Pure-radiation gravitational fields with a simple twist and a Killing vector

Pure-radiation solutions are found, exploiting the analogy with the Euler- Darboux equation for aligned colliding plane waves and the Euler-Tricomi equation in hydrodynamics of two-dimensional flow. They do not depend on one of the spacelike coordinates and comprise the Hauser solution as a special subcase.Comment: revtex, 9 page

High shock release in ultrafast laser irradiated metals: Scenario for material ejection

We present one-dimensional numerical simulations describing the behavior of solid matter exposed to subpicosecond near infrared pulsed laser radiation. We point out to the role of strong isochoric heating as a mechanism for producing highly non-equilibrium thermodynamic states. In the case of metals, the conditions of material ejection from the surface are discussed in a hydrodynamic context, allowing correlation of the thermodynamic features with ablation mechanisms. A convenient synthetic representation of the thermodynamic processes is presented, emphasizing different competitive pathways of material ejection. Based on the study of the relaxation and cooling processes which constrain the system to follow original thermodynamic paths, we establish that the metal surface can exhibit several kinds of phase evolution which can result in phase explosion or fragmentation. An estimation of the amount of material exceeding the specific energy required for melting is reported for copper and aluminum and a theoretical value of the limit-size of the recast material after ultrashort laser irradiation is determined. Ablation by mechanical fragmentation is also analysed and compared to experimental data for aluminum subjected to high tensile pressures and ultrafast loading rates. Spallation is expected to occur at the rear surface of the aluminum foils and a comparison with simulation results can determine a spall strength value related to high strain rates

Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions

In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and supersymmetric versions of this hydrodynamical model are analyzed through the use of group-theoretical methods applied to partial differential equations involving both bosonic and fermionic variables. More specifically, we compute the Lie superalgebras of both models and perform classifications of their respective subalgebras. A systematic use of the subalgebra structures allow us to construct several classes of invariant solutions, including travelling waves, centered waves and solutions involving monomials, exponentials and radicals.Comment: 30 page

Commensurability and beyond: from Mises and Neurath to the future of the socialist calculation debate

Mises' 'calculation argument' against socialism argues that monetary calculation is indispensable as a commensurable unit for evaluating factors of production. This is not due to his conception of rationality being purely 'algorithmic,' for it accommodates non-monetary, incommensurable values. Commensurability is needed, rather, as an aid in the face of economic complexity. The socialist Neurath's response to Mises is unsatisfactory in rejecting the need to explore possible non-market techniques for achieving a certain degree of commensurability. Yet Neurath's contribution is valuable in emphasizing the need for a balanced, comparative approach to the question of market versus non-market that puts the commensurability question in context. These central issues raised by adversaries in the early socialist calculation debate have continued relevance for the contemporary discussion

Multidimensional simple waves in fully relativistic fluids

A special version of multi--dimensional simple waves given in [G. Boillat, {\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed for fully relativistic fluid and plasma flows. Three essential modes: vortex, entropy and sound modes are derived where each of them is different from its nonrelativistic analogue. Vortex and entropy modes are formally solved in both the laboratory frame and the wave frame (co-moving with the wave front) while the sound mode is formally solved only in the wave frame at ultra-relativistic temperatures. In addition, the surface which is the boundary between the permitted and forbidden regions of the solution is introduced and determined. Finally a symmetry analysis is performed for the vortex mode equation up to both point and contact transformations. Fundamental invariants and a form of general solutions of point transformations along with some specific examples are also derived.Comment: 21 page

Generalized probabilities taking values in non-Archimedean fields and topological groups

We develop an analogue of probability theory for probabilities taking values in topological groups. We generalize Kolmogorov's method of axiomatization of probability theory: main distinguishing features of frequency probabilities are taken as axioms in the measure-theoretic approach. We also present a review of non-Kolmogorovian probabilistic models including models with negative, complex, and $p$-adic valued probabilities. The latter model is discussed in details. The introduction of $p$-adic (as well as more general non-Archimedean) probabilities is one of the main motivations for consideration of generalized probabilities taking values in topological groups which are distinct from the field of real numbers. We discuss applications of non-Kolmogorovian models in physics and cognitive sciences. An important part of this paper is devoted to statistical interpretation of probabilities taking values in topological groups (and in particular in non-Archimedean fields)

Multimode solutions of first-order elliptic quasilinear systems obtained from Riemann invariants

Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links between two techniques, that of the symmetry reduction method and of the generalized method of characteristics. A variant of the conditional symmetry method for constructing this type of solution is proposed. A specific feature of that approach is an algebraic-geometric point of view, which allows the introduction of specific first-order side conditions consistent with the original system of PDEs, leading to a generalization of the Riemann invariant method for solving elliptic homogeneous systems of PDEs. A further generalization of the Riemann invariants method to the case of inhomogeneous systems, based on the introduction of specific rotation matrices, enables us to weaken the integrability condition. It allows us to establish a connection between the structure of the set of integral elements and the possibility of constructing specific classes of simple mode solutions. These theoretical considerations are illustrated by the examples of an ideal plastic flow in its elliptic region and a system describing a nonlinear interaction of waves and particles. Several new classes of solutions are obtained in explicit form, including the general integral for the latter system of equations

Inversion of Randomly Corrugated Surfaces Structure from Atom Scattering Data

The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The results suggest that atom (and in particular He) scattering can be used profitably to study hitherto unexplored forms of complex surface disorder.Comment: 10 pages, no figures. Related papers available at http://neon.cchem.berkeley.edu/~dan

Unlocking value from machines: business models and the industrial internet of things

In this article we argue that the Industrial Internet of Things (IIoT) offers new opportunities and harbors threats that companies are not able to address with existing business models. Entrepreneurship and Transaction Cost Theories are used to explore the conditions for designing nonownership business models for the emerging IIoT with its implications for sharing uncertain opportunities and downsides, and for transforming these uncertainties into business opportunities. Nonownership contracts are introduced as the basis for business model design and are proposed as an architecture for the productive sharing of uncertainties in IIoT manufacturing networks. The following three main types of IIoT-enabled business models were identified: (1) Provision of manufacturing assets, maintenance and repair, and their operation, (2) innovative information and analytical services that help manufacturing (e.g., based on artificial intelligence, big data, and analytics), and (3) new services targeted at end-users (e.g., offering efficient customization by integrating end-users into the manufacturing and supply chain ecosystem)