Classical Mechanics

Kibble, T. W. B.; Berkshire, Frank

doi:10.1142/p310

Cited by 139 publications

(119 citation statements)

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“…For the case α = 1 we get the usual damped oscillator [11]. For such a normal case two types of behaviors: the under-damped and the over-damped motions are found.…”

Section: Introductionmentioning

confidence: 90%

“…The use of fractional-differential equations like Eqs. (8,11) became quite common in recent years [8,22], especially in the context of anomalous diffusion [8,23,24]. Several other fractional oscillator equations were considered in the literature [25,26,27] and general solutions for fractional-differential equations of the type Eq.…”

Section: Stat-mech] 26 Feb 2008mentioning

confidence: 99%

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Fractional Langevin equation: Overdamped, underdamped, and critical behaviors

2008

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The dynamical phase diagram of the fractional Langevin equation is investigated for harmonically bound particle. It is shown that critical exponents mark dynamical transitions in the behavior of the system. Four different critical exponents are found. (i) αc = 0.402 ± 0.002 marks a transition to a non-monotonic under-damped phase, (ii) αR = 0.441... marks a transition to a resonance phase when an external oscillating field drives the system, (iii) αχ 1 = 0.527... and (iv) αχ 2 = 0.707... marks transition to a double peak phase of the "loss" when such an oscillating field present. As a physical explanation we present a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing over-damped, under-damped regimes, motion and resonances, show behaviors different from normal.

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“…For the case α = 1 we get the usual damped oscillator [11]. For such a normal case two types of behaviors: the under-damped and the over-damped motions are found.…”

Section: Introductionmentioning

confidence: 90%

Section: Stat-mech] 26 Feb 2008mentioning

confidence: 99%

Fractional Langevin equation: Overdamped, underdamped, and critical behaviors

2008

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“…The exchange cannot occur if the strings meet with very large relative velocity. This may have important implications for the evolution of cosmic superstring networks and non-abelian string networks.There has been renewed interest in cosmic strings, both because of tentative observational evidence [1,2] and because they appear to arise naturally in scenarios based on string theory [3,4,5], as well as in field theories [6,7]. Although the recent close inspection by the Hubble Space Telescope of the area of interest in [1, 2] appears to indicate that no string is present [8], the possibility remains that strings may be found through other types of observation in the Universe.…”

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confidence: 99%

Collisions of Strings with Y Junctions

2006

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We study the dynamics of Nambu-Goto strings with junctions at which three strings meet. In particular, we exhibit one simple exact solution and examine the process of intercommuting of two straight strings, in which they exchange partners but become joined by a third string. We show that there are important kinematical constraints on this process. The exchange cannot occur if the strings meet with very large relative velocity. This may have important implications for the evolution of cosmic superstring networks and non-abelian string networks.There has been renewed interest in cosmic strings, both because of tentative observational evidence [1,2] and because they appear to arise naturally in scenarios based on string theory [3,4,5], as well as in field theories [6,7]. Although the recent close inspection by the Hubble Space Telescope of the area of interest in [1, 2] appears to indicate that no string is present [8], the possibility remains that strings may be found through other types of observation in the Universe. Moreover, in the scenarios based on string theory, several different kinds of cosmic strings may appear, in particular F-and D-strings and (p, q) composites, formed of p F-strings and q D-strings [9]. In such cases, junctions may form at which three different strings meet. Such junctions can also appear in networks of 'non-Abelian strings', for which the fundamental group π 1 (M) of the manifold of degenerate vacua, which classifies the strings, is non-Abelian [10,11]. Several papers have considered the evolution of networks of strings with junctions [12,13,14,15], in particular the question of whether such a network would evolve to a scaling regime as expected for an ordinary cosmic-string network [16].In this paper, we study the dynamics of three-string junctions in a local-string network, that is to say one where the individual strings have no long-range interactions and are well described by the Nambu-Goto action. Our approach is similar to the one adopted by 't Hooft in Ref. [17], in which he represented baryons as pieces of open string connected at one common point. However, our method differs from his in significant ways. In particular, our treatment applies to strings with different tensions, and we use a temporal world-sheet coordinate equal to the global time. For ordinary cosmic strings, the existence of exact solutions for oscillating string loops [18,19] was important in analyzing the likely behavior of loops in general, and some exact solutions are also known for open strings with junctions. Here we give one very simple example of an exact solution, but our main focus is on the question of what happens when two strings cross.When two ordinary cosmic strings intersect they normally 'intercommute', or exchange partners [20,21,22,23,24]. But for the strings we are considering this is generally impossible. What we expect instead is that the strings will become joined by a third string. The dynamical problem of finding the intercommuting probability for junction-forming strings has been dis...

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“…In physics these assumptions diverge into two schools of thought: classical mechanics and quantum mechanics (Bohm, 1973;Raković, 2007). Classical mechanics considers the world to be reducible to machine-like parts which are measurable, orderable, classifiable, and which operate under immutable laws (Bohm, 1971;Kibble & Berkshire, 2005;Zaman, 2001). Quantum mechanics on the other hand arises from an organismic view where everything is highly connected (Arntz, Chasse & Vincente, 2006) and operates upon paradoxical laws-laws which operate in time and space and are governed by a unique set of quantum principles.…”

Section: Quantum Mechanics: a Foundation For Understanding The Quantumentioning

confidence: 99%

Viewing Learning Through a New Lens: The Quantum Perspective of Learing

Janzen¹,

Edwards²

2012

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We are living in a quantum world where virtuality allows us to transcend time and space. Boundaries, which were considered to be predetermined, are no longer absolute. This has important implications for the field of education as educators advance e-learning. However, education theory has been outpaced by practice. In this paper the authors propose a new learning perspective-the quantum perspective of learning which moves beyond current popular educational theories of constructivism (Siemens, 2005) and connectivism (Vygotsky, 1978). The five assumptions of the quantum perspective of learning are explored. Specifically, learning is multi-dimensional, occurs in various planes simultaneously, consists of potentialities which exist infinitely, is holistic/holographic in nature and is patterned within holographic realities, and learning environments are living systems. Implications that arise from this perspective are discussed.

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Classical Mechanics

Cited by 139 publications

References 0 publications

Fractional Langevin equation: Overdamped, underdamped, and critical behaviors

Fractional Langevin equation: Overdamped, underdamped, and critical behaviors

Collisions of Strings with Y Junctions

Viewing Learning Through a New Lens: The Quantum Perspective of Learing

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