arXiv subjects

Clifford Chafin

Publications and source records attributed to Clifford Chafin.

At least 19 recordsLinked to original sources

arXiv2019

Essential Infinite Order Non-PDE Behavior in Continuum Mechanics: Corrections to Hydrodynamics and Diffusion

Longstanding problems regarding the causality of the diffusion equation are resolved through a class of exact solutions. A universal differential solution for diffusive processes is derived that is causal and exact at any analytic point in the data, albeit infinite order in spatial derivatives. This is true for systems both relativistic and nonrelativistic and shows that the hyperbolic and other relativistic extensions of the heat equation are not valid. A similar effect is demonstrated for flow enhanced mixing of solutions but with a new nonanalytic feature. Viscous hydrodynamics of liquids have both features. Both Newtonian and non-Newtonian viscous liquids give a more important and confounding alteration of the N-S equations for nonstationary flows. A careful analysis of liquids in terms of microscopic constituents and Lagrangian paths show there is a well-defined unique microscopic decomposition of fluid deformations into rotation and two modes corresponding to organized layered flow that do not enhance mixing and a mode that induces mixing and preferred static orientations. The resulting equations are both infinite order in spatial derivatives almost everywhere and are divided into two disjoint classes by an essential nonanalytic hypersuface. These give important rheological effects coupling hydrodynamic flow to diffusion and reaction kinetics. Practical consequences include catalysis and reaction yield control by rheological means. Implications of this work should percolate through almost all of continuum mechanics.

physics.flu-dyn↗

arXiv2015

The Absence of Stokes Drift in Waves

Stokes drift has been as central to the history of wave theory as it has been distressingly absent from experiment. Neither wave tanks nor experiments in open bodies detect this without nearly canceling "eulerian flows." Acoustic waves have an analogous problem that is particularly problematic in the vorticity production at the edges of beams. Here we demonstrate that the explanation for this arises from subtle end-of-packet and wavetrain gradient effects such as microbreaking events and wave-flow decomposition subtleties required to conserve mass and momentum and avoid fictitious external forces. These losses occur at both ends of packets and can produce a significant nonviscous energy loss for translating and spreading surface wave packets and wavetrains. In contrast, monochromatic sound wave packets will be shown to asymmetrically distort to conserve momentum. This provides an interesting analogy to how such internal forces arise for gradients of electromagnetic wavetrains in media. Such examples show that the interactions of waves in media are so system dependent as to be completely nonuniversal. These give further examples of how boundary effects must be carefully considered for conservation laws especially when harmonic functions are involved. The induced flows in establishing surface waves are shown to be time changing and dependent on wave history and suggest that some classical work based on mass flux and wave interactions may need to be reconsidered.

physics.flu-dyn↗

arXiv2015

Quantum Corrections to Classical Kinetics: the Weight of Rotation

Hydrodynamics of gases in the classical domain are examined from the perspective that the gas has a well-defined wavefunction description at all times. Specifically, the internal energy and volume exclusion of decorrelated vortex structures are included so that quantum corrections and modifications to Navier-Stokes behavior can be derived. This leads to a small deviation in rigid body rotation for a cylindrically bound gas and the internal energy changes associated with vorticity give deviations in the Reynolds' transport theorem. Some macroscopic observable features arising from this include variations in the specific heat, an anisotropic correction to thermal conductivity and a variation in optical scattering as a function of the declination from the axis of local vorticity. The improvements in magneto-optical traps suggests some interesting experiments to be done in higher temperature regimes where they are not usually employed. It is argued that the finite lifetime of observed vortices in ultracold bosonic gases is only apparent and these volume excluding structures persist in generating angular momentum and pressure in the cloud in a non-imageable form.

physics.gen-ph↗

arXiv2015

Thermalization of Gases: A First Principles Approach

Previous approaches of emergent thermalization for condensed matter based on typical wavefunctions are extended to generate an intrinsically quantum theory of gases. Gases are fundamentally quantum objects at all temperatures, by virtue of rapid delocalization of their constituents. When there is a sufficiently broad spread in the energy of eigenstates, a well-defined temperature is shown to arise by photon production when the samples are optically thick. This produces a highly accurate approximation to the Planck distribution so that thermalization arises from the initial data as a consequence of purely quantum and unitary dynamics. These results are used as a foil for some common hydrodynamic theory of ultracold gases. It is suggested here that strong history dependence typically remains in these gases and so limits the validity of thermodynamics in their description. These problems are even more profound in the extension of hydrodynamics to such gases when they are optically thin, even when their internal energy is not low. We investigate rotation of elliptically trapped gases and consistency problems with deriving a local hydrodynamic approach. The presence of vorticity that is "hidden" from order parameter approaches is discussed along with some buoyancy intrinsically associated with vorticity that gives essential quantum corrections to gases in the regimes where standard perturbation approaches to the Boltzmann equations are known to fail to converge. These results suggest that studying of trapped gases in the far from ultracold regions may yield interesting results not described by classical hydrodynamics.

physics.gen-ph↗

arXiv2015

Two Experimental Tests to Distinguish Decoherence from the Slicing Theory of Measurement

Here we propose a pair of experiments to distinguish the recently proposed "slicing theory" of quantum measurement, which gives a transient many worlds picture, and decoherence. Since these two theories are essentially "opposites" in their approach and both claim to arise from the many body Schrödinger equation itself, there is no chance of them being equivalent representations of the same reality. It will be explicitly shown that each theory gives very different answers to the questions of back reaction and revival of phase effects after measurement. We suggest that the kinds of isolated systems now possible in optical traps is now sufficient to generate a selective distinction between these two theories. In particular we show that the slicing theory gives examples of interference from "revival of histories" in controlled examples but no back reaction on the measurement devices whereas decoherence gives the opposite.

physics.gen-ph↗

arXiv2015

The Slicing Theory of Quantum Measurement: Derivation of Transient Many Worlds Behavior

An emergent theory of quantum measurement arises directly by considering the particular subset of many body wavefunctions that can be associated with classical condensed matter and its interaction with delocalized wavefunctions. This transfers questions of the "strangeness" of quantum mechanics from the wavefunction to the macroscopic material itself. An effectively many-worlds picture of measurement results for long times and induces a natural arrow of time. The challenging part is then justifying why our macroscopic world is dominated by such far-from-eigenstate matter. Condensing cold mesoscopic clusters provide a pathway to a partitioning of a highly correlated many body wavefunction to long lasting islands composed of classical-like bodies widely separated in Fock space. Low mass rapidly delocalizing matter that recombines with the solids "slice" the system into a set of nearby yet very weakly interacting subsystems weighted according to the Born statistics and yields a kind of many worlds picture but with the possibility of revived phase interference on iterative particle desorption, delocalization and readsorption. A proliferation of low energy photons competes with such a possibility. Causality problems associated with correlated quantum measurement are resolved and conserved quantities are preserved for the overall many body function despite their failure in each observer's bifurcating "slice-path." The necessity of such a state for a two state logic and reliable discrete state machine suggests that later stages of the universe's evolution will destroy the physical underpinnings required for consciousness and the arrow of time even without heat-death or atomic destruction. Some exotic possibilities outside the domain of usual quantum measurement are considered such as measurement with delocalized devices and revival of information from past measurements.

quant-ph↗

arXiv2015

Exactly Solvable Dielectrics, Radiation Induced Forces and Causality

We present an exactly solvable model of a classical dielectric medium that gives an unambiguous local decomposition of field and charge motion and their contribution to the conserved quantities. The result is a set of four branches to the dispersion law that gives full independent freedom in the selection of initial data of the fields and charge motion, in contrast with constitutive laws. This is done with special care to the forces that exist at surfaces, coatings and the ends of packets. As a result the utility of a stress-tensor as a function of field strengths and dielectric response for deriving general forces is called into question. The Abraham-Minkowskii paradox is clarified from this point of view and the export of such notions to realistic media and metamaterials are discussed. One result of this model is a mathematically simpler and more intuitive understanding of causality in media than the Brillouin and Sommerfeld theories. Necessary elastic medium response is estimated and some implications of this picture for quantum effects are included based on conservation laws. This model can be extended to manifestly maintain these features as general nonlinear and time and space dependent changes in medium response are introduced. The extent to which this can provide a universal description for all dielectrics is discussed. A microscopic treatment of negative index materials from this point of view is included as an illustration of the extreme economy and simplicity of these methods.

physics.optics↗

arXiv2015

Thermalization in Quantum Systems: An Emergent Approach

The problems with an emergent approach to quantum statistical mechanics are discussed and shown to follow from some of the same sources as those of quantum measurement. A wavefunction of an N atom solid is described in the ground and excited eigenstates with explicit modifications for phonons. Using the particular subclass of wavefunctions that can correspond to classical solids we investigate the localization properties of atomic centers of mass motion and contrast it with more general linear combinations of phonon states. The effectively large mass of longer modes means that localization present in the ground state persists on excitation of the material by macroscopic coherent disturbances. The "thermalization" that arises then follows from the long term well defined motion of these localized peaks in their 3N dimensional harmonic wells in the same fashion as that of a classical solid in phase space. Thermal production of photons then create an internal radiation field and provides the first dynamical derivation of the Planck distribution from material motions. Significantly, this approach resolves a long standing paradox of thermalization of many body quantum systems from Schrödinger dynamics alone.

quant-ph↗

arXiv2014

Objective Nontensor Rheology: Unique Flow Decompositions from Correlated Microscopic Motions

The use of continuum mechanics and invariants built from the deviator as an adequate foundation for rheology has been recently disputed by this author. Here we give a specific example of the kind of parcel deformations that are uniquely decomposed by way of microscopic motions into a maximal rotation, a pure shear and an extension. The construction of these equations depends on only one free material parameter but they have no nice form in terms of the operations of vector and tensor calculus which may be why they were overlooked. Although the first order flow is often sufficient to give the rheological information, finite sized parcel deformations can give confusion because of boundary effects, the relevance of which are highly dependent on the global geometry of the experiment.

physics.flu-dyn↗

arXiv2014

Hidden Invariants in Rheology: The Persistent Granular Nature of Liquids

This article will use arguments derived from the deformation driven component of mixing, especially important for microfluidics, to show that the standard invariant based approaches to rheology are lacking. It is shown that the deviator, $D_{ij}$, after the process of symmetrization, loses microscopically determined information that distinguish rotation from shear and extension in a unique fashion. We recover this information through an analysis of the discrete processes that must underlie deformation driven mixing in highly correlated fluids. Without this we show there is no hope of ever deriving adequate general material parameters for rheology from microscopic dynamics. There is an unambiguous microscopic notion of the rotation rate for every parcel and we derive a general class of invariant rheological theories from it. We discuss some implications of higher order flows on solutions and suspensions including possibilities for driving and stabilization of nonuniform distributions using hydrodynamic forces alone.

physics.flu-dyn↗

arXiv2014

Inconsistencies in the Notions of Acoustic Stress and Streaming

Inviscid hydrodynamics mediates forces through pressure and other, typically irrotational, external forces. Acoustically induced forces must be consistent with arising from such a pressure field. The use of "acoustic stress" is shown to have inconsistencies with such an analysis and generally arise from mathematical expediency but poor overall conceptualization of such systems. This contention is further supported by the poor agreement of experiment in many such approaches. The notion of momentum as being an intrinsic property of sound waves is similarly found to be paradoxical. Through an analysis that includes viscosity and attenuation, we conclude that all acoustic streaming must arise from vorticity introduced by viscous forces at the driver or other solid boundaries and that calculations with acoustic stress should be replaced with ones using a nonlinear correction to the overall pressure field.

physics.flu-dyn↗

arXiv2014

Humblonium: Classical Atoms and the Earnshaw Plasma

It is shown that electrostatic and diamagnetic forces can combine to give long lasting metastable bound dimers of macro and mesoscopically sized objects for a physically attainable material regime. This can be a large enough effect to support itself in a trap against Earth's gravity and they can stable at very high temperatures. For a more restricted material parameter set, we investigate the possibility of stable many particle collections that lose their identity as bound pairs and create a kind of plasma. These would constitute a kind of transitional state between fluids and granular materials but, unlike usual approaches, the fluid is a gas rather than a liquid.

physics.atm-clus↗

arXiv2014

Vertically Driven Waves: Energy Transfer Between Gravity Waves Revisited

We investigate the energy transfer from large waves to small ones through vertical acceleration and demonstrate that this is a much larger effect than that of the potential energy changes of the small waves moving over the larger ones. Rates of exponential growth for this process are given and limits on the stable size of small waves in the horizontal accelerations from the larger ones are derived. We discuss the possibility of this being a manifestation of the Benjamin-Feir instability.

physics.ao-ph↗

arXiv2014

Hidden Equilibration Driven Losses in Whitecapping

The role of whitecapping losses of waves is investigated in a simple model based on conservation laws. It is shown that, for Airy waves, at least as much energy is lost in gradual reequilibration as is lost in the whitecapping events themselves. This model is based on the the notion that the waves and losses are small enough that some narrow spectrum of frequencies reappears over time.

physics.ao-ph↗

arXiv2014

Corrected Wavemaker Theory, Momentum Flux and Vorticity

The usual wavemaker theory hides an unjustified integration constant assumption that renders it invalid. We discuss some surprising subtleties of momentum flux in infinite waves, packets and some counterintuitive examples where "hidden" flux contributions can arise. From here, we construct an ideal wavemaker that builds Airy waves from a series of microjets that allows an exact calculation of the forces on boundaries. This allows us to also compute the fluxes of all conserved quantities directly and rule out some of these hidden contributions to momentum flux. We then discuss some realistic flapper wavemakers and the trouble vorticity sources can create in the resulting fluid motion. Along the way we present a completely local derivation of the group velocity using fluxes.

physics.flu-dyn↗

arXiv2014

Conservation Laws and Bounds on the Efficiency of Wind-Wave Growth

We examine two means by which wind can impart energy to waves: sheltering and deposition of material upwards from windward surface shear. The shear driven deposition is shown to be the more efficient process. Lengthening of waves to match the wind speed is shown to be very inefficient and consume a large fraction of the energy imparted by the wind. The surface shear provides a low energy sink that absorbs most of the momentum from the wind. These produce bounds on the efficiency of wave growth. The results here are computed in a model independent and perturbation free fashion by a careful consideration of conservation laws. By combining these effects we can place bounds on the rates waves can grow in a given fetch and the relative amount of shear flow versus the, relatively small, Stokes drift that must arise.

physics.ao-ph↗

arXiv2014

Surface Shear and Persistent Wave Groups

We investigate the interaction of waves with surface flows by considering the full set of conserved quantities, subtle but important surface elevation changes induced by wave packets and by directly considering the necessary forces to prevent packet spreading in the deep water limit. Narrow surface shear flows are shown to exert strong localizing and stabilizing forces on wavepackets to maintain their strength and amplify their intensity even in the linear regime. Subtle packet scale nonlinear elevation changes from wave motion are crucial here and it suggest that popular notions of wave stress and action are naive. Quantitative bounds on the surface shear flow necessary to stabilize packets of any wave amplitude are given. One implication of this mechanism is that rogue wave stabilization must be due to a purely nonperturbative process.

physics.ao-ph↗

arXiv2014

Automorphism Induced Nonlocal Conservation Laws

The conservation laws of electromagnetism, and implicitly all theories built from quadratic Lagrangians, are extended to a continuum of nonlocal versions. These are associated with symmetries of a class of equal time field correlation functions and give results for both connected and disconnected branches of the general linear group of the space. It is generally assumed that manifestly covariant Lagrangians are the necessary starting point for physical theories. Here we show that the EOM derived from any of these can also follow from a broad class of nonlocal ones and each generally gives a different nonlocal Noether current. When the equations are put into a linear form and evaluated on a flat spacetime, a simple ansatz exists to give a class of conservation laws corresponding to all affine transformations of the underlying space. A general procedure is given to generate a class of nonlocal conservation laws for solutions to a very large class of nonlinear PDEs.

math-ph↗