arXiv subjects

Tijana T. Ivancevic

Publications and source records attributed to Tijana T. Ivancevic.

At least 19 recordsLinked to original sources

arXiv2013

Sine-Gordon Solitons, Kinks and Breathers as Physical Models of Nonlinear Excitations in Living Cellular Structures

Nonlinear space-time dynamics, defined in terms of celebrated 'solitonic' equations, brings indispensable tools for understanding, prediction and control of complex behaviors in both physical and life sciences. In this paper, we review sine-Gordon solitons, kinks and breathers as models of nonlinear excitations in complex systems in physics and in living cellular structures, both intra-cellular (DNA, protein folding and microtubules) and inter-cellular (neural impulses and muscular contractions). Key words: Sine-Gordon solitons, kinks and breathers, DNA, Protein folding, Microtubules, Neural conduction, Muscular contraction

q-bio.OT↗

arXiv2011

Ricci Flow and Nonlinear Reaction--Diffusion Systems in Biology, Chemistry, and Physics

This paper proposes the Ricci-flow equation from Riemannian geometry as a general geometric framework for various nonlinear reaction-diffusion systems (and related dissipative solitons) in mathematical biology. More precisely, we propose a conjecture that any kind of reaction-diffusion processes in biology, chemistry and physics can be modelled by the combined geometric-diffusion system. In order to demonstrate the validity of this hypothesis, we review a number of popular nonlinear reaction-diffusion systems and try to show that they can all be subsumed by the presented geometric framework of the Ricci flow. Keywords: geometrical Ricci flow, nonlinear reaction-diffusion, dissipative solitons and breathers

nlin.PS↗

arXiv2011

Undergraduate Lecture Notes in De Rham-Hodge Theory

These lecture notes in the De Rham-Hodge theory are designed for a 1-semester undergraduate course (in mathematics, physics, engineering, chemistry or biology). This landmark theory of the 20th Century mathematics gives a rigorous foundation to modern field and gauge theories in physics, engineering and physiology. The only necessary background for comprehensive reading of these notes is Green's theorem from multivariable calculus.

math.DG↗

arXiv2011

Dynamics and Control of Humanoid Robots: A Geometrical Approach

his paper reviews modern geometrical dynamics and control of humanoid robots. This general Lagrangian and Hamiltonian formalism starts with a proper definition of humanoid's configuration manifold, which is a set of all robot's active joint angles. Based on the `covariant force law', the general humanoid's dynamics and control are developed. Autonomous Lagrangian dynamics is formulated on the associated `humanoid velocity phase space', while autonomous Hamiltonian dynamics is formulated on the associated `humanoid momentum phase space'. Neural-like hierarchical humanoid control naturally follows this geometrical prescription. This purely rotational and autonomous dynamics and control is then generalized into the framework of modern non-autonomous biomechanics, defining the Hamiltonian fitness function. The paper concludes with several simulation examples. Keywords: Humanoid robots, Lagrangian and Hamiltonian formalisms, neural-like humanoid control, time-dependent biodynamics

nlin.AO↗

arXiv2011

Lecture Notes in Lie Groups

These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous foundation to modern dynamics, as well as field and gauge theories in physics, engineering and biomechanics. We give both physical and medical examples of Lie groups. The only necessary background for comprehensive reading of these notes are advanced calculus and linear algebra.

math.DG↗

arXiv2009

Jet Spaces in Modern Hamiltonian Biomechanics

In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. Starting with the Covariant Force Law, we first develop autonomous Hamiltonian biomechanics. Then we extend it using a powerful geometrical machinery consisting of fibre bundles and jet manifolds associated to the biomechanical configuration manifold. We derive time-dependent, dissipative, Hamiltonian equations and the fitness evolution equation for the general time-dependent human biomechanical system. Keywords: Human biomechanics, covariant force law, configuration manifold, jet manifolds, time-dependent Hamiltonian dynamics

physics.bio-ph↗

arXiv2009

Time & Fitness-Dependent Hamiltonian Biomechanics

In this paper we propose the time & fitness-dependent Hamiltonian form of human biomechanics, in which total mechanical + biochemical energy is not conserved. Starting with the Covariant Force Law, we first develop autonomous Hamiltonian biomechanics. Then we extend it using a powerful geometrical machinery consisting of fibre bundles, jet manifolds, polysymplectic geometry and Hamiltonian connections. In this way we derive time-dependent dissipative Hamiltonian equations and the fitness evolution equation for the general time & fitness-dependent human biomechanical system. Keywords: Human biomechanics, configuration bundle, Hamiltonian connections, jet manifolds, time & fitness-dependent dynamics

physics.bio-ph↗

arXiv2009

Jet Methods in Time-Dependent Lagrangian Biomechanics

In this paper we propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds associated to the extended musculo-skeletal configuration manifold, called the configuration bundle. We start with an ordinary configuration manifold of human body motion, given as a set of its all active degrees of freedom (DOF) for a particular movement. This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. By this extension, using techniques from fibre bundles, we defined the biomechanical configuration bundle. On the biomechanical bundle we define vector-fields, differential forms and affine connections, as well as the associated jet manifolds. Using the formalism of jet manifolds of velocities and accelerations, we develop the time-dependent Lagrangian biomechanics. Its underlying geometric evolution is given by the Ricci flow equation. Keywords: Human time-dependent biomechanics, configuration bundle, jet spaces, Ricci flow

physics.bio-ph↗

arXiv2009

Jet-Ricci Geometry of Time-Dependent Human Biomechanics

We propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds derived from the extended musculo-skeletal configuration manifold. The corresponding Riemannian geometrical evolution follows the Ricci flow diffusion. In particular, we show that the exponential-like decay of total biomechanical energy (due to exhaustion of biochemical resources) is closely related to the Ricci flow on the biomechanical configuration manifold. Keywords: Time-dependent biomechanics, extended configuration manifold, configuration bundle, jet manifolds, Ricci flow diffusion

physics.bio-ph↗

arXiv2009

Human Operator Modeling and Lie-Derivative Based Control

The motivation behind mathematically modeling the human operator is to help explain the response characteristics of the complex dynamical system including the human manual controller. In this paper, we present two approaches to human operator modeling: classical linear control approach and modern nonlinear control approach. The latter one is formalized using both fixed and adaptive Lie-Derivative based controllers. Keywords: Human operator, linear control, nonlinear control, Lie derivative operator

math.OC↗

arXiv2009

Time-Dependent Lagrangian Biomechanics

In this paper we present the time-dependent generalization of an 'ordinary' autonomous human musculo-skeletal biomechanics. We start with the configuration manifold of human body, given as a set of its all active degrees of freedom (DOF). This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. On this extended configuration space we develop time-dependent biomechanical Lagrangian dynamics, using derived jet spaces of velocities and accelerations, as well as the underlying geometric evolution of the mass-inertia matrix. Keywords: Human time-dependent biomechanics, configuration manifold, jet spaces, geometric evolution

physics.bio-ph↗

arXiv2009

Fuzzy Control Strategies in Human Operator and Sport Modeling

The motivation behind mathematically modeling the human operator is to help explain the response characteristics of the complex dynamical system including the human manual controller. In this paper, we present two different fuzzy logic strategies for human operator and sport modeling: fixed fuzzy-logic inference control and adaptive fuzzy-logic control, including neuro-fuzzy-fractal control. As an application of the presented fuzzy strategies, we present a fuzzy-control based tennis simulator.

physics.bio-ph↗

arXiv2009

Applied Categories and Functors for Undergraduates

These are lecture notes for a 1-semester undergraduate course (in computer science, mathematics, physics, engineering, chemistry or biology) in applied categorical meta-language. The only necessary background for comprehensive reading of these notes are first-year calculus and linear algebra.

math.HO↗

arXiv2008

Undergraduate Lecture Notes in Topological Quantum Field Theory

These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism. Keywords: quantum mechanics/field theory, path integral, Hodge decomposition, Chern-Simons and Yang-Mills gauge theories, conformal field theory

math-ph↗

arXiv2008

A Mathematical Model of Chaotic Attractor in Tumor Growth and Decay

We propose a strange-attractor model of tumor growth and metastasis. It is a 4-dimensional spatio-temporal cancer model with strong nonlinear couplings. Even the same type of tumor is different in every patient both in size and appearance, as well as in temporal behavior. This is clearly a characteristic of dynamical systems sensitive to initial conditions. The new chaotic model of tumor growth and decay is biologically motivated. It has been developed as a live Mathematica demonstration, see Wolfram Demonstrator site: http://demonstrations.wolfram.com/ChaoticAttractorInTumorGrowth/ Key words: Reaction-diffusion tumor growth model, chaotic attractor, sensitive dependence on initial tumor characteristics

q-bio.CB↗

arXiv2008

Macro- and Microscopic Self-Similarity in Neuro- and Psycho-Dynamics

The unique Hamiltonian description of neuro- and psycho-dynamics at the macroscopic, classical, inter-neuronal level of brain's neural networks, and microscopic, quantum, intra-neuronal level of brain's microtubules, is presented in the form of open Liouville equations. This implies the arrow of time in both neuro- and psycho-dynamic processes and shows the existence of the formal neuro-biological space-time self-similarity. Keywords: Neuro- and psycho-dynamics, Brain microtubules, Hamiltonian and Liouville dynamics, Neuro-biological self-similarity

q-bio.NC↗

arXiv2008

$\infty-$Dimensional Cerebellar Controller for Realistic Human Biodynamics

In this paper we propose an $\infty-$dimensional cerebellar model of neural controller for realistic human biodynamics. The model is developed using Feynman's action-amplitude (partition function) formalism. The cerebellum controller is acting as a supervisor for an autogenetic servo control of human musculo-skeletal dynamics, which is presented in (dissipative, driven) Hamiltonian form. The $\infty-$dimensional cerebellar controller is closely related to entropic motor control. Keywords: realistic human biodynamics, cerebellum motion control, $\infty-$dimensional neural network

q-bio.NC↗

arXiv2008

Geometrical Bioelectrodynamics

This paper proposes rigorous geometrical treatment of bioelectrodynamics, underpinning two fast-growing biomedical research fields: bioelectromagnetism, which deals with the ability of life to produce its own electromagnetism, and bioelectromagnetics, which deals with the effect on life from external electromagnetism. Keywords: Bioelectrodynamics, exterior geometrical machinery, Dirac-Feynman quantum electrodynamics, functional electrical stimulation

q-bio.QM↗