Conservation laws for self-adjoint first order evolution equations

In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using the recent Ibragimov's Theorem on conservation laws, we establish the conservation laws of the equations admiting self-adjoint equations. We illustrate our results applying them to the inviscid Burgers' equation. In particular an infinite number of new symmetries of these equations are found and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of Nonlinear Mathematical Physic

Projective analysis and preliminary group classification of the nonlinear fin equation ut=(E(u)ux)x+h(x)uu_t=(E(u)u_x)_x + h(x)u

In this paper we investigate for further symmetry properties of the nonlinear fin equations of the general form $u_t=(E(u)u_x)_x + h(x)u$ rather than recent works on these equations. At first, we study the projective (fiber-preserving) symmetry to show that equations of the above class can not be reduced to linear equations. Then we determine an equivalence classification which admits an extension by one dimension of the principal Lie algebra of the equation. The invariant solutions of equivalence transformations and classification of nonlinear fin equations among with additional operators are also given.Comment: 9 page

Realizations of Real Low-Dimensional Lie Algebras

Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in vector fields on a space of an arbitrary (finite) number of variables. Our classification amends and essentially generalizes earlier works on the subject. Known results on classification of low-dimensional real Lie algebras, their automorphisms, differentiations, ideals, subalgebras and realizations are reviewed.Comment: LaTeX2e, 39 pages. Essentially exetended version. Misprints in Appendix are correcte

Implicit trust in clinical decision-making by multidisciplinary teams

In clinical practice, decision-making is not performed by individual knowers but by an assemblage of people and instruments in which no one member has full access to every piece of evidence. This is due to decision making teams consisting of members with different kinds of expertise, as well as to organisational and time constraints. This raises important questions for the epistemology of medicine, which is inherently social in this kind of setting, and implies epistemic dependence on others. Trust in these contexts is a highly complex social practice, involving different forms of relationships between trust and reasons for trust: based on reasons, and not based on reasons; based on reasons that are easily accessible to reflection and others that are not. In this paper, we focus on what it means to have reasons to trust colleagues in an established clinical team, collectively supporting or carrying out every day clinical decision-making. We show two important points about these reasons, firstly, they are not sought or given in advance of a situation of epistemic dependence, but are established within these situations; secondly they are implicit in the sense of being contained or nested within other actions that are not directly about trusting another person. The processes of establishing these reasons are directly about accomplishing a task, and indirectly about trusting someone else’s expertise or competence. These processes establish a space of reasons within which what it means to have reasons for trust, or not, gains a meaning and traction in these team-work settings. Based on a qualitative study of decision-making in image assisted diagnosis and treatment of a complex disease called pulmonary hypertension (PH), we show how an intersubjective framework, or ‘space of reasons’ is established through team members forging together a common way of identifying and dealing with evidence. In dealing with images as a central diagnostic tool, this also involves a common way of looking at the images, a common mode or style of perception. These frameworks are developed through many iterations of adjusting and calibrating interpretations in relation to those of others, establishing what counts as evidence, and ranking different kinds of evidence. Implicit trust is at work throughout this process. Trusting the expertise of others in clinical decision-making teams occurs while the members of the team are busy on other tasks, most importantly, building up a framework of common modes of seeing, and common ways of identifying and assessing evidence emerge. It is only in this way that trusting or mistrusting becomes meaningful in these contexts, and that a framework for epistemic dependence is established

Implicit trust in clinical decision-making by multidisciplinary teams

In clinical practice, decision-making is not performed by individual knowers but by an assemblage of people and instruments in which no one member has full access to every piece of evidence. This is due to decision making teams consisting of members with different kinds of expertise, as well as to organisational and time constraints. This raises important questions for the epistemology of medicine, which is inherently social in this kind of setting, and implies epistemic dependence on others. Trust in these contexts is a highly complex social practice, involving different forms of relationships between trust and reasons for trust: based on reasons, and not based on reasons; based on reasons that are easily accessible to reflection and others that are not. In this paper, we focus on what it means to have reasons to trust colleagues in an established clinical team, collectively supporting or carrying out every day clinical decision-making. We show two important points about these reasons, firstly, they are not sought or given in advance of a situation of epistemic dependence, but are established within these situations; secondly they are implicit in the sense of being contained or nested within other actions that are not directly about trusting another person. The processes of establishing these reasons are directly about accomplishing a task, and indirectly about trusting someone else’s expertise or competence. These processes establish a space of reasons within which what it means to have reasons for trust, or not, gains a meaning and traction in these team-work settings. Based on a qualitative study of decision-making in image assisted diagnosis and treatment of a complex disease called pulmonary hypertension (PH), we show how an intersubjective framework, or ‘space of reasons’ is established through team members forging together a common way of identifying and dealing with evidence. In dealing with images as a central diagnostic tool, this also involves a common way of looking at the images, a common mode or style of perception. These frameworks are developed through many iterations of adjusting and calibrating interpretations in relation to those of others, establishing what counts as evidence, and ranking different kinds of evidence. Implicit trust is at work throughout this process. Trusting the expertise of others in clinical decision-making teams occurs while the members of the team are busy on other tasks, most importantly, building up a framework of common modes of seeing, and common ways of identifying and assessing evidence emerge. It is only in this way that trusting or mistrusting becomes meaningful in these contexts, and that a framework for epistemic dependence is established

Conceptual design report for the LUXE experiment

This Conceptual Design Report describes LUXE (Laser Und XFEL Experiment), an experimental campaign that aims to combine the high-quality and high-energy electron beam of the European XFEL with a powerful laser to explore the uncharted terrain of quantum electrodynamics characterised by both high energy and high intensity. We will reach this hitherto inaccessible regime of quantum physics by analysing high-energy electron-photon and photon-photon interactions in the extreme environment provided by an intense laser focus. The physics background and its relevance are presented in the science case which in turn leads to, and justifies, the ensuing plan for all aspects of the experiment: Our choice of experimental parameters allows (i) field strengths to be probed where the coupling to charges becomes non-perturbative and (ii) a precision to be achieved that permits a detailed comparison of the measured data with calculations. In addition, the high photon flux predicted will enable a sensitive search for new physics beyond the Standard Model. The initial phase of the experiment will employ an existing 40 TW laser, whereas the second phase will utilise an upgraded laser power of 350 TW. All expectations regarding the performance of the experimental set-up as well as the expected physics results are based on detailed numerical simulations throughout

Conceptual design report for the LUXE experiment

AbstractThis Conceptual Design Report describes LUXE (Laser Und XFEL Experiment), an experimental campaign that aims to combine the high-quality and high-energy electron beam of the European XFEL with a powerful laser to explore the uncharted terrain of quantum electrodynamics characterised by both high energy and high intensity. We will reach this hitherto inaccessible regime of quantum physics by analysing high-energy electron-photon and photon-photon interactions in the extreme environment provided by an intense laser focus. The physics background and its relevance are presented in the science case which in turn leads to, and justifies, the ensuing plan for all aspects of the experiment: Our choice of experimental parameters allows (i) field strengths to be probed where the coupling to charges becomes non-perturbative and (ii) a precision to be achieved that permits a detailed comparison of the measured data with calculations. In addition, the high photon flux predicted will enable a sensitive search for new physics beyond the Standard Model. The initial phase of the experiment will employ an existing 40 TW laser, whereas the second phase will utilise an upgraded laser power of 350 TW. All expectations regarding the performance of the experimental set-up as well as the expected physics results are based on detailed numerical simulations throughout.</jats:p