Are there more than five linearly-independent collision invariants for the Boltzmann equation?

The problem of finding the summational collision invariants for the Boltzmann equation is tackled with the aim of proving that the most general solution of the problem is not different from the standard one even when the equation defining a collision invariant is only satisfied almost everywhere inR ³×R ³×S ². The collision invariant is assumed to be in the Hilbert spaceH of the functions which are square integrable with respect to a Maxwellian weight.     

Do people react more strongly to aircraft noise today than in the past?

Some researchers have suggested that recent studies of aircraft noise annoyance indicate that people react more strongly to a given noise exposure level today than in the past, but is there good statistical evidence to support this hypothesis? This paper reviews the correspondence between aircraft noise exposure and annoyance responses reported in aircraft noise study analyses undertaken over a period of decades. Simple linear regression models and textbook statistical analyses are used to test the data. There are some indications of an upward trend in annoyance versus noise exposure over the last 25 years, but basic tests show that the statistical evidence for an upward trend is weak, and may simply be due to sampling and/or methodological differences between the studies. The survey collection method may play a role. In some cases, study participation rate effects may exaggerate community responses.     

Protein Sequence and Structure: Is One More Fundamental than the Other?

We argue that protein native state structures reside in a novel “phase” of matter which confers on proteins their many amazing characteristics. This phase arises from the common features of all globular proteins and is characterized by a sequence-independent free energy landscape with relatively few low energy minima with funnel-like character. The choice of a sequence that fits well into one of these predetermined structures facilitates rapid and cooperative folding. Our model calculations show that this novel phase facilitates the formation of an efficient route for sequence design starting from random peptides.     

N=2 superstrings in more than two dimensions?

For a string propagating in a Parisi-Sourlas superspace the critical dimension equals the difference in the number of positive-and negative-dimensional coordinates. In this way the dimension of the Minkowski subspace can be increased. Here we apply this to the N=2 superstring, with D_c=2 and find anomaly-free N=2 superstrings in all positive even dimensions. Nontrivial theories can be constructed from these N=2 theories by truncation: In a Parisi-Sourlas superspace with a ten-dimensional Minkowski subspace we find the N=1 NSR superstring, and with a four-dimensional Minkowski subspace we find an N=1 superstring, classically related to the D=10 NSR superstring by a canonical transformation.     

Likelihood functions for supersymmetric observables in?frequentist analyses of the CMSSM and NUHM1

On the basis of frequentist analyses of experimental constraints from electroweak precision data, (g−2) _μ , B-physics and cosmological data, we investigate the parameters of the constrained MSSM (CMSSM) with universal soft supersymmetry-breaking mass parameters, and a model with common non-universal Higgs masses (NUHM1). We present χ ² likelihood functions for the masses of supersymmetric particles and Higgs bosons, as well as BR(b→s γ), BR(B _s →μ ⁺ μ ⁻) and the spin-independent dark-matter scattering cross section, σ _p ^SI. In the CMSSM we find preferences for sparticle masses that are relatively light. In the NUHM1 the best-fit values for many sparticle masses are even slightly smaller, but with greater uncertainties. The likelihood functions for most sparticle masses are cut off sharply at small masses, in particular by the LEP Higgs mass constraint. Both in the CMSSM and the NUHM1, the coannihilation region is favored over the focus-point region at about the 3-σ level, largely but not exclusively because of (g−2) _μ . Many sparticle masses are highly correlated in both the CMSSM and NUHM1, and most of the regions preferred at the 95% C.L. are accessible to early LHC running, though high-luminosity running would be needed to cover the regions allowed at the 3-σ levels. Some slepton and chargino/neutralino masses should be in reach at the ILC. The masses of the heavier Higgs bosons should be accessible at the LHC and the ILC in portions of the preferred regions in the (M _A ,tan β) plane. In the CMSSM, the likelihood function for BR(B _s →μ ⁺ μ ⁻) is peaked close to the Standard Model value, but much larger values are possible in the NUHM1. We find that values of σ _p ^SI>10⁻¹⁰ pb are preferred in both the CMSSM and the NUHM1. We study the effects of dropping the (g−2) _μ , BR(b→s γ), Ω _χ h ² and M _h constraints, demonstrating that they are not in tension with the other constraints.     

Is the Devil in h?

This note is a part of my effort to rid quantum mechanics (QM) nonlocality. Quantum nonlocality is a two faced Janus: one face is a genuine quantum mechanical nonlocality (defined by the Lüders’ projection postulate). Another face is the nonlocality of the hidden variables model that was invented by Bell. This paper is devoted the deconstruction of the latter. The main casualty of Bell’s model is that it straightforwardly contradicts Heisenberg’s uncertainty and Bohr’s complementarity principles generally. Thus, we do not criticize the derivation or interpretation of the Bell inequality (as was done by numerous authors). Our critique is directed against the model as such. The original Einstein-Podolsky-Rosen (EPR) argument assumed the Heisenberg’s principle without questioning its validity. Hence, the arguments of EPR and Bell differ crucially, and it is necessary to establish the physical ground of the aforementioned principles. This is the quantum postulate: the existence of an indivisible quantum of action given by the Planck constant. Bell’s approach with hidden variables implicitly implies rejection of the quantum postulate, since the latter is the basis of the reference principles.     

Is the derivation of the Langevin formula correct?

The derivation of the Langevin formula is analyzed. It is shown that a basic assumption in it is incorrect. A more correct derivation of a similar formula is proposed.     

Is the collapse a phase transition?

It is shown that the process of the collapse during quantum measurements is a consequence of the quantum symmetry built in the formalism: there exists a nontrivial group of symmetry under which all possible states are invariant after the measurement of the given observable. On the basis of this fact, the postulate of collapse is derived with purely group theoretical considerations. These are analogous to the ones used in Landau's problem of phase transitions. Some further analogies of the processes of the collapse and the phase transitions are discussed.     

Is the nucleon a bound state?

In this paper we deal with the question of whether or not the nucleon is a bound state. It is shown that previous work on this problem is not conclusive. We find, however, a simple criterion which allows for an experimental decision of this question. For the nucleon to be a bound state, thep _1/2,1/2 phase has to have a negative sign at the inelastic threshold. A positive phase excludes the bound state picture but allows ap _1/2,1/2 resonance to occur.     

Is the low-l microwave background cosmic?

The large-angle (low-l) correlations of the cosmic microwave background exhibit several statistically significant anomalies compared to the standard inflationary cosmology. We show that the quadrupole plane and the three octopole planes are far more aligned than previously thought (99.9% C.L.). Three of these planes are orthogonal to the ecliptic at 99.1% C.L., and the normals to these planes are aligned at 99.6% C.L. with the direction of the cosmological dipole and with the equinoxes. The remaining octopole plane is orthogonal to the supergalactic plane at 99.6% C.L.     

Is the compactified vacuum semiclassically unstable?

It is shown, by applying the positive-energy theorem, that the present vacuum (M⁴×K^D) in some higher-dimensional theories (e.g. the Candelas-Weinberg model) is stable against decay by quantum tunnelling without change of topology. Frieman and Kolb have found a quantum tunnelling instability of the present vacuum in the same models. But they did not take into account the gravitational effect, which is important and prevents the universe from decaying into the higher-dimensional de Sitter phase.     

Energy efficient nonlinear optics in silicon: are slow-light structures more efficient than nanowires?

We compare the energy performance of four-wave mixing in nanowires and slow-light photonic crystals and outline the regimes where each platform exhibits salient advantages and limitations, including analysis of the impact of future fabrication improvement. These results suggest a route towards energy efficient silicon integrated photonics.