Explicit Bounds on the Number of Degrees of Freedom and the Dimension of Attractors of Some Physical Systems

1997 ◽  
pp. 380-464
Author(s):  
Roger Temam
Keyword(s):  
Degrees Of Freedom ◽  
Physical Systems ◽  
Explicit Bounds

scholarly journals Exact mapping between a laser network loss rate and the classical XY Hamiltonian by laser loss control

Nanophotonics ◽  
2020 ◽  
Vol 9 (13) ◽  
pp. 4117-4126 ◽  
Author(s):  
Igor Gershenzon ◽  
Geva Arwas ◽  
Sagie Gadasi ◽  
Chene Tradonsky ◽  
Asher Friesem ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Loss Rate ◽  
Oscillation Amplitude ◽  
Xy Model ◽  
Spin Hamiltonian ◽  
Laser Oscillator ◽  
Physical Systems ◽  
Network State ◽  
Spin Hamiltonians ◽  
Loss Control

AbstractRecently, there has been growing interest in the utilization of physical systems as heuristic optimizers for classical spin Hamiltonians. A prominent approach employs gain-dissipative optical oscillator networks for this purpose. Unfortunately, these systems inherently suffer from an inexact mapping between the oscillator network loss rate and the spin Hamiltonian due to additional degrees of freedom present in the system such as oscillation amplitude. In this work, we theoretically analyze and experimentally demonstrate a scheme for the alleviation of this difficulty. The scheme involves control over the laser oscillator amplitude through modification of individual laser oscillator loss. We demonstrate this approach in a laser network classical XY model simulator based on a digital degenerate cavity laser. We prove that for each XY model energy minimum there corresponds a unique set of laser loss values that leads to a network state with identical oscillation amplitudes and to phase values that coincide with the XY model minimum. We experimentally demonstrate an eight fold improvement in the deviation from the minimal XY energy by employing our proposed solution scheme.

Computation and cognition: issues in the foundations of cognitive science

1980 ◽  
Vol 3 (1) ◽  
pp. 111-132 ◽  
Author(s):  
Zenon W. Pylyshyn
Keyword(s):  
Tacit Knowledge ◽  
Degrees Of Freedom ◽  
Ad Hoc ◽  
Physical Systems ◽  
Symbolic Representations ◽  
Natural Domain ◽  
Human Functioning ◽  
Biological Laws ◽  
Post Hoc ◽  
Level Of Analysis

AbstractThe computational view of mind rests on certain intuitions regarding the fundamental similarity between computation and cognition. We examine some of these intuitions and suggest that they derive from the fact that computers and human organisms are both physical systems whose behavior is correctly described as being governed by rules acting on symbolic representations. Some of the implications of this view are discussed. It is suggested that a fundamental hypothesis of this approach (the “proprietary vocabulary hypothesis”) is that there is a natural domain of human functioning (roughly what we intuitively associate with perceiving, reasoning, and acting) that can be addressed exclusively in terms of a formal symbolic or algorithmic vocabulary or level of analysis.Much of the paper elaborates various conditions that need to be met if a literal view of mental activity as computation is to serve as the basis for explanatory theories. The coherence of such a view depends on there being a principled distinction between functions whose explanation requires that we posit internal representations and those that we can appropriately describe as merely instantiating causal physical or biological laws. In this paper the distinction is empirically grounded in a methodological criterion called the “cognitive impenetrability condition.” Functions are said to be cognitively impenetrable if they cannot be influenced by such purely cognitive factors as goals, beliefs, inferences, tacit knowledge, and so on. Such a criterion makes it possible to empirically separate the fixed capacities of mind (called its “functional architecture”) from the particular representations and algorithms used on specific occasions. In order for computational theories to avoid being ad hoc, they must deal effectively with the “degrees of freedom” problem by constraining the extent to which they can be arbitrarily adjusted post hoc to fit some particular set of observations. This in turn requires that the fixed architectural function and the algorithms be independently validated. It is argued that the architectural assumptions implicit in many contemporary models run afoul of the cognitive impenetrability condition, since the required fixed functions are demonstrably sensitive to tacit knowledge and goals. The paper concludes with some tactical suggestions for the development of computational cognitive theories.

scholarly journals WAVELESS APPROXIMATION THEORIES OF GRAVITY

2008 ◽  
Vol 17 (02) ◽  
pp. 265-273 ◽  
Author(s):  
JAMES A. ISENBERG
Keyword(s):  
Gravitational Field ◽  
Gravitational Radiation ◽  
Elliptic Equations ◽  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Accurate Approximation ◽  
Time Step ◽  
Einstein Theory ◽  
Physical Systems ◽  
Theories Of Gravity

The analysis of a general multibody physical system governed by Einstein's equations is quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties — many coupled degrees of freedom, dynamic instability — are associated with the presence of gravitational waves. We have developed a number of "waveless approximation theories" (WAT's) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.

scholarly journals Energy Consumption and Tailpipe Emission Reductions by Personalized Control of Connected Vehicles

2017 ◽  
Vol 139 (09) ◽  
pp. S5-S11
Author(s):  
Junmin Wang
Keyword(s):  
Energy Consumption ◽  
Control Systems ◽  
Degrees Of Freedom ◽  
Connected Vehicles ◽  
Emission Reductions ◽  
Physical Systems ◽  
Information Richness ◽  
Optimization And Control ◽  
Vehicle Automation ◽  
And Control

This article demonstrates several approaches to the vehicle energy consumption and tailpipe emission reduction opportunities. The article leverages the vehicle storage dynamics through smart and personalized optimization and control approaches in the context of connected vehicles. Recent advances in vehicle connectivity and automation have brought unprecedented information richness and new degrees of freedom that can be synergized with insightful understanding of vehicle powertrain and aftertreatment physical systems. Vehicle automation also provides new degrees of freedom that can be further leveraged by the vehicle control systems to improve vehicle energy efficiency and reduce tailpipe emissions. While vehicle automation levels probably will keep increasing, humans will still be involved in vehicle operations at various levels for the foreseeable future. The prediction of future vehicle’s power demand based on vehicle connectivity can significantly benefit tailpipe emission reductions and fuel economy.

scholarly journals Spacetime Quantum Reference Frames and superpositions of proper times

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 508
Author(s):  
Flaminia Giacomini
Keyword(s):  
Hilbert Space ◽  
Reference Frame ◽  
Degrees Of Freedom ◽  
Reference Frames ◽  
Proper Time ◽  
Relativistic Quantum ◽  
Dynamical Evolution ◽  
Quantum Superposition ◽  
Local Frame ◽  
Physical Systems

In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames (QRFs), through which spacetime can be given an operational meaning. Here, we introduce the notion of a spacetime quantum reference frame, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of allowing us to describe the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the parameter in which the rest of the physical systems evolves coincides with the proper time of the particle taken as the QRF. Crucially, the proper times in two different QRFs are not related by a standard transformation, but they might be in a quantum superposition one with respect to the other.Concretely, we consider a system of N relativistic quantum particles in a weak gravitational field, and introduce a timeless formulation in which the global state of the N particles appears "frozen", but the dynamical evolution is recovered in terms of relational quantities. The position and momentum Hilbert space of the particles is used to fix the QRF via a transformation to the local frame of the particle such that the metric is locally inertial at the origin of the QRF. The internal Hilbert space corresponds to the clock space, which keeps the proper time in the local frame of the particle. Thanks to this fully relational construction we show how the remaining particles evolve dynamically in the relational variables from the perspective of the QRF. The construction proposed here includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we find that a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations can be observed in the QRF.

scholarly journals Does Universal Controllability of Physical Systems Prohibit Thermodynamic Cycles?

2018 ◽  
Vol 25 (03) ◽  
pp. 1850016
Author(s):  
Dominik Janzing ◽  
Paweł Wocjan
Keyword(s):  
Degrees Of Freedom ◽  
Thermodynamic Cycle ◽  
Two Dimensions ◽  
Noisy Environment ◽  
Target Region ◽  
Physical Systems ◽  
Thermodynamic Cycles ◽  
Strong Notion ◽  
The Cost ◽  
And Control

Here we study the thermodynamic cost of computation and control using ‘physically universal’ cellular automata (CAs) or Hamiltonians. The latter were previously defined as systems that admit the implementation of any desired transformation on a finite target region by first initializing the state of the surrounding and then letting the system evolve according to its autonomous dynamics. This way, one obtains a model of control where each region can play both roles, the controller or the system to be controlled. In physically universal systems every degree of freedom is indirectly accessible by operating on the remaining degrees of freedom. In a nutshell, the thermodynamic cost of an operation is then given by the size of the region around the target region that needs to be initialized. In the meantime, physically universal CAs have been constructed by Schaeffer (in two dimensions) and Salo & Törmä (in one dimension). Here we show that in Schaeffer’s CA the cost for implementing n operations grows linearly in n, while operating in a thermodynamic cycle requires sublinear growth to ensure zero cost per operation in the limit n → ∞. Although this particular result need not hold for general physically universal CAs, this strong notion of universality does imply a certain kind of instability of information, which could result in lower bounds on the cost of protecting information from its noisy environment. The technical results of the paper are sparse and quite simple. The contribution of the paper is mainly conceptual and consists in illustrating the type of thermodynamic questions raised by models of control that rely on the concept of physical universality.

scholarly journals Informational architecture across non-living and living collectives

2021 ◽  
Author(s):  
Hyunju Kim ◽  
Gabriele Valentini ◽  
Jake Hanson ◽  
Sara Imari Walker
Keyword(s):  
Collective Behavior ◽  
Intelligent Systems ◽  
Degrees Of Freedom ◽  
Physical Models ◽  
Information Architecture ◽  
Biological Phenomenon ◽  
Future Directions ◽  
Collective Behaviors ◽  
Information Theoretic ◽  
Physical Systems

AbstractCollective behavior is widely regarded as a hallmark property of living and intelligent systems. Yet, many examples are known of simple physical systems that are not alive, which nonetheless display collective behavior too, prompting simple physical models to often be adopted to explain living collective behaviors. To understand collective behavior as it occurs in living examples, it is important to determine whether or not there exist fundamental differences in how non-living and living systems act collectively, as well as the limits of the intuition that can be built from simpler, physical examples in explaining biological phenomenon. Here, we propose a framework for comparing non-living and living collectives as a continuum based on their information architecture: that is, how information is stored and processed across different degrees of freedom. We review diverse examples of collective phenomena, characterized from an information-theoretic perspective, and offer views on future directions for quantifying living collective behaviors based on their informational structure.

scholarly journals Complex Dynamics and Statistics of 1-D Hamiltonian Lattices: Long Range Interactions and Supratransmission

2020 ◽  
Vol 23 (2) ◽  
pp. 133-148
Author(s):  
Anastasios Bountis
Keyword(s):  
Degrees Of Freedom ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Invariant Tori ◽  
Kam Theory ◽  
Small Perturbations ◽  
Physical Systems ◽  
Long Range Interactions ◽  
The 1960S ◽  
Ordered Motion

In this paper, I review a number of results that my co-workers and I have obtained in the field of 1-Dimensional (1D) Hamiltonian lattices. This field has grown in recent years, due to its importance in revealing many phenomena that concern the occurrence of chaotic behavior in conservative physical systems with a high number of degrees of freedom. After the establishment of the Kolomogorov-Arnol'd-Moser (KAM) theory in the 1960s, a wealth of results were obtained about such systems as small perturbations of completely integrable Ndegree- of-freedom Hamiltonians, where ordered motion is dominant in the form of invariant tori. Since the 1980s, however, and particularly in the last two decades, there has been great progress in understanding the properties of Hamiltonian 1D lattices far from the KAM regime, where "weak" and "strong" forms of chaos begin to play an increasingly significant role. It is the purpose of this review to address and highlight some of these advances, in which the author has made several contributions concerning the dynamics and statistics of these lattices.

scholarly journals Perturbation solutions of fifth order oscillatory nonlinear systems

2011 ◽  
Vol 16 (2) ◽  
pp. 123-134
Author(s):  
M. Ali Akbar ◽  
Sk. Tanzer Ahmed Siddique
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Weakly Nonlinear ◽  
Physical Systems ◽  
Oscillatory Systems ◽  
Engineering Problems ◽  
Kbm Method ◽  
Fifth Order ◽  
Method Show ◽  
Good Agreement

Oscillatory systems play an important role in the nature. Many engineering problems and physical systems of fifth degrees of freedom are oscillatory and their governing equations are fifth order nonlinear differential equations. To investigate the solution of fifth order weakly nonlinear oscillatory systems, in this article the Krylov–Bogoliubov–Mitropolskii (KBM) method has been extended and desired solution is found. An example is solved to illustrate the method. The results obtain by the extended KBM method show good agreement with those obtained by numerical method.

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