Slow-burning instabilities of Dufort-Frankel finite differencing

2021 ◽  
Vol 63 ◽  
pp. 23-38
Author(s):  
David Galloway ◽  
David J Ivers

DuFort–Frankel averaging is a tactic to stabilize Richardson’s unstable three-level leapfrog timestepping scheme. By including the next time level in the right-hand-side evaluation, it is implicit, but it can be rearranged to give an explicit updating formula, thus apparently giving the best of both worlds. Textbooks prove unconditional stability for the heat equation, and extensive use on a variety of advection–diffusion equations has produced many useful results. Nonetheless, for some problems the scheme can fail in an interesting and surprising way, leading to instability at very long times. An analysis for a simple problem involving a pair of evolution equations that describe the spread of a rabies epidemic gives insight into how this occurs. An even simpler modified diffusion equation suffers from the same instability. Finally, the rabies problem is revisited and a stable method is found for a restricted range of parameter values, although no prescriptive recipe is known which selects this particular choice.   doi:10.1017/S1446181121000043

2021 ◽  
pp. 1-16
Author(s):  
DAVID GALLOWAY ◽  
DAVID IVERS

Abstract DuFort–Frankel averaging is a tactic to stabilize Richardson’s unstable three-level leapfrog timestepping scheme. By including the next time level in the right-hand-side evaluation, it is implicit, but it can be rearranged to give an explicit updating formula, thus apparently giving the best of both worlds. Textbooks prove unconditional stability for the heat equation, and extensive use on a variety of advection–diffusion equations has produced many useful results. Nonetheless, for some problems the scheme can fail in an interesting and surprising way, leading to instability at very long times. An analysis for a simple problem involving a pair of evolution equations that describe the spread of a rabies epidemic gives insight into how this occurs. An even simpler modified diffusion equation suffers from the same instability. Finally, the rabies problem is revisited and a stable method is found for a restricted range of parameter values, although no prescriptive recipe is known which selects this particular choice.


2020 ◽  
Vol 17 (1) ◽  
pp. 56-69
Author(s):  
Aishath Muneeza ◽  
Zakariya Mustapha

Limitations of action designate extent of time after an event, as set by statutes of limitations, within which legal action can be initiated by a party to a transaction. No event is actionable outside the designated time as same is rendered statute-barred. This study aims to provide an insight into application and significance of Limitations Act 1950 and Limitation Ordinance 1952 to Islamic banking matters in Malaysia as well as Shariah viewpoint on the issue of limitation of action. In conducting the study, a qualitative research methodology is employed where reported Islamic banking cases from 1983 to 2018 in Malaysia were reviewed and analysed to ascertain the application of those statutes of limitations to Islamic banking. Likewise, relevant provisions of the statutes as invoked in the cases were examined to determine possible legislative conflicts between the provisions and the rule of Islamic law in governing the right and limitation of action in Islamic banking cases under the law. The reviewed cases show the extent to which statutes of limitations were invoked in Malaysian courts in determining validity of Islamic banking matters. The limitation provisions so referred to are largely sections 6(1)(a) and 21(1) Limitations Act 1953 and section 19 Limitation Ordinance 1953, which do not conflict with Shariah viewpoint on the matter. This study will prove invaluable to financial institutions and their customers alike in promoting knowledge and creating awareness over actionable event in the course of their transactions.


Author(s):  
Deep K. Datta-Ray

The history of Indian diplomacy conceptualises diplomacy racially—as invented by the West—and restrictively—to offence. This is ‘analytic-violence’ and it explains the berating of Indians for mimicking diplomacy incorrectly or unthinkingly, and the deleting, dismissing, or denigrating, of diplomatic practices contradicting history’s conception. To relieve history from these offences, a new method is presented, ‘Producer-Centred Research’ (PCR). Initiating with abduction, an insight into a problem—in this case Indian diplomacy’s compromised historicisation—PCR solves it by converting history’s racist rationality into ‘rationalities’. The plurality renders rationality one of many, permitting PCR’s searching for rationalities not as a function of rationality but robust practices explicable in producer’s terms. Doing so is exegesis. It reveals India’s nuclear diplomacy as unique, for being organised by defence, not offence. Moreover, offence’s premise of security as exceeding opponent’s hostility renders it chimerical for such a security is, paradoxically, reliant on expanding arsenals. Additionally, doing so is a response to opponents. This fragments sovereignty and abdicates control for one is dependent on opponent’s choices. Defence, however, does not instigate opponents and so really delivers security by minimising arsenals since offence is eschewed. Doing so is not a response to opponents and so maintains sovereignty and retains control by denying others the right to offense. The cost of defence is courage, for instance, choosing to live in the shadow of nuclear annihilation. Exegesis discloses Balakot as a shift from defence to offence, so to relieve the Bharatiya Janata Party’s (BJP) leadership of having to be courageous. The intensity of the intention to discard courage is apparent in the price the BJP paid. This included equating India with Pakistan, permitting it to escalate the conflict, and so imperiling all humanity in a manner beyond history.


2019 ◽  
Vol 3 (Supplement_1) ◽  
Author(s):  
Andrea Warren ◽  
Edward Frongillo ◽  
Shana Alford ◽  
Erin McDonald ◽  
Jessica Escobar-Alegria

Abstract Objectives The objective of this study was to understand needs among seniors for food and food assistance and to develop a comprehensive taxonomy for these needs. Methods A total of 147 seniors were purposively sampled from 12 food-assistance programs in 9 states. Of the 12 programs, 10 provided unprepared foods and 2 provided pre-cooked meals. Data were semi-structured qualitative interviews. Coding and analysis of transcripts followed an inductive qualitative analysis approach. A series of thematic summaries were prepared to reflect the content of the interviews for discussion and refinement of the analytic approach. Results An emergent taxonomy comprised 3 categories consisting of abilities and ranges or variants of those abilities. The category of physical ability consists of physical strength, the ability to prepare food, the ability to walk or stand, and health status. These relate to an individual's functional abilities to live and act independently and may be considered pre-conditions for program uptake and benefit distinct from dietary and food security-related needs and limitations. The category of consuming food consists of preferences, accessibility, affordability, and dietary needs. This category highlights the relationship between economic constraints and dietary needs that often necessitates meaningful tradeoffs in consuming the right foods for their health. The category of access and use of transportation consists of own means, friends or family, and public or private services. This category highlights challenges in accessing programs and provides insight into seniors’ experiences of poverty, declining functional abilities, social networks and connectedness, geography, and public services. Conclusions The process used to develop the taxonomy and the taxonomy itself provide an exemplar for implementation research when the nature of need is complex and programs integrated across sectors are required to address the need. The taxonomy provides structure to facilitate the identification of key factors in program engagement—and insight into the economic and social environments in which they occur—that translate into needs relevant to the design, targeting, and uptake of food assistance in a diverse population of seniors. Funding Sources Enterprise Rent-a-Car Foundation.


2020 ◽  
pp. 108705472096456
Author(s):  
Yue Yang ◽  
Gang Peng ◽  
Hongwu Zeng ◽  
Diangang Fang ◽  
Linlin Zhang ◽  
...  

Objective: The present study aimed to examine the effects of SNAP25 on the integration ability of intrinsic brain functions in children with ADHD, and whether the integration ability was associated with working memory (WM). Methods: A sliding time window method was used to calculate the spatial and temporal concordance among five rs-fMRI regional indices in 55 children with ADHD and 20 healthy controls. Results: The SNAP25 exhibited significant interaction effects with ADHD diagnosis on the voxel-wise concordance in the right posterior central gyrus, fusiform gyrus and lingual gyrus. Specifically, for children with ADHD, G-carriers showed increased voxel-wise concordance in comparison to TT homozygotes in the right precentral gyrus, superior frontal gyrus, postcentral gyrus, and middle frontal gyrus. The voxel-wise concordance was also found to be related to WM. Conclusion: Our findings provided a new insight into the neural mechanisms of the brain function of ADHD children.


Problemos ◽  
2007 ◽  
Vol 71 ◽  
Author(s):  
Skirmantas Jankauskas

Straipsnyje mėginama rekonstruoti platoniškosios meilės sampratos fenomenologinį aspektą. Šios sampratos kontūrus Platonas nužymi dar „Puotoje“, tačiau daugiausia dėmesio jai skiria bene poetiškiausiame ir mįslingiausiame savo dialoge „Faidras“. Įvadinėje dalyje teigiama, kad graikiškasis filosofavimas klostosi natūraliai, t. y. tematizuoja filosofavimui rūpimus turinius, tik susiklostant filosofavimui palankioms aplinkybėms. Brandą pasiekusi filosofija jau mėgina perprasti save, taigi ir įsisąmoninti tas natūralias prielaidas. Platonas dar „Puotoje“ nustato, kad palankiausia filosofavimui natūrali žmogaus būsena yra meilė. „Puotoje“ jam pavyksta išryškinti vertybinį meilės profilį, o filosofavimas čia aprašomas kaip grožio vertybės užangažuotas „teisingasis kelias“, kreipiantis mąstymą grynojo teorinio žinojimo link. Pati meilė čia traktuojama dar gana neapibrėžtai, t. y. kaip „gimdymas grožyje“. Sutelkdamas dėmesį į žmogiškąjį santykį, „Faidre“ Platonas kaip tik imasi detalizuoti „gimdymo grožyje“ fenomenologiją. Platonas struktūruoja sielą, t. y. pavaizduoja ją kaip vadeliotojo važnyčiojamą sparnuotą dvikinkę. Grožio veikiama ši dvikinkė pasikelia į uždangės sritį, ir vadeliotojui palankiausiu atveju pavyksta išvysti „tiesos lygumą“. Metaforiškai aprašytos sielos dalys straipsnyje susiejamos su atitinkamomis kasdienio ir etinio mąstymo temomis bei teoriniu mąstymu apskritai, o sparnuotumas – su vertybiškumu. Sekant Platono aprašyta sielos dalių dinamika pavyksta parodyti, kaip veikiant grožiui teorinis mąstymas gali tematizuoti etiškumo temą ir veikiai pelnyti būties įžvalgą. Pagrindiniai žodžiai: meilė, šėlas, tiesa, būtis, grožis, gėris, natūralus filosofavimas, fenomenologijaPhaidros: Phenomenology of “Giving Forth upon the Beautiful”Skirmantas Jankauskas   SummaryThe author makes an attempt to reconstruct the phenomenological aspect of Plato’s concept of love. The contours of this concept are only outlined by Plato in his Symposium to be later developed in his probably the most poetic and enigmatic dialogue Phaedrus. A hypothesis is put forward here that love as ‘madness’ – as described in Phaedrus – could be treated as a further elaboration of the concept of ‘giving forth upon the beautiful’ as portrayed in Symposium. The article starts with a thesis that Greek philosophizing  proceeds in a natural way, i.e. it thematises the preferred contents only within favorable external circumstances. As philosophy reaches its maturity, it tries to learn itself, i.e. to realize these favorable natural circumstances. It is already in Symposium that Plato establishes that love is the most favorable condition for philosophizing. In this dialogue Plato manages to elucidate the axiological profile of love. Philosophizing is presented as the ‘right way’ to be engaged by the beautiful and to lead towards pure theoretical thinking. Love itself is treated in an inde terminate way as ‘giving forth upon the beautiful’. By putting the human relation in the focus of attention, Plato reveals in his Phaedrus the phenomenology of ‘giving forth upon the beautiful’. He describes the soul as ‘a team of winged steeds and their winged charioteer’. Affected by the beautiful, this ‘team’ climbs the boundaries of the heavens and the ‘charioteer’, in the utmost case, manages to contemplate the ‘plain of truth’. In the article, those metaphorically described parts of the soul are associated correspondingly with themes of everyday thinking and ethical thinking as well as theoretical thinking in general, while wingness is related to valuesness. Tracing the dynamics of the parts of the soul, as portrayed in Phaedrus, the author manages to describe the way in which theoretical thinking thematises the theme of ethical thinking and attains the insight into being under the impact of the beautiful. Keywords: love, madness, truth, being, the beautiful, the good, natural philosophising, phenomenology.p;


2021 ◽  
Vol 331 ◽  
pp. 02016
Author(s):  
Ikhsan Purnama ◽  
Muhammad Imran Hamid

A work accident can occur anytime and anywhere to the worker if they take unsafe action and are in an unsafe condition. Mining areas located in the hills have unsafe conditions for operating heavy equipment, such as steep terrain conditions, slippery roads, and foggy weather, and lack of lighting. Installation of light assign is the right step in reducing work accidents at night, foggy and rainy weather. Measurement of wind data and calculation of wind potential statistically using Weibull distribution. The parameter values of scale and shape are 1.67 and 1,71 respectively, with an average wind speed of 1,49 m/s and the wind power potential of 3.14 W/m2. Based on measurement and analysis results, this quarry always gets wind gusts both day and night, so it has the potential to take advantage of wind energy either on a small turbine scale or in small and medium electric power.


2018 ◽  
Vol III (I) ◽  
pp. 1-9
Author(s):  
Muhammad Rizwan ◽  
Manzoor Ahmad ◽  
Syed Asif Anwar Bukhari

Soon after its creation, Pakistan confronted many issues including refugee problem, scarcity of able political leadership, absence of mutual consensus between both wings of the country and confusing nature of the relationship between Islam and state etc. took almost nine years to frame the permanent constitution for Pakistan. Constitution, the basic document of a state, determines the shape of its laws, structure of governance and system of rights and duties. The effectiveness of a constitution is judged by its practicability in the given area where it is enforced by the state machinery. Although, all civilized states of the world do possess a constitution, yet a good constitution is one which must protect the basic human rights by ensuring the independence of judiciary. Due to countless hurdles at the beginning of its journey, Pakistan’s constitutional development in the right direction could not take place. The main objective of the present study is to provide deep insight into the events and factors causing a delay in the constitution-making for the newly created state of Pakistan. The various events which took place from 1947 to 1956 have been analyzed in a subtle way.


2010 ◽  
Vol 22 (1) ◽  
pp. 190-243 ◽  
Author(s):  
Elisa Magosso ◽  
Melissa Zavaglia ◽  
Andrea Serino ◽  
Giuseppe di Pellegrino ◽  
Mauro Ursino

Neurophysiological and behavioral studies suggest that the peripersonal space is represented in a multisensory fashion by integrating stimuli of different modalities. We developed a neural network to simulate the visual-tactile representation of the peripersonal space around the right and left hands. The model is composed of two networks (one per hemisphere), each with three areas of neurons: two are unimodal (visual and tactile) and communicate by synaptic connections with a third downstream multimodal (visual-tactile) area. The hemispheres are interconnected by inhibitory synapses. We applied a combination of analytic and computer simulation techniques. The analytic approach requires some simplifying assumptions and approximations (linearization and a reduced number of neurons) and is used to investigate network stability as a function of parameter values, providing some emergent properties. These are then tested and extended by computer simulations of a more complex nonlinear network that does not rely on the previous simplifications. With basal parameter values, the extended network reproduces several in vivo phenomena: multisensory coding of peripersonal space, reinforcement of unisensory perception by multimodal stimulation, and coexistence of simultaneous right- and left-hand representations in bilateral stimulation. By reducing the strength of the synapses from the right tactile neurons, the network is able to mimic the responses characteristic of right-brain-damaged patients with left tactile extinction: perception of unilateral left tactile stimulation, cross-modal extinction and cross-modal facilitation in bilateral stimulation. Finally, a variety of sensitivity analyses on some key parameters was performed to shed light on the contribution of single-model components in network behaviour. The model may help us understand the neural circuitry underlying peripersonal space representation and identify its alterations explaining neurological deficits. In perspective, it could help in interpreting results of psychophysical and behavioral trials and clarifying the neural correlates of multisensory-based rehabilitation procedures.


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