The distribution function describing the acceleration of relativistic particles in an advection-d... more The distribution function describing the acceleration of relativistic particles in an advection-dominated accretion disk is analyzed using a transport formalism that includes first-order Fermi acceleration, advection, spatial diffusion, and the escape of particles through the upper and lower surfaces of the disk. When a centrifugally supported shock is present in the disk, the concentrated particle acceleration occurring in the vicinity of the shock channels a significant fraction of the binding energy of the accreting gas into a population of relativistic particles. These high-energy particles diffuse vertically through the disk and escape, carrying away both energy and entropy and allowing the remaining gas to accrete. The dynamical structure of the disk/shock system is computed self-consistently using a model previously developed by the authors that successfully accounts for the production of the observed relativistic outflows (jets) in M87 and Sgr A*. This ensures that the rate at which energy is carried away from the disk by the escaping relativistic particles is equal to the drop in the radial energy flux at the shock location, as is required for energy conservation. We investigate the influence of advection, diffusion, and acceleration on the particle distribution by computing the nonthermal Green's function, which displays a relatively flat power-law tail at high energies. We also obtain the energy distribution for the particles escaping from the disk, and we conclude by discussing the spectrum of the observable secondary radiation produced by the escaping particles.
Abstract: This paper deals with visual design and reasoning. A visual language with its internal ... more Abstract: This paper deals with visual design and reasoning. A visual language with its internal representation in the form of attributed hierarchical hypergraphs is discussed. Hypergraph attributes allow for defining and analysing constraints im-posed by design knowledge. Operations ...
The article shows sufficient conditions for the existence of positive solutions to a multi-point ... more The article shows sufficient conditions for the existence of positive solutions to a multi-point boundary-value problem for a fourth-order differen-tial equation. Our main tools are the Guo-Krasnoselskii fixed point theorem and the monotone iterative technique. We also show that the set of positive solutions is compact.
ABSTRACT We study the acceleration of relativistic particles in a viscous, advection dominated ac... more ABSTRACT We study the acceleration of relativistic particles in a viscous, advection dominated accretion disk containing a centrifugally supported standing shock waves in the context of energetic outflows observed around radio-loud black holes. The dynamical structure of the accreting gas is described using a new model for viscous, shocked disks recently reported by the authors, and a rigorous mathematical method is employed to solve the transport equation for the relativistic particle distribution. We observe that particle acceleration around the standing shock converts a significant fraction of the gravitational potential energy of the accretion flow into a population of relativistic particles. These particles diffuse from the disk vertically outwards, carrying away both energy and entropy and the remaining gas accrets into the black hole. We confirm that the above formalism successfully demonstrate the bulk properties of the jet outflows observed in M87 and Sgr A*. Accordingly, we argue that a standing shock may be an essential ingredient in accretion onto underfed black holes.
Stochastic acceleration of charged particles due to interactions with magnetohydrodynamic (MHD) p... more Stochastic acceleration of charged particles due to interactions with magnetohydrodynamic (MHD) plasma waves is the dominant process leading to the formation of the high-energy electron and ion distributions in a variety of astrophysical systems. Collisions with the waves influence both the energization and the spatial transport of the particles, and therefore it is important to treat these two aspects of the problem in a self-consistent manner. We solve the representative Fokker-Planck equation to obtain a new, closed-form solution for the time-dependent Green's function describing the acceleration and escape of relativistic particles interacting with Alfvén or fast-mode waves characterized by momentum diffusion coefficient D(p)~pq and mean particle escape timescale tesc(p)~pq-2, where p is the particle momentum and q is the power-law index of the MHD wave spectrum. In particular, we obtain solutions for the momentum distribution of the ions in the plasma and also for the momentum distribution of the escaping particles, which may form an energetic outflow. The general features of the solutions are illustrated via examples based on either a Kolmogorov or Kraichnan wave spectrum. The new expressions complement the results obtained by Park and Petrosian, who presented exact solutions for the hard-sphere scattering case (q=2) in addition to other scenarios in which the escape timescale has a power-law dependence on the momentum. Our results have direct relevance for models of high-energy radiation and cosmic-ray production in astrophysical environments such as γ-ray bursts, active galaxies, and magnetized coronae around black holes. In particular, we outline an application of the new results to black hole sources that produce outflows of relativistic hadrons, with associated predictions that can be tested using GLAST.
We study the initial-boundary value problem for a nonlinear wave equation given by u tt -u xx +K|... more We study the initial-boundary value problem for a nonlinear wave equation given by u tt -u xx +K|u| p-2 u+λ|u t | q-2 u t =F(x,t),0<x<1,0<t<T,u x (0,t)=P(t),u(1,t)=0,u(x,0)=u 0 (x),u t (x,0)=u 1 (x),(1) where p≥2, q>1, K, λ are given constants and u 0 , u 1 , F are given functions, the unknown function u(x,t) and the unknown boundary value P(t) satisfy the following nonlinear integral equation P(t)=g(t)+K 1 |u(0,t)| α-2 u(0,t)+|u t (0,t)| β-2 u t (0,t)-∫ 0 t k(t-s)u(0,s)ds, where K 1 , α, β are given constants and g, k are given functions. In Part 1 we prove a theorem of existence and uniqueness of a weak solution (u,P) of problem (1), (2). The proof is based on the Faedo-Galerkin method associated with a priori estimates, weak convergence and compactness techniques. In Part 3 we obtain an asymptotic expansion of the solution (u,P) of the problem (1), (2) up to order N+1 in three small parameters K, λ, K 1 .
Proceedings of the 2011th Confederated International Conference on on the Move to Meaningful Internet Systems, 2011
We introduce a new programming language called INI, which eases the development of self-adaptive ... more We introduce a new programming language called INI, which eases the development of self-adaptive software. INI combines both rulebased and event-based programming paradigms, by allowing the definitions of rules that can be triggered by events. Besides a convenient language-level support for synchronization, the key point with INI events is that they come with a configuration layer, which is set up through input parameters passed to the events when created. Additionally, events can be stopped, reconfigured, and restarted at runtime by the program itself. Ultimately, this re-configuration can be triggered by other events, thus allowing the program to adapt to new operational environments.
Using the fiber product of Young measures and a new Green type function we present a study of Bol... more Using the fiber product of Young measures and a new Green type function we present a study of Bolza, relaxation and viscosity problems in optimal control theory, where the dynamic is governed by a Second-order Ordinary Differential Equation (SODE) with m-point boundary conditions and control measures.
In this work, the aerodynamic performance of beetle wing in free-forward flight was explored by a... more In this work, the aerodynamic performance of beetle wing in free-forward flight was explored by a three-dimensional computational fluid dynamics (CFDs) simulation with measured wing kinematics. It is shown from the CFD results that twist and camber variation, which represent the wing flexibility, are most important when determining the aerodynamic performance. Twisting wing significantly increased the mean lift and camber variation enhanced the mean thrust while the required power was lower than the case when neither was considered. Thus, in a comparison of the power economy among rigid, twisting and flexible models, the flexible model showed the best performance. When the positive effect of wing interaction was added to that of wing flexibility, we found that the elytron created enough lift to support its weight, and the total lift (48.4 mN) generated from the simulation exceeded the gravity force of the beetle (47.5 mN) during forward flight.
We summarize our model for long-duration gamma ray bursts (GRBs) that fits the redshift (z) distr... more We summarize our model for long-duration gamma ray bursts (GRBs) that fits the redshift (z) distributions measured with Swift and missions before Swift, and the pre-Swift GRB jet opening-angle distribution inferred from achromatic breaks in the optical light curves. We find that the comoving rate density of GRB sources exhibits positive evolution to z > ∼ 3 -5, whereas the star formation rate inferred from measurements of the blue and UV luminosity density peaks at z ∼ 1 -3. The mean intrinsic beaming factor of GRBs is found to be ≈ 34 -42, and we predict that the mean GRB optical jet opening half-angle measured with Swift is ≈ 10 • . We estimate the number of GRBs per year that GLAST is expected to observe based on ratios of BATSE and EGRET GRB fluences.
The effects of chloride concentration on the rates of decomposition of H 2 O 2 by ferric ion and ... more The effects of chloride concentration on the rates of decomposition of H 2 O 2 by ferric ion and on the rate of oxidation of an organic solute in homogeneous aqueous solution have been investigated. Experiments were carried out in a batch reactor, in the dark, at pH ≤ 3, 25.0 ...
The authors investigate second order differential inclusions with m-point boundary value conditio... more The authors investigate second order differential inclusions with m-point boundary value conditions: u '' (t)+cu(t)∈F(t,u(t),u ' (t)),t∈[0,1],u(0)=0,u(1)=∑ i=1 m-2 a i u(b i ); where c>0, 0<b 1 <⋯<b m-2 <1. They first consider the case when F(t,u,u ' )=-∂ϕ(u), the subdifferential of a convex lower semi-continuous map ϕ defined on ℝ d for which there exists a suitable sequence of C 1 , convex, Lipschitzian maps which epiconverges to ϕ. The proof involves the use of Young measures and the weak biting convergence. The solution is not necessarily in the Sobolev space W 2,1 [0,1]. Then the authors treat the case when F is defined on [0,1]×E 2 with closed bounded values and Lipschitzian with respect to the two last variables, where E is a Banach space. Using the Nadler fixed point theorem, they deduce the existence of a solution. Then they show that the solution set is a retract of W 2,1 ([0,1];E).
Animated diagrams may acquire much higher functionality when the construc-tion and animation proc... more Animated diagrams may acquire much higher functionality when the construc-tion and animation process can be made interactive in the sense of full control by the user over dynamic changes of the diagram or its parts. A number of exam-ples of such diagrams were implemented ...
This work examined the effect of sulfate ions on the rate of decomposition of H2O2 by Fe(III) in ... more This work examined the effect of sulfate ions on the rate of decomposition of H2O2 by Fe(III) in homogeneous aqueous solutions. Experiments were carried out at 25 degrees C, pH &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt; or = 3 and the concentrations of sulfate ranged from 0 to 200 mM ([Fe(III)]0 = 0.2 or 1 mM, [H2O2]0 = 10 or 50 mM). The spectrophometric study shows that addition of sulfate decreased the formation of iron(III)-peroxo complexes and that H2O2 does not form complexes with iron(III)-sulfato complexes. The rates of decomposition of H2O2 markedly decreased in the presence of sulfate. The measured rates were accurately predicted by a kinetic model based on reactions previously validated in NaClO4/HClO4 solutions and on additional reactions involving sulfate ions and sulfate radicals. At a fixed pH, the pseudo-first-order rate constants were found to decrease linearly with the molar fraction of Fe(II) complexed with sulfate. The model was also able to predict the rate of oxidation of a probe compound (atrazine) by Fe(III)/H2O2. Computer simulations indicate that the decrease of the rate of oxidation of organic solutes by Fe(III)/H2O2 can be mainly attributed to the complexation of Fe(III) by sulfate ions, while sulfate radicals play a minor role on the overall reaction rates.
System of nonlinear wave equations Mixed nonhomogeneous conditions The helical flows of Maxwell f... more System of nonlinear wave equations Mixed nonhomogeneous conditions The helical flows of Maxwell fluid Faedo-Galerkin method Exponential decay a b s t r a c t
An algebraic transformation to the commonly used diode equation of a solar cell produces an equat... more An algebraic transformation to the commonly used diode equation of a solar cell produces an equation ideally suited for use in modeling power systems incorporating photovoltaic solar arrays. The transformed equation predicts cell current as a function of ...
The effects of chloride concentration on the rates of decomposition of H 2 O 2 by ferric ion and ... more The effects of chloride concentration on the rates of decomposition of H 2 O 2 by ferric ion and on the rate of oxidation of an organic solute in homogeneous aqueous solution have been investigated. Experiments were carried out in a batch reactor, in the dark, at pH ≤ 3, 25.0 ...
The distribution function describing the acceleration of relativistic particles in an advection-d... more The distribution function describing the acceleration of relativistic particles in an advection-dominated accretion disk is analyzed using a transport formalism that includes first-order Fermi acceleration, advection, spatial diffusion, and the escape of particles through the upper and lower surfaces of the disk. When a centrifugally supported shock is present in the disk, the concentrated particle acceleration occurring in the vicinity of the shock channels a significant fraction of the binding energy of the accreting gas into a population of relativistic particles. These high-energy particles diffuse vertically through the disk and escape, carrying away both energy and entropy and allowing the remaining gas to accrete. The dynamical structure of the disk/shock system is computed self-consistently using a model previously developed by the authors that successfully accounts for the production of the observed relativistic outflows (jets) in M87 and Sgr A*. This ensures that the rate at which energy is carried away from the disk by the escaping relativistic particles is equal to the drop in the radial energy flux at the shock location, as is required for energy conservation. We investigate the influence of advection, diffusion, and acceleration on the particle distribution by computing the nonthermal Green's function, which displays a relatively flat power-law tail at high energies. We also obtain the energy distribution for the particles escaping from the disk, and we conclude by discussing the spectrum of the observable secondary radiation produced by the escaping particles.
Abstract: This paper deals with visual design and reasoning. A visual language with its internal ... more Abstract: This paper deals with visual design and reasoning. A visual language with its internal representation in the form of attributed hierarchical hypergraphs is discussed. Hypergraph attributes allow for defining and analysing constraints im-posed by design knowledge. Operations ...
The article shows sufficient conditions for the existence of positive solutions to a multi-point ... more The article shows sufficient conditions for the existence of positive solutions to a multi-point boundary-value problem for a fourth-order differen-tial equation. Our main tools are the Guo-Krasnoselskii fixed point theorem and the monotone iterative technique. We also show that the set of positive solutions is compact.
ABSTRACT We study the acceleration of relativistic particles in a viscous, advection dominated ac... more ABSTRACT We study the acceleration of relativistic particles in a viscous, advection dominated accretion disk containing a centrifugally supported standing shock waves in the context of energetic outflows observed around radio-loud black holes. The dynamical structure of the accreting gas is described using a new model for viscous, shocked disks recently reported by the authors, and a rigorous mathematical method is employed to solve the transport equation for the relativistic particle distribution. We observe that particle acceleration around the standing shock converts a significant fraction of the gravitational potential energy of the accretion flow into a population of relativistic particles. These particles diffuse from the disk vertically outwards, carrying away both energy and entropy and the remaining gas accrets into the black hole. We confirm that the above formalism successfully demonstrate the bulk properties of the jet outflows observed in M87 and Sgr A*. Accordingly, we argue that a standing shock may be an essential ingredient in accretion onto underfed black holes.
Stochastic acceleration of charged particles due to interactions with magnetohydrodynamic (MHD) p... more Stochastic acceleration of charged particles due to interactions with magnetohydrodynamic (MHD) plasma waves is the dominant process leading to the formation of the high-energy electron and ion distributions in a variety of astrophysical systems. Collisions with the waves influence both the energization and the spatial transport of the particles, and therefore it is important to treat these two aspects of the problem in a self-consistent manner. We solve the representative Fokker-Planck equation to obtain a new, closed-form solution for the time-dependent Green's function describing the acceleration and escape of relativistic particles interacting with Alfvén or fast-mode waves characterized by momentum diffusion coefficient D(p)~pq and mean particle escape timescale tesc(p)~pq-2, where p is the particle momentum and q is the power-law index of the MHD wave spectrum. In particular, we obtain solutions for the momentum distribution of the ions in the plasma and also for the momentum distribution of the escaping particles, which may form an energetic outflow. The general features of the solutions are illustrated via examples based on either a Kolmogorov or Kraichnan wave spectrum. The new expressions complement the results obtained by Park and Petrosian, who presented exact solutions for the hard-sphere scattering case (q=2) in addition to other scenarios in which the escape timescale has a power-law dependence on the momentum. Our results have direct relevance for models of high-energy radiation and cosmic-ray production in astrophysical environments such as γ-ray bursts, active galaxies, and magnetized coronae around black holes. In particular, we outline an application of the new results to black hole sources that produce outflows of relativistic hadrons, with associated predictions that can be tested using GLAST.
We study the initial-boundary value problem for a nonlinear wave equation given by u tt -u xx +K|... more We study the initial-boundary value problem for a nonlinear wave equation given by u tt -u xx +K|u| p-2 u+λ|u t | q-2 u t =F(x,t),0<x<1,0<t<T,u x (0,t)=P(t),u(1,t)=0,u(x,0)=u 0 (x),u t (x,0)=u 1 (x),(1) where p≥2, q>1, K, λ are given constants and u 0 , u 1 , F are given functions, the unknown function u(x,t) and the unknown boundary value P(t) satisfy the following nonlinear integral equation P(t)=g(t)+K 1 |u(0,t)| α-2 u(0,t)+|u t (0,t)| β-2 u t (0,t)-∫ 0 t k(t-s)u(0,s)ds, where K 1 , α, β are given constants and g, k are given functions. In Part 1 we prove a theorem of existence and uniqueness of a weak solution (u,P) of problem (1), (2). The proof is based on the Faedo-Galerkin method associated with a priori estimates, weak convergence and compactness techniques. In Part 3 we obtain an asymptotic expansion of the solution (u,P) of the problem (1), (2) up to order N+1 in three small parameters K, λ, K 1 .
Proceedings of the 2011th Confederated International Conference on on the Move to Meaningful Internet Systems, 2011
We introduce a new programming language called INI, which eases the development of self-adaptive ... more We introduce a new programming language called INI, which eases the development of self-adaptive software. INI combines both rulebased and event-based programming paradigms, by allowing the definitions of rules that can be triggered by events. Besides a convenient language-level support for synchronization, the key point with INI events is that they come with a configuration layer, which is set up through input parameters passed to the events when created. Additionally, events can be stopped, reconfigured, and restarted at runtime by the program itself. Ultimately, this re-configuration can be triggered by other events, thus allowing the program to adapt to new operational environments.
Using the fiber product of Young measures and a new Green type function we present a study of Bol... more Using the fiber product of Young measures and a new Green type function we present a study of Bolza, relaxation and viscosity problems in optimal control theory, where the dynamic is governed by a Second-order Ordinary Differential Equation (SODE) with m-point boundary conditions and control measures.
In this work, the aerodynamic performance of beetle wing in free-forward flight was explored by a... more In this work, the aerodynamic performance of beetle wing in free-forward flight was explored by a three-dimensional computational fluid dynamics (CFDs) simulation with measured wing kinematics. It is shown from the CFD results that twist and camber variation, which represent the wing flexibility, are most important when determining the aerodynamic performance. Twisting wing significantly increased the mean lift and camber variation enhanced the mean thrust while the required power was lower than the case when neither was considered. Thus, in a comparison of the power economy among rigid, twisting and flexible models, the flexible model showed the best performance. When the positive effect of wing interaction was added to that of wing flexibility, we found that the elytron created enough lift to support its weight, and the total lift (48.4 mN) generated from the simulation exceeded the gravity force of the beetle (47.5 mN) during forward flight.
We summarize our model for long-duration gamma ray bursts (GRBs) that fits the redshift (z) distr... more We summarize our model for long-duration gamma ray bursts (GRBs) that fits the redshift (z) distributions measured with Swift and missions before Swift, and the pre-Swift GRB jet opening-angle distribution inferred from achromatic breaks in the optical light curves. We find that the comoving rate density of GRB sources exhibits positive evolution to z > ∼ 3 -5, whereas the star formation rate inferred from measurements of the blue and UV luminosity density peaks at z ∼ 1 -3. The mean intrinsic beaming factor of GRBs is found to be ≈ 34 -42, and we predict that the mean GRB optical jet opening half-angle measured with Swift is ≈ 10 • . We estimate the number of GRBs per year that GLAST is expected to observe based on ratios of BATSE and EGRET GRB fluences.
The effects of chloride concentration on the rates of decomposition of H 2 O 2 by ferric ion and ... more The effects of chloride concentration on the rates of decomposition of H 2 O 2 by ferric ion and on the rate of oxidation of an organic solute in homogeneous aqueous solution have been investigated. Experiments were carried out in a batch reactor, in the dark, at pH ≤ 3, 25.0 ...
The authors investigate second order differential inclusions with m-point boundary value conditio... more The authors investigate second order differential inclusions with m-point boundary value conditions: u '' (t)+cu(t)∈F(t,u(t),u ' (t)),t∈[0,1],u(0)=0,u(1)=∑ i=1 m-2 a i u(b i ); where c>0, 0<b 1 <⋯<b m-2 <1. They first consider the case when F(t,u,u ' )=-∂ϕ(u), the subdifferential of a convex lower semi-continuous map ϕ defined on ℝ d for which there exists a suitable sequence of C 1 , convex, Lipschitzian maps which epiconverges to ϕ. The proof involves the use of Young measures and the weak biting convergence. The solution is not necessarily in the Sobolev space W 2,1 [0,1]. Then the authors treat the case when F is defined on [0,1]×E 2 with closed bounded values and Lipschitzian with respect to the two last variables, where E is a Banach space. Using the Nadler fixed point theorem, they deduce the existence of a solution. Then they show that the solution set is a retract of W 2,1 ([0,1];E).
Animated diagrams may acquire much higher functionality when the construc-tion and animation proc... more Animated diagrams may acquire much higher functionality when the construc-tion and animation process can be made interactive in the sense of full control by the user over dynamic changes of the diagram or its parts. A number of exam-ples of such diagrams were implemented ...
This work examined the effect of sulfate ions on the rate of decomposition of H2O2 by Fe(III) in ... more This work examined the effect of sulfate ions on the rate of decomposition of H2O2 by Fe(III) in homogeneous aqueous solutions. Experiments were carried out at 25 degrees C, pH &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt; or = 3 and the concentrations of sulfate ranged from 0 to 200 mM ([Fe(III)]0 = 0.2 or 1 mM, [H2O2]0 = 10 or 50 mM). The spectrophometric study shows that addition of sulfate decreased the formation of iron(III)-peroxo complexes and that H2O2 does not form complexes with iron(III)-sulfato complexes. The rates of decomposition of H2O2 markedly decreased in the presence of sulfate. The measured rates were accurately predicted by a kinetic model based on reactions previously validated in NaClO4/HClO4 solutions and on additional reactions involving sulfate ions and sulfate radicals. At a fixed pH, the pseudo-first-order rate constants were found to decrease linearly with the molar fraction of Fe(II) complexed with sulfate. The model was also able to predict the rate of oxidation of a probe compound (atrazine) by Fe(III)/H2O2. Computer simulations indicate that the decrease of the rate of oxidation of organic solutes by Fe(III)/H2O2 can be mainly attributed to the complexation of Fe(III) by sulfate ions, while sulfate radicals play a minor role on the overall reaction rates.
System of nonlinear wave equations Mixed nonhomogeneous conditions The helical flows of Maxwell f... more System of nonlinear wave equations Mixed nonhomogeneous conditions The helical flows of Maxwell fluid Faedo-Galerkin method Exponential decay a b s t r a c t
An algebraic transformation to the commonly used diode equation of a solar cell produces an equat... more An algebraic transformation to the commonly used diode equation of a solar cell produces an equation ideally suited for use in modeling power systems incorporating photovoltaic solar arrays. The transformed equation predicts cell current as a function of ...
The effects of chloride concentration on the rates of decomposition of H 2 O 2 by ferric ion and ... more The effects of chloride concentration on the rates of decomposition of H 2 O 2 by ferric ion and on the rate of oxidation of an organic solute in homogeneous aqueous solution have been investigated. Experiments were carried out in a batch reactor, in the dark, at pH ≤ 3, 25.0 ...
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