Local Operations and Completely Positive Maps in Algebraic Quantum Field Theory

Einstein introduced the locality principle which states that all physical effect in some finite space-time region does not influence its space-like separated finite region. Recently, in algebraic quantum field theory, R\'{e}dei captured the idea of the locality principle by the notion of operational separability. The operation in operational separability is performed in some finite space-time region, and leaves unchanged the state in its space-like separated finite space-time region. This operation is defined with a completely positive map. In the present paper, we justify using a completely positive map as a local operation in algebraic quantum field theory, and show that this local operation can be approximately written with Kraus operators under the funnel property

Generation of Entanglement Outside of the Light Cone

The Feynman propagator has nonzero values outside of the forward light cone. That does not allow messages to be transmitted faster than the speed of light, but it is shown here that it does allow entanglement and mutual information to be generated at space-like separated points. These effects can be interpreted as being due to the propagation of virtual photons outside of the light cone or as a transfer of pre-existing entanglement from the quantum vacuum. The differences between these two interpretations are discussed.Comment: 25 pages, 7 figures. Additional references and figur

Necrotizing meningoencephalitis in atypical dog breeds: a case series and literature review.

BackgroundCanine necrotizing meningoencephalitis (NME) is a fatal, noninfectious inflammatory disease of unknown etiology. NME has been reported only in a small number of dog breeds, which has led to the presumption that it is a breed-restricted disorder.Hypothesis/objectivesOur objective was to describe histopathologically confirmed NME in dog breeds in which the condition has not been reported previously and to provide preliminary evidence that NME affects a wider spectrum of dog breeds than previously reported.AnimalsFour dogs with NME.MethodsArchives from 3 institutions and from 1 author's (BS) collection were reviewed to identify histopathologically confirmed cases of NME in breeds in which the disease has not been reported previously. Age, sex, breed, survival from onset of clinical signs, and histopathologic findings were evaluated.ResultsNecrotizing meningoencephalitis was identified in 4 small dog breeds (Papillon, Shih Tzu, Coton de Tulear, and Brussels Griffon). Median age at clinical evaluation was 2.5 years. Histopathologic abnormalities included 2 or more of the following: lymphoplasmacytic or histiocytic meningoencephalitis or encephalitis, moderate-to-severe cerebrocortical necrosis, variable involvement of other anatomic locations within the brain (cerebellum, brainstem), and absence of detectable infectious agents.Conclusions and clinical importanceUntil now, NME has only been described in 5 small dog breeds. We document an additional 4 small breeds previously not shown to develop NME. Our cases further illustrate that NME is not a breed-restricted disorder and should be considered in the differential diagnosis for dogs with signalment and clinical signs consistent with inflammatory brain disease

Bounds on Dimension Reduction in the Nuclear Norm

$\newcommand{\schs}{\scriptstyle{\mathsf{S}}_1}$For all $n \ge 1$, we give an explicit construction of $m \times m$ matrices $A_1,\ldots,A_n$ with $m = 2^{\lfloor n/2 \rfloor}$ such that for any $d$ and $d \times d$ matrices $A'_1,\ldots,A'_n$ that satisfy \|A'_i-A'_j\|_{\schs} \,\leq\, \|A_i-A_j\|_{\schs}\,\leq\, (1+\delta) \|A'_i-A'_j\|_{\schs} for all $i,j\in\{1,\ldots,n\}$ and small enough $\delta = O(n^{-c})$, where $c> 0$ is a universal constant, it must be the case that $d \ge 2^{\lfloor n/2\rfloor -1}$. This stands in contrast to the metric theory of commutative $\ell_p$ spaces, as it is known that for any $p\geq 1$, any $n$ points in $\ell_p$ embed exactly in $\ell_p^d$ for $d=n(n-1)/2$. Our proof is based on matrices derived from a representation of the Clifford algebra generated by $n$ anti-commuting Hermitian matrices that square to identity, and borrows ideas from the analysis of nonlocal games in quantum information theory.Comment: 16 page

A numerical evaluation of next generation additive layer manufactured inter-layer channel heat exchanger

A Concept Heat Exchanger (HE) design manufactured using the Additive Layer Manufacturing (ALM) technique Selective Laser Melting (SLM) is proposed and numerically evaluated. It is composed of a HE corrugation which introduces inter-layer flow conduits between the parallel HE layers of the same fluid. These pathways are provided by hollow elliptical tubes which serve several functions: to disturb the flow to promote heat transfer, to provide additional heat transfer area and to minimise flow maldistribution inside the HE core. The corrugation is incorporated into a counter-flow prototype HE unit model meaning to exploit the installation volume and design freedom made possible via ALM. Three Computational Fluid Dynamics (CFD) models are utilised to evaluate the performance of the proposed HE unit. Firstly, a traditional two step HE design methodology is utilised which works by initially evaluating a fully symmetric channel of the proposed HE corrugation (termed single channel). Then the results this model are incorporated into a simplified HE unit model. The second approach evaluates the HE unit performance based on a fully detailed CFD analysis that fully resolves flow and heat transfer inside the HE core. The third modelling approach involves splitting the inter-layer HE unit model into parts, which results in HE header models and allows simplification of the HE core into a single corrugation period width HE core model (termed superchannel). The results of these models are then compared to a conventional pin–fin HE unit model, formed by blocking the elliptical inter-layer conduits. It was found that in all the HE unit models the pressure drop is similar whilst the heat transfer was enhanced by between 7% and 13% in terms of the overall ΔT by the inter-layer channels (increasing with the Reynolds number). All simulations were completed using a CFD package OpenFOAM

A multi-scale conjugate heat transfer modelling approach for corrugated heat exchangers

The paper compares two serrated plate-fin Heat Exchanger (HE) corrugation modelling methods using Computational Fluid Dynamics (CFD). The first method follows closely recent literature studies and models a finite length single channel of a corrugation layer inside the HE core. The second method utilises the conjugate heat transfer methodology and models a section of the HE core with both cold and hot fluid streams separated by a solid conducting wall (HE corrugation). The results of latter model are then extrapolated for the full dimensions of a HE core layer to obtain flow and heat transfer characteristics. The conjugate heat transfer analysis methodology presented is novel and eliminates the need for analytical/empirical modelling currently widely used within industry. Furthermore, it provides more detailed information about the flow and heat transfer inside the HE core enabling potential for more efficient HE designs. Predictions at the corrugation level were carried out at with mesh independence studies completed for all the computational domains. The results obtained in the HE corrugation predictions were then implemented to the multi-scale HE unit model where the flow inside the HE core was modelled using two porous media simplifications whilst the heat transfer was simplified using the effectiveness source term. The HE unit predictions were validated against industrial experimental data with good agreement found between the numerical and experimental results. All the simulations were completed using the open-source CFD package OpenFOAM

Experimental and numerical study of the additive layer manufactured inter-layer channel heat exchanger

In this paper the performance of a recently patented additive layer manufactured (ALM) concept inter-layer heat exchanger (HE) is evaluated experimentally and numerically. Two numerical HE models are developed using the conjugate heat transfer (CHT) methodology. The first is an idealised HE core model, consisting of a single period width HE corrugation section (termed superchannel). The second approach uses a fully detailed HE unit model which resolves the flow and heat transfer inside the complete HE unit. A close agreement was found between the HE unit simulations and the experimentally obtained results, such that the fully detailed HE model could be validated. It was also shown that, a full CHT approach is necessary to accurately evaluate complex inter-layer ALM HE core flow and heat transfer behaviour and can serve as an approach for optimising HE designs. The results also reinforce the occurrence of the inter-layer flow mixing inside the HE core of the same flow streams and allows the mass flow to redistribute inside the HE core which is impossible with the current HE generation geometries. The superchannel model results in a slight over-estimation in heat transfer ( K on average) making the simplified model acceptable as a conservative estimate. Using validated simulations a parametric study was conducted by changing the solid properties of the full CHT HE model to aluminium to investigate the effects of a significantly more conductive material. This resulted in higher heat transfer effectiveness () of the HE unit. All the simulations were carried out using CFD package OpenFOAM

Bounds on Dimension Reduction in the Nuclear Norm

For all n ≥ 1, we give an explicit construction of m × m matrices A_1,…,A_n with m = 2^([n/2]) such that for any d and d × d matrices A′_1,…,A′_n that satisfy ∥A_′i−A′_j∥S_1 ≤ ∥A_i−A_j∥S_1 ≤ (1+δ)∥A′_i−A′_j∥S_1 for all i,j∈{1,…,n} and small enough δ = O(n^(−c)), where c > 0 is a universal constant, it must be the case that d ≥ 2^([n/2]−1). This stands in contrast to the metric theory of commutative ℓ_p spaces, as it is known that for any p ≥ 1, any n points in ℓ_p embed exactly in ℓ^d_p for d = n(n−1)/2. Our proof is based on matrices derived from a representation of the Clifford algebra generated by n anti-commuting Hermitian matrices that square to identity, and borrows ideas from the analysis of nonlocal games in quantum information theory

"Thinking about numbers is not my idea of fun": need for cognition mediates age differences in numeracy performance.

Background. Numeracy refers to people’s ability to use numbers. Low numeracy has been associated with difficulties in understanding risk-benefit information and making health decisions. Older adults tend to perform worse than younger adults on measures of numeracy, but some theories of aging suggest that older adults may lack motivation for such tasks. We therefore test whether age differences in numeracy performance are mediated by a reduced motivation to think hard about complex problems—as measured by need for cognition. Method. We recruited an age-diverse convenience sample of 306 UK adults. They completed measures of numeracy and need for cognition. They self-reported their educational attainment and other demographics. Results. Older age was related to lower numeracy and lower need for cognition. The negative relationship between age and numeracy was mediated by need for cognition. These findings held after we controlled for educational attainment and other demographic factors. Discussion. Older adults may show lower numeracy performance due to lack of motivation. We discuss strategies for improving people’s motivation to complete numeracy measures and other numerical tasks