Results 1  10
of
20
Formal Darwinism, the individualasmaximizingagent analogy and bethedging
 B
, 1999
"... The central argument of The origin of species was that mechanical processes (inheritance of features and the di¡erential reproduction they cause) can give rise to the appearance of design. The `mechanical processes' are now mathematically represented by the dynamic systems of population genetics, an ..."
Abstract

Cited by 23 (7 self)
 Add to MetaCart
The central argument of The origin of species was that mechanical processes (inheritance of features and the di¡erential reproduction they cause) can give rise to the appearance of design. The `mechanical processes' are now mathematically represented by the dynamic systems of population genetics, and the appearance of design by optimization and game theory in which the individual plays the part of the maximizing agent. Establishing a precise individualasmaximizingagent (IMA) analogy for a population genetics system justi¢es optimization approaches, and so provides a modern formal representation of the core of Darwinism. It is a hitherto unnoticed implication of recent populationgenetics models that, contrary to a decadeslong consensus, an IMA analogy can be found in models with stochastic environments (subject to a convexity assumption), in which individuals maximize expected reproductive value. The key is that the total reproductive value of a species must be considered as constant, so therefore reproductive value should always be calculated in relative terms. This result removes a major obstacle from the theoretical challenge to ¢nd a unifying framework which establishes the IMA analogy for all of Darwinian biology, including as special cases inclusive ¢tness, evolutionarily stable strategies, evolutionary lifehistory theory, agestructured models and sex ratio theory. This would provide a formal, mathematical justi¢cation of fruitful and widespread but `intentional ' terms in evolutionary biology, such as `sel¢sh', `altruism ' and
Discrete variational Hamiltonian mechanics
 Journal of Physics A (Mathematical and General
"... The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. W ..."
Abstract

Cited by 19 (1 self)
 Add to MetaCart
The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms.
Set Theory and Physics
 FOUNDATIONS OF PHYSICS, VOL. 25, NO. 11
, 1995
"... Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of soli ..."
Abstract

Cited by 8 (7 self)
 Add to MetaCart
Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of solid threedimensional objects, (iii) in the theory of effective computability (ChurchTurhrg thesis) related to the possible "solution of supertasks," and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for" physical applications are discussed: Cantorian "naive" (i.e., nonaxiomatic) set theory, contructivism, and operationalism, hr the arrthor's ophrion, an attitude of "suspended attention" (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same thne, physicists shouM be open to "bizarre" or "mindboggling" new formalisms, which treed not be operationalizable or testable at the thne of their " creation, but which may successfully lead to novel fields of phenomenology and technology.
On the numerical integration of motion for rigid polyatomics: The modified quaternion approach
 Computers in Physics 12
, 1998
"... A revised version of the quaternion approach for numerical integration of the equations of motion for rigid polyatomic molecules is proposed. The modified approach is based on a formulation of the quaternion dynamics with constraints. This allows to resolve the rigidity problem rigorously using cons ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
A revised version of the quaternion approach for numerical integration of the equations of motion for rigid polyatomic molecules is proposed. The modified approach is based on a formulation of the quaternion dynamics with constraints. This allows to resolve the rigidity problem rigorously using constraint forces. It is shown that the procedure for preservation of molecular rigidity can be realized particularly simply within the Verlet algorithm in velocity form. We demonstrate that the presented method leads to an improved numerical stability with respect to the usual quaternion rescaling scheme and it is roughly as good as the cumbersome atomicconstraint technique. 2 1
Classical electromagnetic interaction of a point charge and a magnetic moment: considerations related to the AharonovBohm phase shift
 Found. Phys
, 2002
"... A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v 2 /c 2 is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem’s strange polarization of the classical hydrogen atom, and ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v 2 /c 2 is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem’s strange polarization of the classical hydrogen atom, and the Aharonov–Bohm phase shift. First we review the predictions following from the traditional particleonafrictionlessrigidring model for a magnetic moment. This model, which is not relativistic to order v 2 /c 2, does reveal a connection between the electric field of the point charge and hidden momentum in the magnetic moment; however, the electric field back at the point charge due to the Faradayinduced changing magnetic moment is of order 1/c 4 and hence is negligible in a 1/c 2 analysis. Next we use a relativistic magnetic moment model consisting of many superimposed classical hydrogen atoms (and antiatoms) interacting through the Darwin Lagrangian with an external charge but not with each other. The analysis of Solem regarding the strange polarization of the classical hydrogen atom is seen to give a fundamentally different mechanism for the electric field of the passing charge to change the
Efficient Algorithms for Simulating Complex Mechanical Systems Using Constraint Dynamics
, 1994
"... The constrained Lagrangian and constrained Hamiltonian equations of motion for a general nonrelativistic classical mechanical system subject to rheonomous holonomic constraints are derived in an easy and straightforward manner. The numerical integration of the constrained equations of motion are dis ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
The constrained Lagrangian and constrained Hamiltonian equations of motion for a general nonrelativistic classical mechanical system subject to rheonomous holonomic constraints are derived in an easy and straightforward manner. The numerical integration of the constrained equations of motion are discussed. It is shown how constraint errors introduced by the numerical integration can be avoided by introducing simple constraint correction schemes. As an example, the developed constrained methods are applied to the periodically driven inverted nlinked pendulum. It is demonstrated how the constrained methods leads to very efficient numerical algorithms. In the case of the nlinked pendulum the computational complexity using the constrained methods is O(n) compared to O(n³) using the conventional unconstrained approach.
Artificial Life and Historical Processes
 In J. Kelemen & P. Sosik (Eds.), Proceedings of the Sixth European Conference on Artificial Life
, 2001
"... Artificial Life is partly aimed at understanding the organisation and complexity of living processes. In this paper the concept of a historical process is discussed with the aim of providing a framework with which to approach diverse phenomena in organismic, ecological, and evolutionary contexts ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Artificial Life is partly aimed at understanding the organisation and complexity of living processes. In this paper the concept of a historical process is discussed with the aim of providing a framework with which to approach diverse phenomena in organismic, ecological, and evolutionary contexts. A historical process is such, not because it is subject to contingencies, nor because it may be explained in historical terms, but because it presents a special relation between its dynamics and changes in its own conditions of realisation. Such processes may lead to durable spontaneous patterns and novelty. It is argued that such patterns can provide powerful explanatory tools and that Artificial Life simulation techniques are well fitted for their exploration. To different degrees of explicitness, the central theme of much of the work that currently goes under the rubric of Artificial Life (AL) is the understanding of processes that lead to innovations, transitions, and spontane...
Lexical acquisition at the syntaxsemantics interface: diathesis alternations, subcategorization frames and selectional preferences
"... Dedicated to Klaus Kirchgässner on the occasion of his 70th birthday Abstract. We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T 3 on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated wit ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Dedicated to Klaus Kirchgässner on the occasion of his 70th birthday Abstract. We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T 3 on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S 1 action on the union of the nondegenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J 2dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J 2Hamiltonian is a collective Hamiltonian of the T 3 momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J 2 effect as geometric phases. Key words: Kepler vector field, derivation of variables, orbits dynamics and phases 1.
Tidal and TidalResonant Effects in Coalescing Binaries
, 2008
"... Tidal and tidalresonant effects in coalescing compact binary systems are investigated by direct numerical integration of the equations of motion. For the stars polytropic models are used. The tidal effects are found to be dominated by the (nonresonant) fmodes. The effect of the gmodetidal reson ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Tidal and tidalresonant effects in coalescing compact binary systems are investigated by direct numerical integration of the equations of motion. For the stars polytropic models are used. The tidal effects are found to be dominated by the (nonresonant) fmodes. The effect of the gmodetidal resonances is obtained. The tidal interaction is shown to be of interest especially for lowmass binaries. There exists a characteristic final plunge orbit beyond which the system cannot remain stable even if radiation reaction is not taken into account; in agreement with results obtained by Lai et al. (1993). The importance of the investigated effects for the observation of gravitational waves on Earth is discussed.
EXPONENTIAL STABILIZATION OF THE INERTIA WHEEL PENDULUM USING DYNAMIC SURFACE CONTROL
, 2006
"... This paper considers the stabilization problem of Inertia Wheel Pendulum, a widely studied benchmark nonlinear system. It is a classical example of a flat underactuated mechanical system, for which the design of control law becomes a challenging task owing to its underactuated nature. A novel nonlin ..."
Abstract
 Add to MetaCart
This paper considers the stabilization problem of Inertia Wheel Pendulum, a widely studied benchmark nonlinear system. It is a classical example of a flat underactuated mechanical system, for which the design of control law becomes a challenging task owing to its underactuated nature. A novel nonlinear controller design, fusing the recently introduced Dynamic Surface Control and the Control Lyapunov Function method, is presented as the solution. Stability is analyzed using concepts from Singular Perturbation Theory. The proposed design procedure is shown to be simpler and more intuitive than existing designs. Advantages over conventional Energy Shaping and Backstepping controllers are analyzed theoretically and verified using numerical simulations.