Entropy-expansiveness for partially hyperbolic diffeomorphisms

We show that diffeomorphisms with a dominated splitting of the form $E^s\oplus E^c\oplus E^u$, where $E^c$ is a nonhyperbolic central bundle that splits in a dominated way into 1-dimensional subbundles, are entropy-expansive. In particular, they have a principal symbolic extension and equilibrium states.Comment: 15 pages, 1 figur

Exponential speed of mixing for skew-products with singularities

Let $f: [0,1]\times [0,1] \setminus {1/2} \to [0,1]\times [0,1]$ be the $C^\infty$ endomorphism given by $$f(x,y)=(2x- [2x], y+ c/|x-1/2|- [y+ c/|x-1/2|]),$$ where $c$ is a positive real number. We prove that $f$ is topologically mixing and if $c>1/4$ then $f$ is mixing with respect to Lebesgue measure. Furthermore we prove that the speed of mixing is exponential.Comment: 23 pages, 3 figure

Shell structure at N=28 near the dripline: spectroscopy of 42^{42}Si, 43^{43}P and 44^{44}S

Measurements of the N=28 isotones 42Si, 43P and 44S using one- and two-proton knockout reactions from the radioactive beam nuclei 44S and 46Ar are reported. The knockout reaction cross sections for populating 42Si and 43P and a 184 keV gamma-ray observed in 43P establish that the d_{3/2} and s_{1/2} proton orbits are nearly degenerate in these nuclei and that there is a substantial Z=14 subshell closure separating these two orbits from the d_{5/2} orbit. The increase in the inclusive two-proton knockout cross section from 42Si to 44S demonstrates the importance of the availability of valence protons for determining the cross section. New calculations of the two-proton knockout reactions that include diffractive effects are presented. In addition, it is proposed that a search for the d_{5/2} proton strength in 43P via a higher statistics one-proton knockout experiment could help determine the size of the Z=14 closure.Comment: Phys. Rev. C, in pres

Robust entropy expansiveness implies generic domination

Let $f: M \to M$ be a $C^r$-diffeomorphism, $r\geq 1$, defined on a compact boundaryless $d$-dimensional manifold $M$, $d\geq 2$, and let $H(p)$ be the homoclinic class associated to the hyperbolic periodic point $p$. We prove that if there exists a $C^1$ neighborhood $\mathcal{U}$ of $f$ such that for every $g\in {\mathcal U}$ the continuation $H(p_g)$ of $H(p)$ is entropy-expansive then there is a $Df$-invariant dominated splitting for $H(p)$ of the form $E\oplus F_1\oplus... \oplus F_c\oplus G$ where $E$ is contracting, $G$ is expanding and all $F_j$ are one dimensional and not hyperbolic.Comment: 24 page

From exercise intolerance to functional improvement: The second wind phenomenon in the identification of McArdle disease

McArdle disease is the most common of the glycogen storage diseases. Onset of symptoms is usually in childhood with muscle pain and restricted exercise capacity. Signs and symptoms are often ignored in children or put down to 'growing pains' and thus diagnosis is often delayed. Misdiagnosis is not uncommon because several other conditions such as muscular dystrophy and muscle channelopathies can manifest with similar symptoms. A simple exercise test performed in the clinic can however help to identify patients by revealing the second wind phenomenon which is pathognomonic of the condition. Here a patient is reported illustrating the value of using a simple 12 minute walk test.RSS is funded by Ciências sem Fronteiras/CAPES Foundation. The authors would like to thank the Association for Glycogen Storage Disease (UK), the EUROMAC Registry funded by the European Union, the Muscular Dystrophy Campaign, the NHS National Specialist Commissioning Group and the Myositis Support Group for funding

Absolute and Relative Surrogate Measurements of the \u3csup\u3e236\u3c/sup\u3eU(\u3cem\u3en,f\u3c/em\u3e) Cross Section as a Probe of Angular Momentum Effects

Using both the absolute and relative surrogate techniques, the 236U(n,f) cross section was deduced over an equivalent neutron energy range of 0 to 20 MeV. A 42 MeV 3He beam from the 88 Inch Cyclotron at Lawrence Berkeley National Laboratory was used to perform a (3He,α) pickup reaction on targets of 235U (Jπ=7/2−) and 238U (Jπ = 0+) and the fission decay probabilities were determined. The 235U(3He,αf) and 238U(3He,αf) were surrogates for 233U(n,f) and 236U(n,f), respectively. The cross sections extracted using the surrogate method were compared to directly measured cross sections. The sensitivity of these cross sections to the Jπ -population distributions was explored

Statistical \u3cem\u3eγ\u3c/em\u3e Rays in the Analysis of Surrogate Nuclear Reactions

The surrogate nuclear reaction method is being applied in many efforts to indirectly determine neutron-induced reaction cross sections on short-lived isotopes. This technique aims to extract accurate (n,γ) cross sections from measured decay properties of the compound nucleus of interest (created using a different reaction). The advantages and limitations of a method that identifies the γ-ray decay channel by detecting any high-energy (“statistical”) γ ray emitted during the relaxation of the compound nucleus were investigated. Data collected using the Silicon Telescope Array for Reaction Studies and Livermore-Berkeley Array for Collaborative Experiments silicon and germanium detector arrays were used to study the decay of excited gadolinium nuclei following inelastic proton scattering. In many cases, this method of identifying the γ-ray decay channel can simplify the experimental data collection and greatly improve the detection efficiency for γ-ray cascades. The results show sensitivity to angular-momentum differences between the surrogate reaction and the desired (n,γ) reaction similar to an analysis performed using low-lying discrete transitions even when ratios of cross sections are considered

Surrogate Ratio Method in the Actinide Region Using the (\u3cem\u3eα,α\u27f\u3c/em\u3e) Reaction

In the Surrogate Method, the measured decay probability of a compound nucleus formed via a direct reaction is used to extract the cross section for a reaction with a different entrance channel that proceeds through the same compound nucleus. An extension of the Surrogate Method, the Surrogate Ratio Method (SRM), uses a ratio of measured decay probabilities to infer an unknown cross section relative to a known one. To test the SRM we compare the direct-reaction-induced fission probability ratio of 234U(α, α’ f ) to 236U(α, α’f ) with the ratio of cross sections of 233U(n, f ) to 235U(n, f ). These ratios were found to be in agreement over an equivalent neutron energy range of 0.4–18 MeV