On the correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations

The relationship between Koopman mode decomposition, resolvent mode decomposition and exact invariant solutions of the Navier-Stokes equations is clarified. The correspondence rests upon the invariance of the system operators under symmetry operations such as spatial translation. The usual interpretation of the Koopman operator is generalised to permit combinations of such operations, in addition to translation in time. This invariance is related to the spectrum of a spatio-temporal Koopman operator, which has a travelling wave interpretation. The relationship leads to a generalisation of dynamic mode decomposition, in which symmetry operations are applied to restrict the dynamic modes to span a subspace subject to those symmetries. The resolvent is interpreted as the mapping between the Koopman modes of the Reynolds stress divergence and the velocity field. It is shown that the singular vectors of the resolvent (the resolvent modes) are the optimal basis in which to express the velocity field Koopman modes where the latter are not a priori known

A foundation for analytical developments in the logarithmic region of turbulent channels

An analytical framework for studying the logarithmic region of turbulent channels is formulated. We build on recent findings (Moarref et al., J. Fluid Mech., 734, 2013) that the velocity fluctuations in the logarithmic region can be decomposed into a weighted sum of geometrically self-similar resolvent modes. The resolvent modes and the weights represent the linear amplification mechanisms and the scaling influence of the nonlinear interactions in the Navier-Stokes equations (NSE), respectively (McKeon & Sharma, J. Fluid Mech., 658, 2010). Originating from the NSE, this framework provides an analytical support for Townsend's attached-eddy model. Our main result is that self-similarity enables order reduction in modeling the logarithmic region by establishing a quantitative link between the self-similar structures and the velocity spectra. Specifically, the energy intensities, the Reynolds stresses, and the energy budget are expressed in terms of the resolvent modes with speeds corresponding to the top of the logarithmic region. The weights of the triad modes -the modes that directly interact via the quadratic nonlinearity in the NSE- are coupled via the interaction coefficients that depend solely on the resolvent modes (McKeon et al., Phys. Fluids, 25, 2013). We use the hierarchies of self-similar modes in the logarithmic region to extend the notion of triad modes to triad hierarchies. It is shown that the interaction coefficients for the triad modes that belong to a triad hierarchy follow an exponential function. The combination of these findings can be used to better understand the dynamics and interaction of flow structures in the logarithmic region. The compatibility of the proposed model with theoretical and experimental results is further discussed.Comment: Submitted to J. Fluid Mec

Relationships between threshold-based PROP sensitivity and food preferences of Tunisians

International audienceThe extent to which taste responses - and notably the genetically determined sensitivity to 6-npropylthiouracil (PROP) - influences food preferences and food use is still a matter of debate. We addressed the issue on the basis of a behavioural and anthropological study performed in Tunis in 1999. The working sample consists of 123 adults of both sexes (38 men, 85 women), aged 19 to 59, in various social categories. Taste recognition thresholds for sucrose, fructose, sodium chloride, quinine hydrochloride, citric acid, tannic acid, oak tannin and PROP were determined by presenting, in a semi-randomised order (blind-test), series of graded aqueous solutions of each product. Subjects also tasted and rated the pleasantness/unpleasantness of 4 supra-threshold solutions of NaCl and sucrose. All subjects completed a checklist of 43 food items representative of Tunisian diet, rated in terms of flavour, cost, effect on health and prestige on a Labelled Affective Magnitude (LAM) scale. According to the underlying distribution of PROP thresholds, the subjects were separated into three categories: "non-tasters", "medium-threshold tasters", and "low-threshold tasters". Results bring out the specificity of low-threshold tasters, as exhibiting a greater taste sensitivity for most tested substances. Low-threshold taster status is also linked to higher mean food preferences ratings irrespective of sex, age and socio-cultural influences. Tasters as a group (medium-threshold tasters + low-threshold tasters) do not exhibit a higher percentage of food dislikes; however PROP sensitivity is negatively correlated with hedonic responses to NaCl solutions. These results together with the evidence of a limited set of food actually used by low-threshold tasters suggest that these subjects might have difficulties at overcoming an inherent neophobia

Identification and frequency of consumption of wild edible plants over a year in central Tunisia: a mixed-methods approach

Objective: To identify wild plants used as food and assess their frequency of consumption over a year in a region of Tunisia where agriculture is undergoing a major transformation from smallholder farming to an intensive high-input agricultural system. Design: Qualitative ethnobotanical study followed by a survey of women's frequency of consumption of wild plants conducted using FFQ at quarterly intervals. Setting: Sidi Bouzid governorate of central Tunisia. Participants: Mixed-gender group of key informants (n 14) and focus group participants (n 43). Survey sample of women aged 20-49 years, representative at governorate level (n 584). Results: Ethnobotanical study: thirty folk species of wild edible plants corresponding to thirty-five taxa were identified by key informants, while twenty folk species (twenty-five taxa) were described by focus groups as commonly eaten. Population-based survey: 98 % of women had consumed a wild plant over the year, with a median frequency of 2 d/month. Wild and semi-domesticated fennel (Foeniculum vulgare Mill. and Anethum graveolens) was the most frequently consumed folk species. Women in the upper tertile of wild plant consumption frequency were more likely to be in their 30s, to live in an urban area, to have non-monetary access to foods from their extended family and to belong to wealthier households. Conclusions: In this population, wild edible plants, predominantly leafy vegetables, are appreciated but consumed infrequently. Their favourable perception, however, offers an opportunity for promoting their consumption which could play a role in providing healthy diets and mitigating the obesity epidemic that is affecting the Tunisian population

Correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations

The relationship between Koopman mode decomposition, resolvent mode decomposition, and exact invariant solutions of the Navier-Stokes equations is clarified. The correspondence rests upon the invariance of the system operators under symmetry operations such as spatial translation. The usual interpretation of the Koopman operator is generalized to permit combinations of such operations, in addition to translation in time. This invariance is related to the spectrum of a spatiotemporal Koopman operator, which has a traveling-wave interpretation. The relationship leads to a generalization of dynamic mode decomposition, in which symmetry operations are applied to restrict the dynamic modes to span a subspace subject to those symmetries. The resolvent is interpreted as the mapping between the Koopman modes of the Reynolds stress divergence and the velocity field. It is shown that the singular vectors of the resolvent (the resolvent modes) are the optimal basis in which to express the velocity field Koopman modes where the latter are not a priori known

Magyarország és az 1967-es arab–izraeli háború

The Arab countries were heavily defeated in the “blitz” that broke out on 5th June 1967 and lasted for six days. This inflicted a blow on the allies of Egypt and Syria, the Soviet Union and the socialist countries. The Hungarian leaders continued to provide support for the Arab countries hit by Israeli aggression. However, they criticized the extreme, reckless, often demagogic statements of certain Arab politicians (Syrians, the leader of the Palestine Liberation Organization). Part of the general public had doubts that the Arabs should be backed, as they had suffered a heavy defeat very quickly. The two authors of the article studied documents from Hungarian archives (e.g. reports by embassies in Damascus, Moscow and Cairo); documents of the communist party and the press in Hungary-Egypt, including Népszabadság, Népszava, al-Ahram, Ruza al-Yusuf, al-Mesa and The Egyptian Gazette.Az 1967. június 5-én kirobbant, hat napig tartó „villámháborúban” az arab országok súlyos vereséget szenvedtek. Ez Egyiptom és Szíria szövetségesei, a Szovjetunió és a szocialista országok vereségét is jelentette. A magyar vezetők továbbra is támogatásukról biztosították az izraeli agresszió által sújtott arab népeket. Ugyanakkor bírálták is egyes arab politikusok (szíriaiak, a Palesztinai Felszabadítási Szervezet vezetője) szélsőséges, felelőtlen, gyakran demagóg kijelentéseit. A közvélemény egy része kételkedett abban, hogy érdemese támogatni az arabokat, hiszen nagyon gyorsan súlyos vereséget szenvedtek. A cikk két írója a magyar levéltári dokumentumokat (pl. a damaszkuszi, a moszkvai és a kairói nagykövetségek jelentéseit), a kommunista párt iratait és a magyar–egyiptomi napi sajtót – beleértve a Népszabadságot, Népszavát, al-Ahrámot, Rúzá al-Júszufot, al-Mészát és a The Egyptian Gazette-t – dolgozta fel

Magyarország és az 1967-es arab-izraeli háború : arab és magyar levéltári iratok és a sajtó tükrében

Az 1967. június 5-én kirobbant, hat napig tartó „villámháborúban” az arab országok súlyos vereséget szenvedtek. Ez Egyiptom és Szíria szövetségesei, a Szovjetunió és a szocialista országok vereségét is jelentette. A magyar vezetők továbbra is támogatásukról biztosították az izraeli agresszió által sújtott arab népeket. Ugyanakkor bírálták is egyes arab politikusok (szíriaiak, a Palesztinai Felszabadítási Szervezet vezetője) szélsőséges, felelőtlen, gyakran demagóg kijelentéseit. A közvélemény egy része kételkedett abban, hogy érdemese támogatni az arabokat, hiszen nagyon gyorsan súlyos vereséget szenvedtek. A cikk két írója a magyar levéltári dokumentumokat (pl. a damaszkuszi, a moszkvai és a kairói nagykövetségek jelentéseit), a kommunista párt iratait és a magyar–egyiptomi napi sajtót – beleértve a Népszabadságot, 1 Népszavát, 2 al-Ahrámot,3 Rúzá al-Júszufot,4 al-Mészát 5 és a The Egyptian Gazette-t 6 – dolgozta fel. The Arab countries were heavily defeated in the “blitz” that broke out on 5th June 1967 and lasted for six days. This inflicted a blow on the allies of Egypt and Syria, the Soviet Union and the socialist countries. The Hungarian leaders continued to provide support for the Arab countries hit by Israeli aggression. However, they criticized the extreme, reckless, often demagogic statements of certain Arab politicians (Syrians, the leader of the Palestine Liberation Organization). Part of the general public had doubts that the Arabs should be backed, as they had suffered a heavy defeat very quickly. The two authors of the article studied documents from Hungarian archives (e.g. reports by embassies in Damascus, Moscow and Cairo); documents of the communist party and the press in Hungary-Egypt, including Népszabadság, Népszava, al-Ahram, Ruza al-Yusuf, al-Mesa and The Egyptian Gazette. Dans la guerre d’éclaire (ou de six jours) déclenchée le 5 juin 1967, les pays arabes ont subi une défaite cuisante qui était non seulement celle de l’Egypte et de la Syrie, mais aussi celle des ses alliés, les pays socialistes et l’URSS. Malgré la défaite la Hongrie continuait à soutenir les peuples arabes frappés par l’agression israélienne, mais en même temps elle critiqait certains dirigeants arabes (les Syriens, OLP) pour leur déclarations extrémistes et irresponsables. Une partie de l’opinion publique pensait que les arabes vaincus d’une manière humiliante ne méritent pas le soutien, contrairement aux Vietnamiens qui menaient un combat héroïque. L’article est basé sur les documents de l’Archives nationales hongroise (p.ex. les rapports des ambassades du Damas, du Caire et de Moscou), sur les documents du parti communiste et les presses hongroise et égyptienne