1
|
Davis BH, Troutman-Jordan M, Maclagan M. Your phrases matter: Third waves in research approaches and new contexts for formulaic language. Int J Lang Commun Disord 2024; 59:84-93. [PMID: 37340952 DOI: 10.1111/1460-6984.12915] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2023] [Accepted: 06/01/2023] [Indexed: 06/22/2023]
Abstract
BACKGROUND This study reports on new contexts in which formulaic language has been used in the years since 2013 when the last synthesis was carried out. The background presents an old but still useful definition and lists themes under which research was arranged in 2013 and which continue to be used. AIMS This study has a particular emphasis on the relevance of formulaic language to people living with dementia. METHODS Section 3, identifying new directions, reviews new 'third waves' of research priorities in several fields in which formulaic sequences play a major role, including sociolinguistic variation, corpus-based and corpus-driven analyses, pragmatics, human-computer interaction, and psycholinguistics, all of which are relevant to speech-language therapists. Section 4, outreach and expansions, illustrates new contributions from cognitively impaired person-to-person exchanges in online environments, recent examinations of infant- and pet-directed speech incorporating formulaic language, and online graphic explorations such as emojis. Section 5 focuses on growth of research in theoretical and clinical applications by Van Lancker Sidtis, as illustrated by references to her recent work. MAIN CONTRIBUTION The paper's main contribution is to summarize the work on formulaic language over the last 10 years, to indicate its continued importance and relevance in ordinary conversation, and especially in allowing people living with dementia to continue to interact with others. CONCLUSION The paper concludes by suggesting that more focus be placed on the analysis of formulaic language with an emphasis on its relevance for speech-language therapists and other clinicians. WHAT THIS PAPER ADDS What is already known on the subject Research has been growing since the late 1970s and early 1980s on non-propositional language (as opposed at that time to the Chomskyan paradigm) and especially on lexical bundles, idioms, second language acquisition and multiword expressions. Studies beginning with Hughlings Jackson (1874) have been annotated through early 2012 (Wray, 2013). What this study adds This study examines 'third waves' in pragmatics, sociolinguistics and areas of neurology and speech perception contributing to what Van Lancker Sidtis (2021) calls the third wave of acceptance of the range and depth of formulaic sequences in ordinary or familiar language. What are the clinical implications of this work? Conversations with pet robots or web-based composition with emojis are but two of the developing areas built on formulaic sequences currently being used for communication interventions with persons living with dementia or other major neurocognitive disorder. Overviews of major contributions in theory and social contexts by Wray (2020, 2021) and theoretical and cognitive applications by Van Lancker Sidtis (2021) detail new areas for the study of formulaic sequences and their contributions to a range of neurocognitive disorders.
Collapse
Affiliation(s)
- Boyd H Davis
- Emerita Linguistics/English, Nursing, University of North Carolina-Charlotte, Charlotte, North Carolina, USA
| | - Meredith Troutman-Jordan
- Emerita Linguistics/English, Nursing, University of North Carolina-Charlotte, Charlotte, North Carolina, USA
| | - Margaret Maclagan
- Retired, Psychology, Speech and Hearing, NZ Institute of Language, Brain and Behavior, University of Canterbury, Christchurch, New Zealand
| |
Collapse
|
2
|
Hammadi L, Raillani H, Ndiaye BM, Aggoug B, El Ballouti A, Jidane S, Belyamani L, Souza de Cursi E. Uncertainty Quantification for Epidemic Risk Management: Case of SARS-CoV-2 in Morocco. Int J Environ Res Public Health 2023; 20:4102. [PMID: 36901113 PMCID: PMC10002057 DOI: 10.3390/ijerph20054102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/28/2022] [Revised: 02/12/2023] [Accepted: 02/12/2023] [Indexed: 06/18/2023]
Abstract
In this paper, we propose a new method for epidemic risk modelling and prediction, based on uncertainty quantification (UQ) approaches. In UQ, we consider the state variables as members of a convenient separable Hilbert space, and we look for their representation in finite dimensional subspaces generated by truncations of a suitable Hilbert basis. The coefficients of the finite expansion can be determined by approaches established in the literature, adapted to the determination of the probability distribution of epidemic risk variables. Here, we consider two approaches: collocation (COL) and moment matching (MM). Both are applied to the case of SARS-CoV-2 in Morocco, as an epidemic risk example. For all the epidemic risk indicators computed in this study (number of detections, number of deaths, number of new cases, predictions and human impact probabilities), the proposed models were able to estimate the values of the state variables with precision, i.e., with very low root mean square errors (RMSE) between predicted values and observed ones. Finally, the proposed approaches are used to generate a decision-making tool for future epidemic risk management, or, more generally, a quantitative disaster management approach in the humanitarian supply chain.
Collapse
Affiliation(s)
- Lamia Hammadi
- Laboratory of Engineering Sciences for Energy, National School of Applied Sciences ENSAJ, UCD, El Jadida 24000, Morocco
- Laboratory of Mechanics of Normandy, National Institute of Applied Sciences INSA of Rouen-Normandy, 76800 Saint Etienne du Rouvray, France
| | - Hajar Raillani
- Laboratory of Engineering Sciences for Energy, National School of Applied Sciences ENSAJ, UCD, El Jadida 24000, Morocco
- Laboratory of Mechanics of Normandy, National Institute of Applied Sciences INSA of Rouen-Normandy, 76800 Saint Etienne du Rouvray, France
| | - Babacar Mbaye Ndiaye
- Laboratory of Mathematics of Decision and Numerical Analysis, University of Cheikh Anta Diop, Dakar 10700, Senegal
| | - Badria Aggoug
- Emergency Department, SAMU 02, CHU Ibn Rochd, Casablanca 20100, Morocco
| | - Abdessamad El Ballouti
- Laboratory of Engineering Sciences for Energy, National School of Applied Sciences ENSAJ, UCD, El Jadida 24000, Morocco
| | - Said Jidane
- Emergency Department, Mohammed V Military Hospital, Faculty of Medicine and Pharmacy, Mohammed V University, Rabat 10100, Morocco
| | - Lahcen Belyamani
- Emergency Department, Mohammed V Military Hospital, Faculty of Medicine and Pharmacy, Mohammed V University, Rabat 10100, Morocco
| | - Eduardo Souza de Cursi
- Laboratory of Mechanics of Normandy, National Institute of Applied Sciences INSA of Rouen-Normandy, 76800 Saint Etienne du Rouvray, France
| |
Collapse
|
3
|
Collins L, Brezina V, Demjén Z, Semino E, Woods A. Corpus linguistics and clinical psychology: Investigating personification in first-person accounts of voice-hearing. Int J Corpus Linguist 2023; 28:28-59. [PMID: 37090241 PMCID: PMC7614468 DOI: 10.1075/ijcl.21019.col] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Triangulating corpus linguistic approaches with other (linguistic and non-linguistic) approaches enhances "both the rigour of corpus linguistics and its incorporation into all kinds of research" (McEnery & Hardie, 2012:227). Our study investigates an important area of mental health research: the experiences of those who hear voices that others cannot hear, and particularly the ways in which those voices are described as person-like. We apply corpus methods to augment the findings of a qualitative approach to 40 interviews with voice-hearers, whereby each interview was coded as involving 'minimal' or 'complex' personification of voices. Our analysis provides linguistic evidence in support of the qualitative coding of the interviews, but also goes beyond a binary approach by revealing different types and degrees of personification of voices, based on how they are referred to and described by voice-hearers. We relate these findings to concepts that inform therapeutic interventions in clinical psychology.
Collapse
Affiliation(s)
- Luke Collins
- Linguistics and English Language, Lancaster University
| | | | | | - Elena Semino
- Linguistics and English Language, Lancaster University
| | - Angela Woods
- Department of English Studies, Durham University
| |
Collapse
|
4
|
Hauser DJ, Schwarz N. Implicit Bias Reflects the Company That Words Keep. Front Psychol 2022; 13:871221. [PMID: 35769747 PMCID: PMC9234450 DOI: 10.3389/fpsyg.2022.871221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2022] [Accepted: 05/23/2022] [Indexed: 11/13/2022] Open
Abstract
In everyday language, concepts appear alongside (i.e., collocate with) related concepts. Societal biases often emerge in these collocations; e.g., female (vs. male) names collocate with art- (vs. science-) related concepts, and African American (vs. White American) names collocate with negative (vs. positive) concepts. It is unknown whether such collocations merely reflect societal biases or contribute to them. Concepts that are themselves neutral in valence but nevertheless collocate with valenced concepts provide a unique opportunity to address this question. For example, when asked, most people evaluate the concept "cause" as neutral, but "cause" is frequently followed by negative concepts (e.g., death, pain, and trouble). We use such semantically prosodic concepts to test the influence of collocation on the emergence of implicit bias: do neutral concepts that frequently collocate with valenced concepts have corresponding implicit bias? In evaluative priming tasks, participants evaluated positive/negative nouns (Study 1) or pictures (Study 2) after seeing verb primes that were (a) strongly valenced (e.g., hate and comfort), (b) neutral in valence but collocated with valenced concepts in corpora (e.g., ease and gain), or (c) neutral in valence and not collocated with valenced concepts in corpora (e.g., reply and describe). Throughout, neutral primes with positive (negative) collocates facilitated the evaluation of positive (negative) targets much like strongly valenced primes, whereas neutral primes without valenced collocates did not. That neutral concepts with valenced collocates parallel the influence of valenced concepts suggests that their collocations in natural language may be sufficient for fostering implicit bias. Societal implications of the causal embedding hypothesis are discussed.
Collapse
Affiliation(s)
- David J. Hauser
- Department of Psychology, Queen’s University, Kingston, ON, Canada
| | - Norbert Schwarz
- Mind and Society Center, Department of Psychology, University of Southern California, Los Angeles, CA, United States
| |
Collapse
|
5
|
Li H, Paterson KB, Warrington KL, Wang X. Insights Into the Processing of Collocations During L2 English Reading: Evidence From Eye Movements. Front Psychol 2022; 13:845590. [PMID: 35432115 PMCID: PMC9005965 DOI: 10.3389/fpsyg.2022.845590] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2021] [Accepted: 02/15/2022] [Indexed: 11/13/2022] Open
Abstract
We report an eye movement experiment that investigates the effects of collocation strength and contextual predictability on the reading of collocative phrases by L2 English readers. Thirty-eight Chinese English as foreign language learners (EFL) read 40 sentences, each including a specific two-word phrase that was either a strong (e.g., black coffee) or weak (e.g., bitter coffee) adjective-noun collocation and was either highly predictable or unpredictable from the previous sentence context. Eye movement measures showed that L2 reading times for the collocative phrases were sensitive to both collocation strength and contextual predictability. However, an interaction effect between these factors, which appeared relatively late in the eye movement record, additionally revealed that contextual predictability more strongly influenced time spent reading weak compared with strong collocations. This was most likely because the greater familiarity of strong collocations facilitated their integration, even in the absence of strong contextual constraint. We discuss the findings in terms of the value of collocations in second language learning.
Collapse
Affiliation(s)
- Hui Li
- School of International Studies, NingboTech University, Ningbo, China
| | - Kevin B. Paterson
- Department of Neuroscience, Psychology and Behaviour, University of Leicester, Leicester, United Kingdom
| | | | - Xiaolu Wang
- School of Foreign Languages, Zhejiang University City College, Hangzhou, China
- School of International Studies, Zhejiang University, Hangzhou, China
- School of Humanities and Communication Arts, Western Sydney University, Penrith, NSW, Australia
| |
Collapse
|
6
|
Otwinowska A, Marecka M, Casado A, Durlik J, Szewczyk J, Opacki M, Wodniecka Z. Does L2 Proficiency Impact L2-L1 Transfer While Reading L1 Collocations? Evidence From Behavioral and ERP Data. Front Psychol 2021; 12:673761. [PMID: 34658998 PMCID: PMC8513778 DOI: 10.3389/fpsyg.2021.673761] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Accepted: 08/23/2021] [Indexed: 11/22/2022] Open
Abstract
Multi-word expressions (MWEs) are fixed, conventional phrases often used by native speakers of a given language (L1). The type of MWEs investigated in this study were collocations. For bilinguals who have intensive contact with the second language (L2), collocational patterns can be transferred from the L2 to the L1 as a result of cross-linguistic influence (CLI). For example, bilingual migrants can accept collocations from their L2 translated to their L1 as correct. In this study, we asked whether such CLI is possible in native speakers living in the L1 environment and whether it depends on their L2 English proficiency. To this end, we created three lists of expressions in Polish: (1) well-formed Polish verb-noun collocations (e.g., ma sens – ∗has sense), (2) collocational calques from English (loan translations), where the English verb was replaced by a Polish translation equivalent (e.g., ∗robi sens – makes sense), and, as a reference (3) absurd verb-noun expression, where the verb did not collocate with the noun (e.g., ∗zjada sens – ∗eats sense). We embedded the three types of collocations in sentences and presented them to L1 Polish participants of varying L2 English proficiency in two experiments. We investigated whether L2 calques would (1) be explicitly judged as non-native in the L1; (2) whether they would evoke differential brain response than native L1 Polish equivalents in the event-related potentials (ERPs). We also explored whether the sensitivity to CLI in calques depended on participants’ level of proficiency in L2 English. The results indicated that native speakers of Polish assessed the calques from English as less acceptable than the correct Polish collocations. Still, there was no difference in online processing of correct and calques collocations as measured by the ERPs. This suggests a dissociation between explicit offline judgments and indices of online language processing. Interestingly, English L2 proficiency did not modulate these effects. The results indicate that the influence of English on Polish is so pervasive that collocational calques from this language are likely to become accepted and used by Poles.
Collapse
Affiliation(s)
- Agnieszka Otwinowska
- Faculty of Modern Languages, Institute of English Studies, University of Warsaw, Warsaw, Poland
| | - Marta Marecka
- Faculty of Philosophy, Institute of Psychology, Jagiellonian University, Kraków, Poland
| | - Alba Casado
- Faculty of Philosophy, Institute of Psychology, Jagiellonian University, Kraków, Poland
| | - Joanna Durlik
- Faculty of Philosophy, Institute of Psychology, Jagiellonian University, Kraków, Poland
| | - Jakub Szewczyk
- Faculty of Philosophy, Institute of Psychology, Jagiellonian University, Kraków, Poland.,Department of Psychology, University of Illinois at Urbana-Champaign, Champaign, IL, United States
| | - Marcin Opacki
- Faculty of Modern Languages, Institute of English Studies, University of Warsaw, Warsaw, Poland
| | - Zofia Wodniecka
- Faculty of Philosophy, Institute of Psychology, Jagiellonian University, Kraków, Poland
| |
Collapse
|
7
|
Roesch E, Rackauckas C, Stumpf MPH. Collocation based training of neural ordinary differential equations. Stat Appl Genet Mol Biol 2021; 20:37-49. [PMID: 34237805 DOI: 10.1515/sagmb-2020-0025] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2020] [Accepted: 05/04/2021] [Indexed: 11/15/2022]
Abstract
The predictive power of machine learning models often exceeds that of mechanistic modeling approaches. However, the interpretability of purely data-driven models, without any mechanistic basis is often complicated, and predictive power by itself can be a poor metric by which we might want to judge different methods. In this work, we focus on the relatively new modeling techniques of neural ordinary differential equations. We discuss how they relate to machine learning and mechanistic models, with the potential to narrow the gulf between these two frameworks: they constitute a class of hybrid model that integrates ideas from data-driven and dynamical systems approaches. Training neural ODEs as representations of dynamical systems data has its own specific demands, and we here propose a collocation scheme as a fast and efficient training strategy. This alleviates the need for costly ODE solvers. We illustrate the advantages that collocation approaches offer, as well as their robustness to qualitative features of a dynamical system, and the quantity and quality of observational data. We focus on systems that exemplify some of the hallmarks of complex dynamical systems encountered in systems biology, and we map out how these methods can be used in the analysis of mathematical models of cellular and physiological processes.
Collapse
Affiliation(s)
- Elisabeth Roesch
- Melbourne Integrative Genomics, University of Melbourne, 30 Royal Parade, Parkville, VIC3052, Australia.,School of Mathematics and Statistics, University of Melbourne, 813 Swanston Street, Parkville, VIC3010, Australia
| | - Christopher Rackauckas
- Department of Mathematics, Massachusetts Institute of Technology, 182 Memorial Dr, Cambridge, MA02142, USA.,Julia Computing, 240 Elm Street, 2nd Floor, Somerville, Massachusetts02144, USA.,Pumas-AI, 14711 Kamputa Drive, Centerville, VA20120, USA
| | - Michael P H Stumpf
- Melbourne Integrative Genomics, University of Melbourne, 30 Royal Parade, Parkville, VIC3052, Australia.,School of Mathematics and Statistics, University of Melbourne, 813 Swanston Street, Parkville, VIC3010, Australia
| |
Collapse
|
8
|
Wiśniewski Z, Kamiński W. Estimation and Prediction of Vertical Deformations of Random Surfaces, Applying the Total Least Squares Collocation Method. Sensors (Basel) 2020; 20:s20143913. [PMID: 32674339 PMCID: PMC7412446 DOI: 10.3390/s20143913] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/20/2020] [Revised: 07/10/2020] [Accepted: 07/11/2020] [Indexed: 11/16/2022]
Abstract
This paper proposes a method for determining the vertical deformations treated as random fields. It is assumed that the monitored surfaces are subject not only to deterministic deformations, but also to random fluctuations. Furthermore, the existence of random noise coming from surface’s vibrations is also assumed. Such noise disturbs the deformation’s functional models. Surface monitoring with the use of the geodetic levelling network of a free control network class is carried out. Assuming that, in some cases, the control networks are insufficient in surface’s deformation analysis, additional and non–measurable reference points have been provided. The prediction of these points’ displacements and estimation of the free control network points’ displacement are carried out using the collocation method applying the total least squares adjustment. The proposed theoretical solutions were verified by the simulation methods and on the example of a real control network.
Collapse
Affiliation(s)
- Zbigniew Wiśniewski
- Faculty of Geoengineering, University of Warmia and Mazury in Olsztyn, 10-957 Olsztyn, Poland;
| | - Waldemar Kamiński
- Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, 80-233 Gdańsk, Poland
- Correspondence:
| |
Collapse
|
9
|
Smieszek T, Salathé M. A low-cost method to assess the epidemiological importance of individuals in controlling infectious disease outbreaks. BMC Med 2013; 11:35. [PMID: 23402633 PMCID: PMC3616813 DOI: 10.1186/1741-7015-11-35] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/18/2012] [Accepted: 02/12/2013] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Infectious disease outbreaks in communities can be controlled by early detection and effective prevention measures. Assessing the relative importance of each individual community member with respect to these two processes requires detailed knowledge about the underlying social contact network on which the disease can spread. However, mapping social contact networks is typically too resource-intensive to be a practical possibility for most communities and institutions. METHODS Here, we describe a simple, low-cost method - called collocation ranking - to assess individual importance for early detection and targeted intervention strategies that are easily implementable in practice. The method is based on knowledge about individual collocation which is readily available in many community settings such as schools, offices, hospitals, and so on. We computationally validate our method in a school setting by comparing the outcome of the method against computational predictions based on outbreak simulations on an empirical high-resolution contact network. We compare collocation ranking to other methods for assessing the epidemiological importance of the members of a population. To this end, we select subpopulations of the school population by applying these assessment methods to the population and adding individuals to the subpopulation according to their individual rank. Then, we assess how suited these subpopulations are for early detection and targeted intervention strategies. RESULTS Likelihood and timing of infection during an outbreak are important features for early detection and targeted intervention strategies. Subpopulations selected by the collocation ranking method show a substantially higher average infection probability and an earlier onset of symptoms than randomly selected subpopulations. Furthermore, these subpopulations selected by the collocation ranking method were close to the optimum. CONCLUSIONS Our results indicate that collocation ranking is a highly effective method to assess individual importance, providing critical low-cost information for the development of sentinel surveillance systems and prevention strategies.
Collapse
Affiliation(s)
- Timo Smieszek
- Center for Infectious Disease Dynamics, Department of Biology, The Pennsylvania State University, University Park, PA 16802, USA.
| | | |
Collapse
|
10
|
Irschik H, Krommer M, Vetyukov Y. On the use of piezoelectric sensors in structural mechanics: some novel strategies. Sensors (Basel) 2010; 10:5626-41. [PMID: 22219679 PMCID: PMC3247724 DOI: 10.3390/s100605626] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 03/30/2010] [Revised: 04/26/2010] [Accepted: 04/27/2010] [Indexed: 11/16/2022]
Abstract
In the present paper, a review on piezoelectric sensing of mechanical deformations and vibrations of so-called smart or intelligent structures is given. After a short introduction into piezoelectric sensing and actuation of such controlled structures, we pay special emphasis on the description of some own work, which has been performed at the Institute of Technical Mechanics of the Johannes Kepler University of Linz (JKU) in the last years. Among other aspects, this work has been motivated by the fact that collocated control of smart structures requires a sensor output that is work-conjugated to the input by the actuator. This fact in turn brings into the play the more general question of how to measure mechanically meaningful structural quantities, such as displacements, slopes, or other quantities, which form the work-conjugated quantities of the actuation, by means piezoelectric sensors. At least in the range of small strains, there is confidence that distributed piezoelectric sensors or sensor patches in smart structures do measure weighted integrals over their domain. Therefore, there is a need of distributing or shaping the sensor activity in order to be able to re-interpret the sensor signals in the desired mechanical sense. We sketch a general strategy that is based on a special application of work principles, more generally on displacement virials. We also review our work in the past on bringing this concept to application in smart structures, such as beams, rods and plates.
Collapse
Affiliation(s)
- Hans Irschik
- Institute for Technical Mechanics, Johannes Kepler University Linz, Altenbergerstr.69, Linz, Austria.
| | | | | |
Collapse
|
11
|
Marchiando JF. On Using Collocation in Three Dimensions and Solving a Model Semiconductor Problem. J Res Natl Inst Stand Technol 1995; 100:661-676. [PMID: 29151767 PMCID: PMC4887259 DOI: 10.6028/jres.100.049] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 08/08/1995] [Indexed: 06/07/2023]
Abstract
A research code has been written to solve an elliptic system of coupled nonlinear partial differential equations of conservation form on a rectangularly shaped three-dimensional domain. The code uses the method of collocation of Gauss points with tricubic Hermite piecewise continuous polynomial basis functions. The system of equations is solved by iteration. The system of nonlinear equations is linearized, and the system of linear equations is solved by iterative methods. When the matrix of the collocation equations is duly modified by using a scaled block-limited partial pivoting procedure of Gauss elimination, it is found that the rate of convergence of the iterative method is significantly improved and that a solution becomes possible. The code is used to solve Poisson's equation for a model semiconductor problem. The electric potential distribution is calculated in a metal-oxide-semiconductor structure that is important to the fabrication of electron devices.
Collapse
Affiliation(s)
- J F Marchiando
- National Institute of Standards and Technology, Gaithersburg, MD 20899-0001
| |
Collapse
|