6,920 research outputs found
Discrete scale invariance and complex dimensions
We discuss the concept of discrete scale invariance and how it leads to
complex critical exponents (or dimensions), i.e. to the log-periodic
corrections to scaling. After their initial suggestion as formal solutions of
renormalization group equations in the seventies, complex exponents have been
studied in the eighties in relation to various problems of physics embedded in
hierarchical systems. Only recently has it been realized that discrete scale
invariance and its associated complex exponents may appear ``spontaneously'' in
euclidean systems, i.e. without the need for a pre-existing hierarchy. Examples
are diffusion-limited-aggregation clusters, rupture in heterogeneous systems,
earthquakes, animals (a generalization of percolation) among many other
systems. We review the known mechanisms for the spontaneous generation of
discrete scale invariance and provide an extensive list of situations where
complex exponents have been found. This is done in order to provide a basis for
a better fundamental understanding of discrete scale invariance. The main
motivation to study discrete scale invariance and its signatures is that it
provides new insights in the underlying mechanisms of scale invariance. It may
also be very interesting for prediction purposes.Comment: significantly extended version (Oct. 27, 1998) with new examples in
several domains of the review paper with the same title published in Physics
Reports 297, 239-270 (1998
A universal optical all-fiber omnipolarizer
Wherever the polarization properties of a light beam are of concern, polarizers and polarizing beamsplitters (PBS) are indispensable devices in linear-, nonlinear-and quantum-optical schemes. By the very nature of their operation principle, transformation of incoming unpolarized or partially polarized beams through these devices introduces large intensity variations in the fully polarized outcoming beam(s). Such intensity fluctuations are often detrimental, particularly when light is post-processed by nonlinear crystals or other polarization-sensitive optic elements. Here we demonstrate the unexpected capability of light to self-organize its own state-of-polarization, upon propagation in optical fibers, into universal and environmentally robust states, namely right and left circular polarizations. We experimentally validate a novel polarizing device-the Omnipolarizer, which is understood as a nonlinear dual-mode polarizing optical element capable of operating in two modes-as a digital PBS and as an ideal polarizer. Switching between the two modes of operation requires changing beam's intensity
The Cauchy-Lagrangian method for numerical analysis of Euler flow
A novel semi-Lagrangian method is introduced to solve numerically the Euler
equation for ideal incompressible flow in arbitrary space dimension. It
exploits the time-analyticity of fluid particle trajectories and requires, in
principle, only limited spatial smoothness of the initial data. Efficient
generation of high-order time-Taylor coefficients is made possible by a
recurrence relation that follows from the Cauchy invariants formulation of the
Euler equation (Zheligovsky & Frisch, J. Fluid Mech. 2014, 749, 404-430).
Truncated time-Taylor series of very high order allow the use of time steps
vastly exceeding the Courant-Friedrichs-Lewy limit, without compromising the
accuracy of the solution. Tests performed on the two-dimensional Euler equation
indicate that the Cauchy-Lagrangian method is more - and occasionally much more
- efficient and less prone to instability than Eulerian Runge-Kutta methods,
and less prone to rapid growth of rounding errors than the high-order Eulerian
time-Taylor algorithm. We also develop tools of analysis adapted to the
Cauchy-Lagrangian method, such as the monitoring of the radius of convergence
of the time-Taylor series. Certain other fluid equations can be handled
similarly.Comment: 30 pp., 13 figures, 45 references. Minor revision. In press in
Journal of Scientific Computin
Science Fictioning Singularities: The Diagrammatic Imaginaries of Physics
Data Loam focuses on the future of knowledge systems in texts about artificial intelligence, cybernetics, and cryptoeconomics – as a means of counteracting end-of-the-world fears
Numerical Identity: Process and Substance Metaphysics
Numerical identity is the non-relational sameness of an object to itself. It is concerned with understanding how entities undergo change and maintain their identity. In substance metaphysics, an entity is considered a substance with an essence and such an essence is the source of its power. However, such a framework fails to explain the sense in which an entity is still the entity it was, amidst changes. Those who claim that essence is unaffected by existence are faced with challenge of exploring the epistemic access to such an essence, which is questionable at best. Process metaphysics is a strong candidate for a theory that can ontologically explain regularity and change without appeal to essence. Process and its interactions is the main category. Every process is an emergent organization of constitutive interactions and is individuated on the basis of its interactive powers, that is, the ways in which it interacts with the world around it. Interactions are situated adaptation to changes. In this way, changes are crucial within process metaphysics and are included in the starting point of its investigation. What seems to the naked eyes as one-ness/singularity is a complex process where an organization of interactions is emerging from moment to moment by continually adapting to the changes around and within it. The question of numerical identity over time becomes valid only within substance metaphysics which has no space to accommodate change, due to its allegiance to essence
The Translocal Event and the Polyrhythmic Diagram
This thesis identifies and analyses the key creative protocols in translocal performance practice, and ends with suggestions for new forms of transversal live and mediated
performance practice, informed by theory. It argues that ontologies of emergence in dynamic systems nourish contemporary practice in the digital arts. Feedback
in self-organised, recursive systems and organisms elicit change, and change transforms. The arguments trace concepts from chaos and complexity theory to virtual multiplicity, relationality, intuition and individuation (in the work of Bergson, Deleuze, Guattari, Simondon, Massumi, and other process theorists). It then examines the intersection of methodologies in philosophy, science and art and the
radical contingencies implicit in the technicity of real-time, collaborative composition. Simultaneous forces or tendencies such as perception/memory, content/
expression and instinct/intellect produce composites (experience, meaning, and intuition- respectively) that affect the sensation of interplay. The translocal
event is itself a diagram - an interstice between the forces of the local and the global, between the tendencies of the individual and the collective. The translocal is
a point of reference for exploring the distribution of affect, parameters of control and emergent aesthetics. Translocal interplay, enabled by digital technologies and network protocols, is ontogenetic and autopoietic; diagrammatic and synaesthetic; intuitive and transductive. KeyWorx is a software application developed for realtime, distributed, multimodal media processing. As a technological tool created by artists, KeyWorx supports this intuitive type of creative experience: a real-time, translocal “jamming” that transduces the lived experience of a “biogram,” a synaesthetic hinge-dimension. The emerging aesthetics are processual – intuitive, diagrammatic and transversal
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