Are All Particles Identical?

We consider the possibility that all particles in the world are fundamentally identical, i.e., belong to the same species. Different masses, charges, spins, flavors, or colors then merely correspond to different quantum states of the same particle, just as spin-up and spin-down do. The implications of this viewpoint can be best appreciated within Bohmian mechanics, a precise formulation of quantum mechanics with particle trajectories. The implementation of this viewpoint in such a theory leads to trajectories different from those of the usual formulation, and thus to a version of Bohmian mechanics that is inequivalent to, though arguably empirically indistinguishable from, the usual one. The mathematical core of this viewpoint is however rather independent of the detailed dynamical scheme Bohmian mechanics provides, and it amounts to the assertion that the configuration space for N particles, even N ``distinguishable particles,'' is the set of all N-point subsets of physical 3-space.Comment: 12 pages LaTeX, no figure

Molybdenum Disubstituted Alkylidene Complexes

Through relatively straightforward techniques that begin with Mo(NAr)(CH-t-Bu)[OCMe(CF3)2]2 (Ar = 2,6-i-Pr2C6H3), we have prepared Mo(NAr)(CMePh)(OMesityl)2, [Mo(NAr)(CMePh)(OC6F5)2]2, Mo(NAr)(CMePh)(OC6F5)2(MeCN), Mo(NAr)(CMePh)(OC6F5)2(bipyridyl), Mo(NAr)(CMePh)(Cl)2(bipyridyl), Mo(NAr)(CMePh)(Cl)(OHMT)(MeCN) (OHMT = O-2,6-(2,4,6-Me3C6H2)2C6H3), and Mo(NAr)(CMePh)(Pyrrolide)(OHMT). X-ray studies reveal that in five compounds the alkylidene isomer (A) is that in which the phenyl group in the alkylidene points toward the imido nitrogen. In Mo(NAr)(CMePh)(OC6F5)2(MeCN) the isomer in which the methyl group points toward the imido nitrogen (isomer B) has cocrystallized with isomer A (12%). In two 14e compounds that contain isomer A, the Mo═C-C angles differ by 30-36°, consistent with a Mo...C-Hβ agostic interaction. Several of the complexes reported here react readily with ethylene, 1-decene, or cyclooctene to give the expected products, thus confirming their viability as initiators or intermediates in metathesis reactions

A new method for isolating turbulent states in transitional stratified plane Couette flow

We present a new adaptive control strategy to isolate and stabilize turbulent states in transitional, stably stratified plane Couette flow in which the gravitational acceleration (non-dimensionalized as the bulk Richardson number$Ri$) is adjusted in time to maintain the turbulent kinetic energy (TKE) of the flow. We demonstrate that applying this method at various stages of decaying stratified turbulence halts the decay process and allows a succession of intermediate turbulent states of decreasing energy to be isolated and stabilized. Once the energy of the initial flow becomes small enough, we identify a single minimal turbulent spot, and lower-energy states decay to laminar flow. Interestingly, the turbulent states which emerge from this process have very similar time-averaged$Ri$, but TKE levels different by an order of magnitude. The more energetic states consist of several turbulent spots, each qualitatively similar to the minimal turbulent spot. This suggests that the minimal turbulent spot may well be the lowest-energy turbulent state which forms a basic building block of stratified plane Couette flow. The fact that a minimal spot of turbulence can be stabilized, so that it neither decays nor grows, opens up exciting opportunities for further study of spatiotemporally intermittent stratified turbulence.The EPSRC grant EP/K034529/1 entitled ‘Mathematical Underpinnings of Stratified Turbulence’ is gratefully acknowledged for supporting the research presented here.This is the author accepted manuscript. The final version is available from Cambridge University Press via https://doi.org/10.1017/jfm.2016.62

Disruption of SorCS2 reveals differences in the regulation of stereociliary bundle formation between hair cell types in the inner ear

Behavioural anomalies suggesting an inner ear disorder were observed in a colony of transgenic mice. Affected animals were profoundly deaf. Severe hair bundle defects were identified in all outer and inner hair cells (OHC, IHC) in the cochlea and in hair cells of vestibular macular organs, but hair cells in cristae were essentially unaffected. Evidence suggested the disorder was likely due to gene disruption by a randomly inserted transgene construct. Whole-genome sequencing identified interruption of the SorCS2 (Sortilin-related VPS-10 domain containing protein) locus. Real-time-qPCR demonstrated disrupted expression of SorCS2 RNA in cochlear tissue from affected mice and this was confirmed bySorCS2 immuno-labelling. In all affected hair cells, stereocilia were shorter than normal, but abnormalities of bundle morphology and organisation differed between hair cell types. Bundles on OHC were grossly misshapen with significantly fewer stereocilia than normal. However, stereocilia were organised in rows of increasing height. Bundles on IHC contained significantly more stereocilia than normal with some longer stereocilia towards the centre, or with minimal height differentials. In early postnatal mice, kinocilia (primary cilia) of IHC and of OHC were initially located towards the lateral edge of the hair cell surface but often became surrounded by stereocilia as bundle shape and apical surface contour changed. In macular organs the kinocilium was positioned in the centre of the cell surface throughout maturation. There was disruption of the signalling pathway controlling intrinsic hair cell apical asymmetry. LGN and Gαi3 were largely absent, and atypical Protein Kinase C (aPKC) lost its asymmetric distribution. The results suggest that SorCS2 plays a role upstream of the intrinsic polarity pathway and that there are differences between hair cell types in the deployment of the machinery that generates a precisely organised hair bundle

Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains

We consider the biharmonic operator subject to homogeneous boundary conditions of Neumann type on a planar dumbbell domain which consists of two disjoint domains connected by a thin channel. We analyse the spectral behaviour of the operator, characterizing the limit of the eigenvalues and of the eigenprojections as the thickness of the channel goes to zero. In applications to linear elasticity, the fourth order operator under consideration is related to the deformation of a free elastic plate, a part of which shrinks to a segment. In contrast to what happens with the classical second order case, it turns out that the limiting equation is here distorted by a strange factor depending on a parameter which plays the role of the Poisson coefficient of the represented plate.Comment: To appear in "Integral Equations and Operator Theory

Characterizing human vestibular sensory epithelia for experimental studies: new hair bundles on old tissue and implications for therapeutic interventions in ageing.

Balance disequilibrium is a significant contributor to falls in the elderly. The most common cause of balance dysfunction is loss of sensory cells from the vestibular sensory epithelia of the inner ear. However, inaccessibility of inner ear tissue in humans severely restricts possibilities for experimental manipulation to develop therapies to ameliorate this loss. We provide a structural and functional analysis of human vestibular sensory epithelia harvested at trans-labyrinthine surgery. We demonstrate the viability of the tissue and labeling with specific markers of hair cell function and of ion homeostasis in the epithelium. Samples obtained from the oldest patients revealed a significant loss of hair cells across the tissue surface, but we found immature hair bundles present in epithelia harvested from patients >60 years of age. These results suggest that the environment of the human vestibular sensory epithelium could be responsive to stimulation of developmental pathways to enhance hair cell regeneration, as has been demonstrated successfully in the vestibular organs of adult mice

Bell-Type Quantum Field Theories

In [Phys. Rep. 137, 49 (1986)] John S. Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a |Psi|^2-distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; such processes we call Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to "second quantization." As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field.Comment: 53 pages LaTeX, no figure