Fast and accurate evaluation of Wigner 3j, 6j, and 9j symbols using prime factorisation and multi-word integer arithmetic

We present an efficient implementation for the evaluation of Wigner 3j, 6j, and 9j symbols. These represent numerical transformation coefficients that are used in the quantum theory of angular momentum. They can be expressed as sums and square roots of ratios of integers. The integers can be very large due to factorials. We avoid numerical precision loss due to cancellation through the use of multi-word integer arithmetic for exact accumulation of all sums. A fixed relative accuracy is maintained as the limited number of floating-point operations in the final step only incur rounding errors in the least significant bits. Time spent to evaluate large multi-word integers is in turn reduced by using explicit prime factorisation of the ingoing factorials, thereby improving execution speed. Comparison with existing routines shows the efficiency of our approach and we therefore provide a computer code based on this work.Comment: 7 pages, 2 figures. Accepted for publication in SIAM Journal on Scientific Computing (SISC

Analytical approach to electromagnetic processes in loosely bound nuclei: application to 8B

In this paper we develop an analytical model in order to study electromagnetic processes involving loosely bound neutron--rich and proton--rich nuclei. We construct a model wave function, to describe loosely bound few--body systems, having the correct behaviour both at large and small distances. The continuum states are approximated by regular Coulomb functions. As a test case we consider the two--body Coulomb dissociation of 8B and, the inverse, radiative capture reaction. The difference between using a pure two--body model and the results obtained when incorporating many--body effects, is investigated. We conclude that the interpretation of experimental data is highly model dependent and stress the importance of measuring few--body channels.Comment: Accepted for publication in Physics Letters B. Added a comparison with a potential model calculation in Fig.

Ab initio nuclear response functions for dark matter searches

We study the process of dark matter particles scattering off $^{3,4}$He with nuclear wave functions computed using an ab initio many-body framework. We employ realistic nuclear interactions from chiral effective field theory at next-to-next-to-leading order (NNLO) and develop an ab initio scheme to compute a general set of different nuclear response functions. In particular, we then perform an accompanying uncertainty quantification on these quantities and study error propagation to physical observables. We find a rich structure of allowed nuclear responses with significant uncertainties for certain spin-dependent interactions. The approach and results that are presented in this Paper establish a new framework for nuclear structure calculations and uncertainty quantification in the context of direct and (certain) indirect searches for dark matter.Comment: version accepted for publication in Phys. Rev. D; figures revised (incl. corrected labels); discussion of results extende

Analytical E1 strength functions of two-neutron halo nuclei: the 6-He example

An analytical model is developed to study the spectra of electromagnetic dissociation of two-neutron halo nuclei without precise knowledge about initial and final states. Phenomenological three-cluster bound state wave functions, reproducing the most relevant features of these nuclei, are used along with no interaction final states. The 6-He nucleus is considered as a test case, and a good agreement with experimental data concerning the shape of the spectrum and the magnitude of the strength function is found.Comment: 19 pages, 4 figures Accepted for publishing in Nuclear Physics

“It was a free and healthy job”

The exploitation of northern Sweden's forests began in about the 1830s and continued expanding northwards over the following decades. A key factor that enabling the exploitation of these forests was the natural infrastructure, such as the network of rivers, creeks and flooding during the summer, which made it possible to float timber from the forests to the sawmills on the coast. The overall aim of this work is to analyze timber floating on the river Ångermanälven, highlighting the log drivers’ role in timber supply to the industry and how timber floating was integral to local society. The timber floating in northern Sweden was a complex process, involving technical, ecological, economic, and social factors, which also evolved over a long period of time. To do justice to this complexity, I have used various methods to answer my questions. Firstly, I studied many different historical records at the National Archives of Sweden, Härnösand, including annual reports, maps, salary agreements, photographs, and newspapers. Secondly, I conducted in-depth semi-structured interviews with 20 people who worked in timber floating on the river Ångermanälven. The timber floating season on the river Ångermanälven was a complex process with different stages and work duties through the season with preparations, floating in the creeks and rivers and the final clear-up. The work as a log driver was a high-risk work with jam-breaking and rowing in the rapids. All my male informants said there was a good spirit and cohesion among the log drivers in the team. They also said they enjoyed working in timber floating even though the workdays could be heavy, and many log drivers wanted to work in timber floating year after year. Moreover, women had an important role in timber floating as cooks and served proper food during the heavy work shifts. Timber floating was part of the timber value chain, enabling the transport of wood from forest to industry, and the logging and timber floating seasons created an annual cycle of employment for many men in the northern inland of Sweden. Timber floating had noticeable impacts on the local communities along the river since it created work opportunities for many people. Although the river Even though Ångermanälven was one of the last rivers on which timber floating was performed in Sweden, it could not compete with lorry transport and the other factors that had affected timber floating negatively. Nonetheless, timber floating brought imprints and memories to the people involved. I hope this study will contribute to that the oral history of timber floating on the river Ångermanälven will be preserved to future generations.Exploateringen av skogarna i Norrland började under 1830-talet och fortsatte sedan norrut följande årtionden. Nätverket av bäckar och älvar hade en betydande roll för skogsexploateringen eftersom det möjliggjorde att stora volymer av timmer kunde flottas från inlandet till sågverksindustrin vid kusten. Det övergripande syftet med studien var att analysera flottningen i Ångermanälven, lyfta flottarnas roll i försörjningen av timmer till skogsindustrin, samt hur flottningen var integrerad i lokalsamhället. Flottningen var en komplex process som innefattade tekniska, ekologiska, ekonomiska och sociala faktorer, som även förändrades över tid. Jag har därför använt olika metoder för att besvara mina frågeställningar. För det första studerade jag historiskt källmaterial vid Riksarkivet i Härnösand, där jag bland annat studerade årsrapporter, kartor, lönelistor, fotografier och tidningar. För det andra har jag intervjuat 20 personer som har arbetat som flottare, kockor och timmervakt i flottningen på Ångermanälven. Det var många olika delar och uppgifter under flottningssäsongen med förberedelser, bäckflottning, älvflottning och slutrensningen. Att arbeta som flottare var riskabelt, bland annat genom att ro i forsarna och arbeta på brötarna. Alla mina informanter tyckte att det var en bra stämning och sammanhållning i arbetslaget. De tycke om att arbeta i flottningen även om det var ett hårt arbete, och många flottare ville tillbaka till flottningen år efter år. Kvinnor hade också en betydande roll i flottningen som kockor och serverade bra och nyttig mat under de tunga arbetsdagarna. Flottningen var en del av timmerindustriens värdekedja och möjliggjorde timmertransporten från skog till industri, och avverknings- och flottningssäsongen skapade en arbetscykel under året för inlandsbefolkningen i Norrland. Flottningen hade en betydande påverkan på lokalsamhället längs älven eftersom flottningen gav många arbetstillfällen. Även om Ångermanälven var en de sista älvarna som det flottades i Sverige, kunde flottningsintresset inte konkurrera med lastbilstransporterna och de andra faktorerna som påverkade flottningen negativt. Trots att flottningen behövde avvecklas, lämnade den ett stort avtryck och minnen hos människorna som var involverad i flottningen. Jag hoppas den här studien kommer bidra till att historierna från flottningen i Ångermanälven kommer leva vidare till nästkommande generationer

Families with children in recessionary Finland

&nbsp

Calculation of sound reduction by a screen in a turbulent atmosphere using the parabolic equation method

Results from applying a Crank-Nicholson parabolic equation method (CN-PE) are presented in situations with a thin screen on a hard ground in a turbulent atmosphere, and with the acoustic source at ground level. The results are evaluated by comparison with G. A. Daigle's model, which uses the sound scattering cross-section by V. I. Tatarskii together with diffraction theory. The results show a fairly good agreement for situations where the receiver is above ground, thus indicating that both methods are applicable to the problem. When the receiver is at ground level the two methods lead to large differences in insertion loss since only the PE method predicts that turbulence causes an increased sound level in the case without a screen. For the situations considered in this paper a turbulent atmosphere is shown to significantly decrease the sound reduction by a screen. An approximation in the representation of a turbulent atmosphere in the CN-PE method is presented, and is shown to lead to an acceptable error in limited cases

An extended substitute-sources method for a turbulent atmosphere: Calculations for upward refraction

The substitute-sources method (SSM) was previously implemented for a single noise barrier in a turbulent atmosphere by applying a substitute surface between the barrier and the receiver [1, 2]. Here, the method is extended, aiming to more general applicability to traffic noise propagation in urban environments. In the method, multiple substitute surfaces are used along the propagation path. The atmospheric turbulence causes a transfer of the initially coherent field into a residual, random field along the propagation path. The mean sound level at the receiver position is found from uncorrelated addition of the substitute surfaces' contributions. The calculation of each contribution is based on a mutual coherence function (MCF) for a turbulent atmosphere. The strength of the substitute sources and the Green functions to the received pressure are calculated for a non-turbulent atmosphere, here by using a fast field program (FFP). A special MCF for the residual field is derived. Examples are calculated for a turbulent atmosphere with upward refraction or without refraction. The results are compared with those from a parabolic equation method (PE) for the refractive cases and with an analytical solution otherwise. The results show good agreement, which indicates that the SSM could be useful for predictions of outdoor sound propagation