A variational formulation of relativistic hydrodynamics

We combine Taub's and Ray's variational approaches to relativistic hydrodynamics of perfect fluids into another simple formulation.Comment: 3 pages; published versio

Perfect magnetohydrodynamics as a field theory

We propose the generally covariant action for the theory of a self-coupled complex scalar field and electromagnetism which by virtue of constraints is equivalent, in the regime of long wavelengths, to perfect magnetohydrodynamics (MHD). We recover from it the Euler equation with Lorentz force, and the thermodynamic relations for a prefect fluid. The equation of state of the latter is related to the scalar field's self potential. We introduce 1+3 notation to elucidate the relation between MHD and field variables. In our approach the requirement that the scalar field be single valued leads to the quantization of a certain circulation in steps of $\hbar$; this feature leads, in the classical limit, to the conservation of that circulation. The circulation is identical to that in Oron's generalization of Kelvin's circulation theorem to perfect MHD; we here characterize the new conserved helicity associated with it. We also demonstrate the existence for MHD of two Bernoulli-like theorems for each spacetime symmetry of the flow and geometry; one of these is pertinent to suitably defined potential flow. We exhibit the conserved quantities explicitly in the case that two symmetries are simultaneously present, and give examples. Also in this case we exhibit a new conserved MHD circulation distinct from Oron's, and provide an example.Comment: RevTeX, 16 pages, no figures; clarifications added and typos corrected; version to be published in Phys. Rev.

Mixture of Fluids involving Entropy Gradients and Acceleration Waves in Interfacial Layers

Through an Hamiltonian action we write down the system of equations of motions for a mixture of thermocapillary fluids under the assumption that the internal energy is a function not only of the gradient of the densities but also of the gradient of the entropies of each component. A Lagrangian associated with the kinetic energy and the internal energy allows to obtain the equations of momentum for each component and for the barycentric motion of the mixture. We obtain also the balance of energy and we prove that the equations are compatible with the second law of thermodynamics. Though the system is of parabolic type, we prove that there exist two tangential acceleration waves that characterize the interfacial motion. The dependence of the internal energy of the entropy gradients is mandatory for the existence of this kind of waves. The differential system is non-linear but the waves propagate without distortion due to the fact that they are linearly degenerate (exceptional waves).Comment: 30 page

The Definition of Mach's Principle

Two definitions of Mach's principle are proposed. Both are related to gauge theory, are universal in scope and amount to formulations of causality that take into account the relational nature of position, time, and size. One of them leads directly to general relativity and may have relevance to the problem of creating a quantum theory of gravity.Comment: To be published in Foundations of Physics as invited contribution to Peter Mittelstaedt's 80th Birthday Festschrift. 30 page

Human factors and missed solutions to Enigma design weaknesses

The German World War II Enigma suffered from design weaknesses that facilitated its large-scale decryption by the British throughout the war. The author shows that the main technical weaknesses (self-coding and reciprocal coding) could have been avoided using simple contemporary technology, and therefore the true cause of the weaknesses is not technological but must be sought elsewhere. Specifically, human factors issues resulted in the persistent failure to seek out more effective designs. Similar limitations seem to beset the literature on the period, which misunderstands the Enigma weaknesses and therefore inhibits broader thinking about design or realising the critical role of human factors engineering in cryptography

Nonlinear mode coupling in rotating stars and the r-mode instability in neutron stars

We develop the formalism required to study the nonlinear interaction of modes in rotating Newtonian stars in the weakly nonlinear regime. The formalism simplifies and extends previous treatments. At linear order, we elucidate and extend slightly a formalism due to Schutz, show how to decompose a general motion of a rotating star into a sum over modes, and obtain uncoupled equations of motion for the mode amplitudes under the influence of an external force. Nonlinear effects are added perturbatively via three-mode couplings. We describe a new, efficient way to compute the coupling coefficients, to zeroth order in the stellar rotation rate, using spin-weighted spherical harmonics. We apply this formalism to derive some properties of the coupling coefficients relevant to the nonlinear interactions of unstable r-modes in neutron stars, postponing numerical integrations of the coupled equations of motion to a later paper. From an astrophysical viewpoint, the most interesting result of this paper is that many couplings of r-modes to other rotational modes (modes with zero frequencies in the non-rotating limit) are small: either they vanish altogether because of various selection rules, or they vanish to lowest order in the angular velocity. In zero-buoyancy stars, the coupling of three r-modes is forbidden entirely and the coupling of two r-modes to one hybrid rotational mode vanishes to zeroth order in rotation frequency. In incompressible stars, the coupling of any three rotational modes vanishes to zeroth order in rotation frequency.Comment: 62 pages, no figures. Corrected error in computation of coupling coefficients, added new selection rule and an appendix on energy and angular momentum of mode

Thermal conductivity through the nineteenth century

As a material property and as a metaphor, thermal conductivity occupies an important position in physical, biological and geological sciences. Yet, its precise measurement is dependent on using electricity as a proxy because flowing heat cannot directly be measured.Comment: Submitted to Physics Today. 4,500 words, 4 figure

Variational description of multi-fluid hydrodynamics: Uncharged fluids

We present a formalism for Newtonian multi-fluid hydrodynamics derived from an unconstrained variational principle. This approach provides a natural way of obtaining the general equations of motion for a wide range of hydrodynamic systems containing an arbitrary number of interacting fluids and superfluids. In addition to spatial variations we use ``time shifts'' in the variational principle, which allows us to describe dissipative processes with entropy creation, such as chemical reactions, friction or the effects of external non-conservative forces. The resulting framework incorporates the generalization of the entrainment effect originally discussed in the case of the mixture of two superfluids by Andreev and Bashkin. In addition to the conservation of energy and momentum, we derive the generalized conservation laws of vorticity and helicity, and the special case of Ertel's theorem for the single perfect fluid. We explicitly discuss the application of this framework to thermally conducting fluids, superfluids, and superfluid neutron star matter. The equations governing thermally conducting fluids are found to be more general than the standard description, as the effect of entrainment usually seems to be overlooked in this context. In the case of superfluid He4 we recover the Landau--Khalatnikov equations of the two-fluid model via a translation to the ``orthodox'' framework of superfluidity, which is based on a rather awkward choice of variables. Our two-fluid model for superfluid neutron star matter allows for dissipation via mutual friction and also ``transfusion'' via beta-reactions between the neutron fluid and the proton-electron fluid.Comment: uses RevTeX 4; 20 pages. To appear in PRD. v2: removed discussion of charged fluids and coupling to electromagnetic fields, which are submitted as a separate paper for a clearer presentation v3: fixed typo in Eq.(9), updated some reference

Computing the wavefunction from trajectories: particle and wave pictures in quantum mechanics and their relation

We discuss the particle method in quantum mechanics which provides an exact scheme to calculate the time-dependent wavefunction from a single-valued continuum of trajectories where two spacetime points are linked by at most a single orbit. A natural language for the theory is offered by the hydrodynamic analogy, in which wave mechanics corresponds to the Eulerian picture and the particle theory to the Lagrangian picture. The Lagrangian model for the quantum fluid may be developed from a variational principle. The Euler-Lagrange equations imply a fourth-order nonlinear partial differential equation to calculate the trajectories of the fluid particles as functions of their initial coordinates using as input the initial wavefunction. The admissible solutions are those consistent with quasi-potential flow. The effect of the superposition principle is represented via a nonclassical force on each particle. The wavefunction is computed via the standard map between the Lagrangian coordinates and the Eulerian fields, which provides the analogue in this model of Huygens principle in wave mechanics. The method is illustrated by calculating the time-dependence of a free Gaussian wavefunction. The Eulerian and Lagrangian pictures are complementary descriptions of a quantum process in that they have associated Hamiltonian formulations that are connected by a canonical transformation. The de Broglie-Bohm interpretation, which employs the same set of trajectories, should not be conflated with the Lagrangian version of the hydrodynamic interpretation. The theory implies that the mathematical results of the de Broglie-Bohm model may be regarded as statements about quantum mechanics itself rather than about its interpretation.Comment: 26 page

Colonial lives of the carceral archipelago: rethinking the neoliberal security state

Mass incarceration, police brutality, and border controls are part and parcel of the everyday experiences of marginalized and racialized communities across the world. Recent scholarship in international relations, sociology, and geography has examined the prevalence of these coercive practices through the prism of “disciplinary,” “penal,” or “authoritarian” neoliberalism. In this collective discussion, we argue that although this literature has brought to the fore neoliberalism's reliance on state violence, it has yet to interrogate how these carceral measures are linked to previous forms of global racial ordering. To rectify this moment of “colonial unknowing,” the collective discussion draws on decolonial approaches, Indigenous studies, and theories of racial capitalism. It demonstrates that “new” and “neoliberal” forms of domestic control must be situated within the global longue durée of racialized and colonial accumulation by dispossession. By mapping contemporary modes of policing, incarceration, migration control, and surveillance onto earlier forms of racial–colonial subjugation, we argue that countering the violence of neoliberalism requires more than nostalgic appeals for a return to Keynesianism. What is needed is abolition—not just of the carceral archipelago, but of the very system of racial capitalism that produces and depends on these global vectors of organized violence and abandonment. L'incarcération de masse, la brutalité policière et les contrôles aux frontières constituent une partie intégrante des expériences quotidiennes des communautés marginalisées et racialisées du monde entier. Des études récentes en relations internationales, en sociologie et en géographie ont examiné la prévalence de ces pratiques coercitives par le prisme du néolibéralisme « disciplinaire », « pénal » ou « autoritaire ». Dans cet article, nous soutenons que bien que cette littérature ait mis en évidence la dépendance du néolibéralisme à la violence étatique, elle ne s'est pas encore interrogée sur le lien entre ces mesures carcérales et les formes précédentes d'ordre racial mondial. Cet article s'appuie sur le féminisme noir, les approches décoloniales, les études indigènes et les théories de capitalisme racial pour rectifier cette « ignorance coloniale » marquante. Il démontre que les formes « nouvelles » et « néolibérales » de contrôle national doivent se situer dans la longue durée globale de l'accumulation racialisée et coloniale par dépossession. Nous associons les modes contemporains de maintien de l'ordre, d'incarcération, de contrôle migratoire et de surveillance à des formes antérieures d'assujettissement racial/colonial pour soutenir que contrer la violence du néolibéralisme exige davantage que des appels nostalgiques au retour du keynésianisme. Ce qu'il faut, c'est une abolition : non seulement de l'archipel carcéral, mais aussi du système de capitalisme racial en lui-même qui produit et dépend de ces vecteurs globaux de violence organisée et d'abandon. El encarcelamiento masivo, la brutalidad policial y los controles fronterizos forman parte de las experiencias cotidianas de las comunidades marginadas y racializadas de todo el mundo. Estudios recientes en RI, Sociología y Geografía han examinado la prevalencia de estas prácticas coercitivas a través del prisma del neoliberalismo “disciplinario,” “penal” o “autoritario.” En este artículo, sostenemos que, si bien esta literatura puso en primer plano la dependencia del neoliberalismo de la violencia estatal, aún tiene que cuestionar la manera en que estas medidas carcelarias se vinculan a formas anteriores de ordenamiento racial global. Para rectificar este momento de “desconocimiento colonial,” el artículo recurre al feminismo negro, a los abordajes descoloniales, a los estudios indígenas y a las teorías del capitalismo racial. Demuestra que las formas “nuevas” y “neoliberales” de control interno se deben situar dentro de la longue durée global de la acumulación por desposesión racializada y colonial. Al trazar un mapa de los modos contemporáneos de vigilancia policial, encarcelamiento, control de la migración y vigilancia sobre las formas anteriores de subyugación racial-colonial, sostenemos que contrarrestar la violencia del neoliberalismo requiere algo más que apelaciones nostálgicas de retorno al keynesianismo. Lo que se necesita es la abolición, no solo del archipiélago carcelario, sino también del propio sistema de capitalismo racial que produce y depende de estos vectores globales de violencia y abandono organizados