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The possibility of light sterile neutrinos allows for the resonant production of lepton number in the early universe through matter-affected neutrino mixing. For a given a mixing of the active and sterile neutrino states it has been found that the lepton number generation process is chaotic and strongly oscillatory. We undertake a new study of this process' sensitivity to initial conditions through the quantum rate equations. We confirm the chaoticity of the process in this solution, and moreover find that the resultant lepton number and the sign of the asymmetry produces a fractal in the parameter space of mass, mixing angle and initial baryon number. This has implications for future searches for sterile neutrinos, where arbitrary high sensitivity could not be determinate in forecasting the lepton number of the universe.

We study the coupled translational, electronic, and field dynamics of the combined system "a two-level atom + a single-mode quantized field + a standing-wave ideal cavity". We derive Hamilton -- Schr\"odinger equations for probability amplitudes and averaged position and momentum of a point-like atom interacting with the quantized field in a standing-wave cavity. They constitute, in general, an infinite-dimensional set of equations with an infinite number of integrals of motion which may be reduced to a dynamical system with four degrees of freedom if the quantized field is supposed to be initially prepared in a Fock state. This system is found to produce semiquantum chaos with positive values of the maximal Lyapunov exponent. At large values of detuning $|\delta|\gg 1$, the Rabi atomic oscillations are usually shallow, and the dynamics is found to be almost regular. The Doppler -- Rabi resonance, deep Rabi oscillations that may occur at any large value of $|\delta|$ to be equal to $|\alpha p_0|$, is found numerically and described analytically (with $\alpha$ to be the normalized recoil frequency and $p_0$ the initial atomic momentum). Two gedanken experiments are proposed to detect manifestations of semiquantum chaos in real experiments. In the chaotic regime values of the population inversion $z_{out}$, measured with atoms after transversing a cavity, are so sensitive to small changes in the initial inversion $z_{in}$ that the probability of detecting any value of $z_{out}$ in the admissible interval becomes almost unity in a short time. Chaotic wandering of a two-level atom in a quantized Fock field is shown to be fractal. Fractal-like structures, typical for chaotic scattering, are numerically found in the dependence of the time of exit of atoms from the cavity on their initial momenta.

"Chaos" and "fractals" are two terms signaling a scientific revolution that has taken place in the last 20 years. In this talk, NASA researcher Warren Wiscombe explains how ordinary objects and events such as snowflakes and snowboarding exhibit the characteristics of chaos. Additionally, Wiscombe describes how chaos and fractal theory can shed new light on long-standing scientific conundrums such as weather and climate, fluid flows, cells, and life itself.

"Chaos" and "fractals" are two terms signaling a scientific revolution that has taken place in the last 20 years. In this talk, NASA researcher Warren Wiscombe explains how ordinary objects and events such as snowflakes and snowboarding exhibit the characteristics of chaos. Additionally, Wiscombe describes how chaos and fractal theory can shed new light on long-standing scientific conundrums such as weather and climate, fluid flows, cells, and life itself.

The study of fractal geometry and chaotic dynamical systems has received considerable attention in the past decade. Motivated by the interesting computer graphics produced by these fields, mathematicians have attempted to formalize the theoretical structure of the results, physicists have attempted to apply the theory to real world phenomena, and laymen have enjoyed much of the popular literature and television programs that the field has fostered. Unfortunately, the mathematics associated with these subjects has made them inaccessible to most undergraduates, even if they have a strong background in mathematics. This thesis presents the basic ideas of fractal geometry and chaotic dynamical systems in a setting that can be understood by undergraduate students who have had a course in advanced calculus. We hope it will allow them to gain an appreciation of the fields and motivate them to pursue further study.

Chaos, Solitons and Fractals 1993: Volume 3 , Issue CONTENTS. Digitized from IA1646428-05 . Previous issue: sim_chaos-solitons-and-fractals_november-december-1992_2_6_0 . Next issue: sim_chaos-solitons-and-fractals_january-february-1993_3_1_0 .

Chaos, Solitons and Fractals 1993: Volume 3 , Issue CONTENTS. Digitized from IA1646428-05 . Previous issue: sim_chaos-solitons-and-fractals_november-december-1992_2_6_0 . Next issue: sim_chaos-solitons-and-fractals_january-february-1993_3_1_0 .

Chaos, Solitons and Fractals 1993: Volume 3 , Issue CONTENTS. Digitized from IA1646428-05 . Previous issue: sim_chaos-solitons-and-fractals_november-december-1992_2_6_0 . Next issue: sim_chaos-solitons-and-fractals_january-february-1993_3_1_0 .

Chaos, Solitons and Fractals 1993: Volume 3 , Issue CONTENTS. Digitized from IA1646428-05 . Previous issue: sim_chaos-solitons-and-fractals_november-december-1992_2_6_0 . Next issue: sim_chaos-solitons-and-fractals_january-february-1993_3_1_0 .

Chaos, Solitons and Fractals 1993: Volume 3 , Issue CONTENTS. Digitized from IA1646428-05 . Previous issue: sim_chaos-solitons-and-fractals_november-december-1992_2_6_0 . Next issue: sim_chaos-solitons-and-fractals_january-february-1993_3_1_0 .

Chaos, Solitons and Fractals 1993: Volume 3 , Issue CONTENTS. Digitized from IA1646428-05 . Previous issue: sim_chaos-solitons-and-fractals_november-december-1992_2_6_0 . Next issue: sim_chaos-solitons-and-fractals_january-february-1993_3_1_0 .

CHAOS, FRACTALS AND ORGANISATIONS, BENGALI, NATIONAL BOOK TRUST, NBT, ARVIND KUMAR  

We investigate the occurrence chaos in the escape of test particles moving in the field of a Schwarzschild black hole surrounded by an external halo. The motion of both material particles and zero rest mass particles is considered. The chaos is characterized by the fractal dimension of boundary between the basins of the different escapes, which is a topologically invariant characterization. We find chaos in the motion of both material particles and null geodesics.

Chaos, Solitons & Fractals is an active peer-reviewed interdisciplinary scientific journal covering nonlinear science. It was established in 1991 and is published monthly by Elsevier. The journal publishes original articles in the form of short communications, regular papers, and review papers on a wide range of interdisciplinary subjects including: nonlinear dynamics and non-equilibrium processes in physics and applied mathematics; complex matter and networks; biophysics, systems biology and computational biology; fluctuations and random processes; artificial intelligence, machine learning and big data analytics; self-organisation and emergent phenomena. Subjects are presented with applications to social science, engineering and econophysics. The Internet Archive Collection contains microfilm published between 1991 and 1994. Chaos, Solitons & Fractals can be found online at:  https://www.journals.elsevier.com/chaos-solitons-and-fractals The ISSN is: 0960-0779

Chaos, Solitons & Fractals is an active peer-reviewed interdisciplinary scientific journal covering nonlinear science. It was established in 1991 and is published monthly by Elsevier. The journal publishes original articles in the form of short communications, regular papers, and review papers on a wide range of interdisciplinary subjects including: nonlinear dynamics and non-equilibrium processes in physics and applied mathematics; complex matter and networks; biophysics, systems biology and computational biology; fluctuations and random processes; artificial intelligence, machine learning and big data analytics; self-organisation and emergent phenomena. Subjects are presented with applications to social science, engineering and econophysics. The Internet Archive Collection contains microfilm published between 1991 and 1994. Chaos, Solitons & Fractals can be found online at:  https://www.journals.elsevier.com/chaos-solitons-and-fractals The ISSN is: 0960-0779

Chaos, Solitons & Fractals is an active peer-reviewed interdisciplinary scientific journal covering nonlinear science. It was established in 1991 and is published monthly by Elsevier. The journal publishes original articles in the form of short communications, regular papers, and review papers on a wide range of interdisciplinary subjects including: nonlinear dynamics and non-equilibrium processes in physics and applied mathematics; complex matter and networks; biophysics, systems biology and computational biology; fluctuations and random processes; artificial intelligence, machine learning and big data analytics; self-organisation and emergent phenomena. Subjects are presented with applications to social science, engineering and econophysics. The Internet Archive Collection contains microfilm published between 1991 and 1994. Chaos, Solitons & Fractals can be found online at:  https://www.journals.elsevier.com/chaos-solitons-and-fractals The ISSN is: 0960-0779

Chaos, Solitons & Fractals is an active peer-reviewed interdisciplinary scientific journal covering nonlinear science. It was established in 1991 and is published monthly by Elsevier. The journal publishes original articles in the form of short communications, regular papers, and review papers on a wide range of interdisciplinary subjects including: nonlinear dynamics and non-equilibrium processes in physics and applied mathematics; complex matter and networks; biophysics, systems biology and computational biology; fluctuations and random processes; artificial intelligence, machine learning and big data analytics; self-organisation and emergent phenomena. Subjects are presented with applications to social science, engineering and econophysics. The Internet Archive Collection contains microfilm published between 1991 and 1994. Chaos, Solitons & Fractals can be found online at:  https://www.journals.elsevier.com/chaos-solitons-and-fractals The ISSN is: 0960-0779

Chaos, Solitons & Fractals is an active peer-reviewed interdisciplinary scientific journal covering nonlinear science. It was established in 1991 and is published monthly by Elsevier. The journal publishes original articles in the form of short communications, regular papers, and review papers on a wide range of interdisciplinary subjects including: nonlinear dynamics and non-equilibrium processes in physics and applied mathematics; complex matter and networks; biophysics, systems biology and computational biology; fluctuations and random processes; artificial intelligence, machine learning and big data analytics; self-organisation and emergent phenomena. Subjects are presented with applications to social science, engineering and econophysics. The Internet Archive Collection contains microfilm published between 1991 and 1994. Chaos, Solitons & Fractals can be found online at:  https://www.journals.elsevier.com/chaos-solitons-and-fractals The ISSN is: 0960-0779

Chaos, Solitons & Fractals is an active peer-reviewed interdisciplinary scientific journal covering nonlinear science. It was established in 1991 and is published monthly by Elsevier. The journal publishes original articles in the form of short communications, regular papers, and review papers on a wide range of interdisciplinary subjects including: nonlinear dynamics and non-equilibrium processes in physics and applied mathematics; complex matter and networks; biophysics, systems biology and computational biology; fluctuations and random processes; artificial intelligence, machine learning and big data analytics; self-organisation and emergent phenomena. Subjects are presented with applications to social science, engineering and econophysics. The Internet Archive Collection contains microfilm published between 1991 and 1994. Chaos, Solitons & Fractals can be found online at:  https://www.journals.elsevier.com/chaos-solitons-and-fractals The ISSN is: 0960-0779

Chaos, Solitons & Fractals is an active peer-reviewed interdisciplinary scientific journal covering nonlinear science. It was established in 1991 and is published monthly by Elsevier. The journal publishes original articles in the form of short communications, regular papers, and review papers on a wide range of interdisciplinary subjects including: nonlinear dynamics and non-equilibrium processes in physics and applied mathematics; complex matter and networks; biophysics, systems biology and computational biology; fluctuations and random processes; artificial intelligence, machine learning and big data analytics; self-organisation and emergent phenomena. Subjects are presented with applications to social science, engineering and econophysics. The Internet Archive Collection contains microfilm published between 1991 and 1994. Chaos, Solitons & Fractals can be found online at:  https://www.journals.elsevier.com/chaos-solitons-and-fractals The ISSN is: 0960-0779

Chaos, Solitons & Fractals is an active peer-reviewed interdisciplinary scientific journal covering nonlinear science. It was established in 1991 and is published monthly by Elsevier. The journal publishes original articles in the form of short communications, regular papers, and review papers on a wide range of interdisciplinary subjects including: nonlinear dynamics and non-equilibrium processes in physics and applied mathematics; complex matter and networks; biophysics, systems biology and computational biology; fluctuations and random processes; artificial intelligence, machine learning and big data analytics; self-organisation and emergent phenomena. Subjects are presented with applications to social science, engineering and econophysics. The Internet Archive Collection contains microfilm published between 1991 and 1994. Chaos, Solitons & Fractals can be found online at:  https://www.journals.elsevier.com/chaos-solitons-and-fractals The ISSN is: 0960-0779

Chaos, Solitons & Fractals is an active peer-reviewed interdisciplinary scientific journal covering nonlinear science. It was established in 1991 and is published monthly by Elsevier. The journal publishes original articles in the form of short communications, regular papers, and review papers on a wide range of interdisciplinary subjects including: nonlinear dynamics and non-equilibrium processes in physics and applied mathematics; complex matter and networks; biophysics, systems biology and computational biology; fluctuations and random processes; artificial intelligence, machine learning and big data analytics; self-organisation and emergent phenomena. Subjects are presented with applications to social science, engineering and econophysics. The Internet Archive Collection contains microfilm published between 1991 and 1994. Chaos, Solitons & Fractals can be found online at:  https://www.journals.elsevier.com/chaos-solitons-and-fractals The ISSN is: 0960-0779

Chaos, Solitons & Fractals is an active peer-reviewed interdisciplinary scientific journal covering nonlinear science. It was established in 1991 and is published monthly by Elsevier. The journal publishes original articles in the form of short communications, regular papers, and review papers on a wide range of interdisciplinary subjects including: nonlinear dynamics and non-equilibrium processes in physics and applied mathematics; complex matter and networks; biophysics, systems biology and computational biology; fluctuations and random processes; artificial intelligence, machine learning and big data analytics; self-organisation and emergent phenomena. Subjects are presented with applications to social science, engineering and econophysics. The Internet Archive Collection contains microfilm published between 1991 and 1994. Chaos, Solitons & Fractals can be found online at:  https://www.journals.elsevier.com/chaos-solitons-and-fractals The ISSN is: 0960-0779

Thesis advisors, Maurice D. Weir and Ismor Fischer

Thesis advisors, Maurice D. Weir and Ismor Fischer

"Chaos" and "fractals" are two terms signaling a scientific revolution that has taken place in the last 20 years. In this talk, NASA researcher Warren Wiscombe explains how ordinary objects and events such as snowflakes and snowboarding exhibit the characteristics of chaos. Additionally, Wiscombe describes how chaos and fractal theory can shed new light on long-standing scientific conundrums such as weather and climate, fluid flows, cells, and life itself.

understanding schematics of sacred geometry

Fractals and chaos have gained immense popularity in the last few years. Fractal objects and chaotic dynamics are being postulated and observed in diverse areas of science. This report gives a mathematical introduction to fractals and chaos, including some necessary background for the technical definitions. Partial Contents: Fractal -- Observations and representations; Topology and open covers; Topological dimension; Hausdorff dimension (A definition of fractal); Similarity dimension; The Cantor set; Koch snowflakes; Random coastlines; Another approach - IFS (Iterated Function System); and Further examples; Chaos -- The Poincare map; Iterations of continuous functions -- Orbits; Periodic points; Invariant sets/Attractors; Scrambled Sets -- Definitions of chaos; Universality -- The bifurcation diagram; Higher dimensions; Complex dynamics; and Randomness. (EDC)

Fractals and chaos have gained immense popularity in the last few years. Fractal objects and chaotic dynamics are being postulated and observed in diverse areas of science. This report gives a mathematical introduction to fractals and chaos, including some necessary background for the technical definitions. Partial Contents: Fractal -- Observations and representations; Topology and open covers; Topological dimension; Hausdorff dimension (A definition of fractal); Similarity dimension; The Cantor set; Koch snowflakes; Random coastlines; Another approach - IFS (Iterated Function System); and Further examples; Chaos -- The Poincare map; Iterations of continuous functions -- Orbits; Periodic points; Invariant sets/Attractors; Scrambled Sets -- Definitions of chaos; Universality -- The bifurcation diagram; Higher dimensions; Complex dynamics; and Randomness. (EDC)

CHAOS, FRACTALS AND ORGANISATION, BENGALI, 2000, NATIONAL BOOK TRUST, NBT, ARVIND KUMAR

CHAOS, FRACTALS AND ORGANISATION, BENGALI, 2000, NATIONAL BOOK TRUST, NBT, ARVIND KUMAR

Includes bibliographical references and index

Chaos, Solitons and Fractals 1994: Volume 4 , Issue CONTENTS. Digitized from IA1652629-02 . Previous issue: sim_chaos-solitons-and-fractals_november-december-1993_3_6 . Next issue: sim_chaos-solitons-and-fractals_1994-01_4_1 .

Chaos, Solitons and Fractals 1994: Volume 4 , Issue CONTENTS. Digitized from IA1646428-05 . Previous issue: sim_chaos-solitons-and-fractals_november-december-1993_3_6_0 . Next issue: sim_chaos-solitons-and-fractals_1994-01_4_1_0 .

The study of dynamics in general relativity has been hampered by a lack of coordinate independent measures of chaos. Here I review a variety of invariant measures for quantifying chaotic dynamics in relativity that exploit the coordinate independence of fractal dimensions and symbolic entropies.

In [Aziz-Alaoui, 2002] a three species ODE model, based on a modified Leslie-Gower scheme is investigated. It is shown that under certain restrictions on the parameter space, the model has bounded solutions for all positive initial conditions, which eventually enter an invariant attracting set. We show that this is not true. To the contrary, solutions to the model can blow up in finite time, even under the restrictions derived in [Aziz-Alaoui, 2002], if the initial data is large enough. We also prove similar results for the spatially extended system. We validate all of our results via numerical simulations.

In [Aziz-Alaoui, 2002] a three species ODE model, based on a modified Leslie-Gower scheme is investigated. It is shown that under certain restrictions on the parameter space, the model has bounded solutions for all positive initial conditions, which eventually enter an invariant attracting set. We show that this is not true. To the contrary, solutions to the model can blow up in finite time, even under the restrictions derived in [Aziz-Alaoui, 2002], if the initial data is large enough. We also prove similar results for the spatially extended system. We validate all of our results via numerical simulations.

The study of fractal geometry and chaotic dynamical systems has received considerable attention in the past decade. Motivated by the interesting computer graphics produced by these fields, mathematicians have attempted to formalize the theoretical structure of the results, physicists have attempted to apply the theory to the real world phenomena, and laymen have enjoyed much of the popular literature and television programs that the field has fostered. Unfortunately, the mathematics associated with these subjects has made them inaccessible to most undergraduates, even if they have a strong back ground in mathematics. This thesis presents the basic ideas of fractal geometry and chaotic dynamical systems in a setting that can by understood by undergraduate students who have has a course in advanced calculus. We hope it will allow them to gain an appreciation of the fields and motivate them to pursue further study.

The study of fractal geometry and chaotic dynamical systems has received considerable attention in the past decade. Motivated by the interesting computer graphics produced by these fields, mathematicians have attempted to formalize the theoretical structure of the results, physicists have attempted to apply the theory to the real world phenomena, and laymen have enjoyed much of the popular literature and television programs that the field has fostered. Unfortunately, the mathematics associated with these subjects has made them inaccessible to most undergraduates, even if they have a strong back ground in mathematics. This thesis presents the basic ideas of fractal geometry and chaotic dynamical systems in a setting that can by understood by undergraduate students who have has a course in advanced calculus. We hope it will allow them to gain an appreciation of the fields and motivate them to pursue further study.

Two-dimensional random Lorentz gases with absorbing traps are considered in which a moving point particle undergoes elastic collisions on hard disks and annihilates when reaching a trap. In systems of finite spatial extension, the asymptotic decay of the survival probability is exponential and characterized by an escape rate, which can be related to the average positive Lyapunov exponent and to the dimension of the fractal repeller of the system. For infinite systems, the survival probability obeys a stretched exponential law of the form P(c,t)~exp(-Ct^{1/2}). The transition between the two regimes is studied and we show that, for a given trap density, the non-integer dimension of the fractal repeller increases with the system size to finally reach the integer dimension of the phase space. Nevertheless, the repeller remains fractal. We determine the special scaling properties of this fractal.

Includes bibliographical references (p. [955]-969) and index

Book Source: Digital Library of India Item 2015.291255 dc.contributor.author: Kumaar Arvind dc.date.accessioned: 2015-08-08T20:05:35Z dc.date.available: 2015-08-08T20:05:35Z dc.date.copyright: 2000 dc.date.digitalpublicationdate: 2004/10/18 dc.date.citation: 2000 dc.identifier.barcode: 99999990186313 dc.identifier.origpath: /data2/upload/0040/619 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/291255 dc.description.scannerno: Cdac-1 dc.description.scanningcentre: C-DAC, Noida dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 192 dc.format.mimetype: application/pdf dc.language.iso: Bengali dc.publisher.digitalrepublisher: Digital Library of India dc.publisher: National Book Trust dc.rights: National Book Trust dc.source.library: Nbt dc.subject.classification: Social Sciences dc.title: Chaos Fractals And Organisation dc.type: Print - Paper dc.type: Book

In order to draw out the essential behavior of the universe, investigations of early universe cosmology often reduce the complex system to a simple integrable system. Inflationary models are of this kind as they focus on simple scalar field scenarios with correspondingly simple dynamics. However, we can be assured that the universe is crowded with many interacting fields of which the inflaton is but one. As we describe, the nonlinear nature of these interactions can result in a complex, chaotic evolution of the universe. Here we illustrate how chaotic effects can arise even in basic models such as homogeneous, isotropic universes with two scalar fields. We find inflating universes which act as attractors in the space of initial conditions. These universes display chaotic transients in their early evolution. The chaotic character is reflected by the fractal border to the basin of attraction. The broader implications are likely to be felt in the process of reheating as well as in the nature of the cosmic background radiation.

"Chaos" and "fractals" are two terms signaling a scientific revolution that has taken place in the last 20 years. In this talk, NASA researcher Warren Wiscombe explains how ordinary objects and events such as snowflakes and snowboarding exhibit the characteristics of chaos. Additionally, Wiscombe describes how chaos and fractal theory can shed new light on long-standing scientific conundrums such as weather and climate, fluid flows, cells, and life itself.

"Chaos" and "fractals" are two terms signaling a scientific revolution that has taken place in the last 20 years. In this talk, NASA researcher Warren Wiscombe explains how ordinary objects and events such as snowflakes and snowboarding exhibit the characteristics of chaos. Additionally, Wiscombe describes how chaos and fractal theory can shed new light on long-standing scientific conundrums such as weather and climate, fluid flows, cells, and life itself.

Chaos, Solitons and Fractals 1993: Volume 3 , Issue CONTENTS. Digitized from IA1652629-02 . Previous issue: sim_chaos-solitons-and-fractals_november-december-1992_2_6 . Next issue: sim_chaos-solitons-and-fractals_january-february-1993_3_1 .

Chaos, Solitons and Fractals 1993: Volume 3 , Issue CONTENTS. Digitized from IA1652629-02 . Previous issue: sim_chaos-solitons-and-fractals_november-december-1992_2_6 . Next issue: sim_chaos-solitons-and-fractals_january-february-1993_3_1 .

Chaos, Solitons and Fractals 1991: Volume 1 , Issue CONTENTS. Digitized from IA1646428-05 . Next issue: sim_chaos-solitons-and-fractals_1991_1_1_0 .

Chaos, Solitons and Fractals 1992: Volume 2 , Issue CONTENTS. Digitized from IA1652629-02 . Previous issue: sim_chaos-solitons-and-fractals_1991_1_6 . Next issue: sim_chaos-solitons-and-fractals_january-february-1992_2_1 .

Chaos, Solitons and Fractals 1992: Volume 2 , Issue CONTENTS. Digitized from IA1652629-02 . Previous issue: sim_chaos-solitons-and-fractals_1991_1_6 . Next issue: sim_chaos-solitons-and-fractals_january-february-1992_2_1 .