Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators

2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48.

p Dissipative operator

In this paper the authors prove that the generalized positive p selfadjoint (GPpS) operators in Banach space satisfy the generalized Schwarz inequality, solve the maximal dissipative extension representation of p dissipative operators in Banach space by using the inequality and introducing the generalized indefinite inner product (GIIP) space, and apply the result to a certain type of Schrodinger operator.

On the statistical and transport properties of a non-dissipative Fermi-Ulam model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

(Non)-Dissipative Hydrodynamics on Embedded Surfaces

We construct the theory of dissipative hydrodynamics of uncharged fluids living on embedded space-time surfaces to first order in a derivative expansion in the case of codimension-1 surfaces (including fluid membranes) and the theory of non-dissipative hydrodynamics to second order in a derivative expansion in the case of codimension higher than one under the assumption of no angular momenta in transverse directions to the surface. This construction includes the elastic degrees of freedom, and hence the corresponding transport coefficients, that take into account transverse fluctuations of the geometry where the fluid lives. Requiring the second law of thermodynamics to be satisfied leads us to conclude that in the case of codimension-1 surfaces the stress-energy tensor is characterized by 2 hydrodynamic and 1 elastic independent transport coefficient to first order in the expansion while for codimension higher than one, and for non-dissipative flows, the stress-energy tensor is characterized by 7 hydrodynamic and 3 elastic independent transport coefficients to second order in the expansion. Furthermore, the constraints imposed between the stress-energy tensor, the bending moment and the entropy current of the fluid by these extra non-dissipative contributions are fully captured by equilibrium partition functions. This analysis constrains the Young modulus which can be measured from gravity by elastically perturbing black branes.

Bifurcations in the non-dissipative dynamics of ultra cold atoms

We present the first experimental observation of several bifurcations in a controllable non-linear Hamiltonian system. Dynamics of cold atoms are used to test predictions of non-linear, non-dissipative Hamiltonian dynamics.

On the Character of Growth of a Non-Contracting Semigroup

2000 Mathematics Subject Classification: 47A45.

Boundary crisis and suppression of Fermi acceleration in a dissipative two-dimensional non-integrable time-dependent billiard

Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non-dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time-dependent billiards. (C) 2010 Elsevier B.V. All rights reserved.

Suppressing Fermi acceleration in a two-dimensional non-integrable time-dependent oval-shaped billiard with inelastic collisions

Some dynamical properties of a classical particle confined inside a closed region with an oval-shaped boundary are studied. We have considered both the static and time-dependent boundaries. For the static case, the condition that destroys the invariant spanning curves in the phase space was obtained. For the time-dependent perturbation, two situations were considered: (i) non-dissipative and (ii) dissipative. For the non-dissipative case, our results show that Fermi acceleration is observed. When dissipation, via inelastic collisions, is introduced Fermi acceleration is suppressed. The behaviour of the average velocity for both the dissipative as well as the non-dissipative dynamics is described using the scaling approach. (C) 2009 Elsevier B.V. All rights reserved.

Parameter space for a dissipative Fermi-Ulam model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A dissipative Fermi-Ulam model under two different kinds of dissipation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Linear non-local diffusion problems in metric measure spaces

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator. We then study the solutions of linear evolution non-local diffusion problems, with emphasis on similarities and differences with the standard heat equation in smooth domains. In particular, we prove weak and strong maximum principles and describe the asymptotic behaviour using spectral methods.

Negotiating social and moral order in internet relay chat

Although internet chat is a significant aspect of many internet users’ lives, the manner in which participants in quasi-synchronous chat situations orient to issues of social and moral order remains to be studied in depth. The research presented here is therefore at the forefront of a continually developing area of study. This work contributes new insights into how members construct and make accountable the social and moral orders of an adult-oriented Internet Relay Chat (IRC) channel by addressing three questions: (1) What conversational resources do participants use in addressing matters of social and moral order? (2) How are these conversational resources deployed within IRC interaction? and (3) What interactional work is locally accomplished through use of these resources? A survey of the literature reveals considerable research in the field of computer-mediated communication, exploring both asynchronous and quasi-synchronous discussion forums. The research discussed represents a range of communication interests including group and collaborative interaction, the linguistic construction of social identity, and the linguistic features of online interaction. It is suggested that the present research differs from previous studies in three ways: (1) it focuses on the interaction itself, rather than the ways in which the medium affects the interaction; (2) it offers turn-by-turn analysis of interaction in situ; and (3) it discusses membership categories only insofar as they are shown to be relevant by participants through their talk. Through consideration of the literature, the present study is firmly situated within the broader computer-mediated communication field. Ethnomethodology, conversation analysis and membership categorization analysis were adopted as appropriate methodological approaches to explore the research focus on interaction in situ, and in particular to investigate the ways in which participants negotiate and co-construct social and moral orders in the course of their interaction. IRC logs collected from one chat room were analysed using a two-pass method, based on a modification of the approaches proposed by Pomerantz and Fehr (1997) and ten Have (1999). From this detailed examination of the data corpus three interaction topics are identified by means of which participants clearly orient to issues of social and moral order: challenges to rule violations, ‘trolling’ for cybersex, and experiences regarding the 9/11 attacks. Instances of these interactional topics are subjected to fine-grained analysis, to demonstrate the ways in which participants draw upon various interactional resources in their negotiation and construction of channel social and moral orders. While these analytical topics stand alone in individual focus, together they illustrate different instances in which participants’ talk serves to negotiate social and moral orders or collaboratively construct new orders. Building on the work of Vallis (2001), Chapter 5 illustrates three ways that rule violation is initiated as a channel discussion topic: (1) through a visible violation in open channel, (2) through an official warning or sanction by a channel operator regarding the violation, and (3) through a complaint or announcement of a rule violation by a non-channel operator participant. Once the topic has been initiated, it is shown to become available as a topic for others, including the perceived violator. The fine-grained analysis of challenges to rule violations ultimately demonstrates that channel participants orient to the rules as a resource in developing categorizations of both the rule violation and violator. These categorizations are contextual in that they are locally based and understood within specific contexts and practices. Thus, it is shown that compliance with rules and an orientation to rule violations as inappropriate within the social and moral orders of the channel serves two purposes: (1) to orient the speaker as a group member, and (2) to reinforce the social and moral orders of the group. Chapter 6 explores a particular type of rule violation, solicitations for ‘cybersex’ known in IRC parlance as ‘trolling’. In responding to trolling violations participants are demonstrated to use affiliative and aggressive humour, in particular irony, sarcasm and insults. These conversational resources perform solidarity building within the group, positioning non-Troll respondents as compliant group members. This solidarity work is shown to have three outcomes: (1) consensus building, (2) collaborative construction of group membership, and (3) the continued construction and negotiation of existing social and moral orders. Chapter 7, the final data analysis chapter, offers insight into how participants, in discussing the events of 9/11 on the actual day, collaboratively constructed new social and moral orders, while orienting to issues of appropriate and reasonable emotional responses. This analysis demonstrates how participants go about ‘doing being ordinary’ (Sacks, 1992b) in formulating their ‘first thoughts’ (Jefferson, 2004). Through sharing their initial impressions of the event, participants perform support work within the interaction, in essence working to normalize both the event and their initial misinterpretation of it. Normalising as a support work mechanism is also shown in relation to participants constructing the ‘quiet’ following the event as unusual. Normalising is accomplished by reference to the indexical ‘it’ and location formulations, which participants use both to negotiate who can claim to experience the ‘unnatural quiet’ and to identify the extent of the quiet. Through their talk participants upgrade the quiet from something legitimately experienced by one person in a particular place to something that could be experienced ‘anywhere’, moving the phenomenon from local to global provenance. With its methodological design and detailed analysis and findings, this research contributes to existing knowledge in four ways. First, it shows how rules are used by participants as a resource in negotiating and constructing social and moral orders. Second, it demonstrates that irony, sarcasm and insults are three devices of humour which can be used to perform solidarity work and reinforce existing social and moral orders. Third, it demonstrates how new social and moral orders are collaboratively constructed in relation to extraordinary events, which serve to frame the event and evoke reasonable responses for participants. And last, the detailed analysis and findings further support the use of conversation analysis and membership categorization as valuable methods for approaching quasi-synchronous computer-mediated communication.