijum za dopustivost udarnih talasa. Potom je analizirana ista jednačina u slucaju kada deo fluksa levo  od x = 0 ima maksimum, a deo fluksa desno od x = 0 minimum, dok se oba dela fluksa seku na  krajevima posmatranog intervala. U ovom slučaju, uopšten je uslov entropije. U okviru ove glave je prikazano nekoliko numeričkih primera za oba opisana slučaja. Numerički rezultati  su dobijeni korišcenjem softvera razvijenog za potrebe ove teze u pro gramskom paketu Mathematica.We consider conservation laws with a flux discontinuity at x = 0, where the flux parts from both left and right hand side of x = 0 have at most one extreme on the  observed  domain. The first chapter provides elementary definitions and theorems..The second chapter refers to hyperbolic systems of conservation laws, their solutions, and  numerical procedures. The third chapter is devoted to discrete  shock profiles. The fourth chapter describes conservation laws with discontinuous flux functions and provides basic information upon known results in this field. In the  fifth chapter, we first  analyse the two-flux equation when both flux parts have a minimum and cross at most    at one point in the interior of the domain. Using a flux regularization on the interval [−ε,   ε], for ε > 0 small enough, we show the existence of discrete shock profiles for Godunov’s scheme for conservation laws with discontinuous flux functions. We also define a discrete entropy condition accordingly, and use the existence of an entropy discrete shock profile as an entropy criterion for shocks. Then we analyse the same problem in the case when the flux part on the left of x = 0 has a maximum and the part on the right of x = 0 has a minimum, whereas the fluxes cross at the edges of the interval. We derive a more general discrete entropy condition in this case. We provide several numerical examples in both of the above mentioned flux cases. All the  presented numerical results are obtained using a program written in Mathematica. Finally, in chapter six, we prove the existence of  singular shock waves in the case when the graph of one of the flux parts is above the graph of the other one on the entire domain. For that purpose, we use the shadow wave technique. At the end of this chapter, we provide a numerical verification of the obtained singular solution

Production and application of bioactive proteins and peptides from whey

Bioaktivni peptidi predstavljaju granu naučne oblasti koja se veoma brzo razvija. Tokom istraživanja proteina uočeno je da neki proteini nakon digestije ispoljavaju bioaktivnosti koje ne poseduju u svojoj nativnoj formi. To je bio podsticaj za istraživanje uticaja enzimske hidrolize na bioaktivnost proteina. Trenutni naučni stav je da svaki protein može posedovati fragmente koji ispoljavaju neku od mnogih bioaktivnosti. Bioaktivni peptidi dobijeni enzimskom hidrolizom surutke ispoljili su mnoge pozitivne efekte na ljudsko zdravlje...Bioactive peptides are a rapidly developing field of research. During the research it was observed that some peptides which do not show a particular bioactivity become bioactive after ingestion and passing through the gastrointestinal system. That was the stimulus for the development of research on the effect of enzymatic hydrolysis of the bioactive properties of proteins. According to the current state of scientific knowledge, every protein can contain fragments that possess some of many bioactivities. Bioactive peptides, derived by enzymatic hydrolysis of whey protein, have demonstrated characteristics as health-promoting agents..

Indicators of sprawl in relation to residential preferencesv

Edited by Miodrag Vujošević and Slavka Zekovi

Urban Growth and Urbanization of Sofiа, Belgrade and Rome: the Interaction between Urban Planning and the Market

The paper explores the problems of sustainable and resilient development of the cities in Eastern and South-east Europe on the examples of Sofia, Belgrade and Rome and their urban regions. The research draws comparisons to the forms, patterns and mechanisms of their development.Editors: Atanas Kovachev, Aleksandar D Slaev, Diliana Daskalov

Proizvodnja i primena bioaktivnih proteina i peptida surutke

Bioactive peptides are a rapidly developing field of research. During the research it was observed that some peptides which do not show a particular bioactivity become bioactive after ingestion and passing through the gastrointestinal system. That was the stimulus for the development of research on the effect of enzymatic hydrolysis of the bioactive properties of proteins. According to the current state of scientific knowledge, every protein can contain fragments that possess some of many bioactivities. Bioactive peptides, derived by enzymatic hydrolysis of whey protein, have demonstrated characteristics as health-promoting agents...Bioaktivni peptidi predstavljaju granu naučne oblasti koja se veoma brzo razvija. Tokom istraživanja proteina uočeno je da neki proteini nakon digestije ispoljavaju bioaktivnosti koje ne poseduju u svojoj nativnoj formi. To je bio podsticaj za istraživanje uticaja enzimske hidrolize na bioaktivnost proteina. Trenutni naučni stav je da svaki protein može posedovati fragmente koji ispoljavaju neku od mnogih bioaktivnosti. Bioaktivni peptidi dobijeni enzimskom hidrolizom surutke ispoljili su mnoge pozitivne efekte na ljudsko zdravlje..

Numerical procedures in defining entropy solutions for conservation laws

 U okviru ove doktorske disertacije posmatrani su zakoni održanja sa funkcijom fluksa koja ima prekid u x = 0, pri čemu delovi fluksa levo i desno od x = 0 imaju smo po jedan ekstrem. U prvoj glavi se može naći pregled osnovnih pojmova, definicija i teorema. U drugoj  glavi su opisani hiperbolični sistemi zakona održanja, slaba rešenja, kao  i numerički postupci za njihovo rešavanje. U trećoj glavi su predstavljeni  diskretni profili darnih talasa. U četvrtoj glavi su opisani zakoni održanja  sa prekidnom funkcijom fluksa i ukratko su predstvaljeni rezultati drugih autora iz ove oblasti. U petoj glavi je najpre analizirana tzv. jednačina sa dva fluksa u slučaju kada oba dela fluksa levo i desno od  x = 0 imaju minimum, a pri tome se seku u najviše jednoj tačci unutar intervala. Primenom regularizacije na intervalu [−ε, ε], za ε > 0 dovoljno malo, dokazano je postojanje diskretnih udarnih profila za postupak Godunova za zakone održanja sa promenljivom funkcijom fluksa. Definisan je i odgovarajući diskretan uslov entropije, a postojanje entropijskog diskretnog  udarnog profila je postavljen kao kriterijum za dopustivost udarnih talasa. Potom je analizirana ista jednačina u slucaju kada deo fluksa levo  od x = 0 ima maksimum, a deo fluksa desno od x = 0 minimum, dok se oba dela fluksa seku na  krajevima posmatranog intervala. U ovom slučaju, uopšten je uslov entropije. U okviru ove glave je prikazano nekoliko numeričkih primera za oba opisana slučaja. Numerički rezultati  su dobijeni korišcenjem softvera razvijenog za potrebe ove teze u pro gramskom paketu Mathematica.We consider conservation laws with a flux discontinuity at x = 0, where the flux parts from both left and right hand side of x = 0 have at most one extreme on the  observed  domain. The first chapter provides elementary definitions and theorems..The second chapter refers to hyperbolic systems of conservation laws, their solutions, and  numerical procedures. The third chapter is devoted to discrete  shock profiles. The fourth chapter describes conservation laws with discontinuous flux functions and provides basic information upon known results in this field. In the  fifth chapter, we first  analyse the two-flux equation when both flux parts have a minimum and cross at most    at one point in the interior of the domain. Using a flux regularization on the interval [−ε,   ε], for ε > 0 small enough, we show the existence of discrete shock profiles for Godunov’s scheme for conservation laws with discontinuous flux functions. We also define a discrete entropy condition accordingly, and use the existence of an entropy discrete shock profile as an entropy criterion for shocks. Then we analyse the same problem in the case when the flux part on the left of x = 0 has a maximum and the part on the right of x = 0 has a minimum, whereas the fluxes cross at the edges of the interval. We derive a more general discrete entropy condition in this case. We provide several numerical examples in both of the above mentioned flux cases. All the  presented numerical results are obtained using a program written in Mathematica. Finally, in chapter six, we prove the existence of  singular shock waves in the case when the graph of one of the flux parts is above the graph of the other one on the entire domain. For that purpose, we use the shadow wave technique. At the end of this chapter, we provide a numerical verification of the obtained singular solution

Production and application of bioactive proteins and peptides from whey

Bioaktivni peptidi predstavljaju granu naučne oblasti koja se veoma brzo razvija. Tokom istraživanja proteina uočeno je da neki proteini nakon digestije ispoljavaju bioaktivnosti koje ne poseduju u svojoj nativnoj formi. To je bio podsticaj za istraživanje uticaja enzimske hidrolize na bioaktivnost proteina. Trenutni naučni stav je da svaki protein može posedovati fragmente koji ispoljavaju neku od mnogih bioaktivnosti. Bioaktivni peptidi dobijeni enzimskom hidrolizom surutke ispoljili su mnoge pozitivne efekte na ljudsko zdravlje...Bioactive peptides are a rapidly developing field of research. During the research it was observed that some peptides which do not show a particular bioactivity become bioactive after ingestion and passing through the gastrointestinal system. That was the stimulus for the development of research on the effect of enzymatic hydrolysis of the bioactive properties of proteins. According to the current state of scientific knowledge, every protein can contain fragments that possess some of many bioactivities. Bioactive peptides, derived by enzymatic hydrolysis of whey protein, have demonstrated characteristics as health-promoting agents..

Enriching alginate matrix used for probiotic encapsulation with whey protein concentrate or its trypsin-derived hydrolysate: Impact on antioxidant capacity and stability of fermented whey-based beverages

The present research is part of an effort to create whey-based functional food. Previously, it was concluded that proteins and peptides in an encapsulation matrix contribute to mechanical properties of beads, fermentative activity, acid and bile tolerance, and the survival of probiotics during the simulated gastrointestinal condition. This research evaluates the effects of using whey protein concentrate and trypsin hydrolysate as components of a matrix for probiotic encapsulation on the antioxidant capacity of a beverage. Carrier with hydrolysate showed better encapsulation efficiency, spherical factor, and antioxidant capacity before and after fermentation compared to the carrier with non-hydrolyzed proteins. Hydrolysis of protein used for carrier formulation positively impacts the beverage's antioxidant properties and probiotic viability during 28 days of storage. Using proteins, especially peptides, as a matrix component achieved three objectives: protection of probiotics, enrichment of products with antioxidants, and neutralization of possible bitter taste (because the bitter tasting peptides are incorporated into the matrix and as such cannot contribute to the taste of the product) that bioactive peptides usually possess