Journal articles: 'Model solutions'

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Sapaty, P. S. "Mosaic Warfare: from philosophy to model to solutions." Mathematical machines and systems 3 (2019): 17–34. http://dx.doi.org/10.34121/1028-9763-2019-3-17-34.

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Zemlyanukhin, A. I., and A. V. Bochkarev. "Analytical Properties and Solutions of the FitzHugh – Rinzel Model." Nelineinaya Dinamika 15, no. 1 (2019): 3–12. http://dx.doi.org/10.20537/nd190101.

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Hillert, Mats. "A modified regular-solution model for terminal solutions." Metallurgical Transactions A 17, no. 10 (October 1986): 1878–79. http://dx.doi.org/10.1007/bf02817285.

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Valentová, H., S. Škrovánková, Z. Panovská, and J. Pokorný. "Determination of astringent taste in model solutions and in beverages." Czech Journal of Food Sciences 19, No. 5 (February 10, 2013): 196–200. http://dx.doi.org/10.17221/6607-cjfs.

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The astringent taste is important for the sensory quality of beverages. Perception thresholds of two important astringent compounds – tannic acid and (+)-catechin were determined using two procedures. The concentration-intensity dependence was linear at low concentrations and up to medium intensities of the astringent taste if unstructured graphical scales were used, but the saturation threshold was soon attained in the case of tannic acid. Recording the results on printed forms gave similar results as using a touch-sensitive monitor. The optimum tasting was achieved at swallowing after degustation of 5 s. The duration of degustation increased the intensity. The astringent flavour was suppressed by sugar, but was not significantly influenced by ethanol, citric acid or quinine hydrochloride. Astringent substances were accurately perceived and rated in wine, tea infusion and orange drink, but the increase of astringency was smaller than in model solutions. The astringent taste was easily distinguished from the bitter taste.

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Han, Yucen, Jianyuan Yin, Yucheng Hu, Apala Majumdar, and Lei Zhang. "Solution landscapes of the simplified Ericksen–Leslie model and its comparisonwith the reduced Landau–deGennes model." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2253 (September 2021): 20210458. http://dx.doi.org/10.1098/rspa.2021.0458.

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We investigate the solution landscapes of a simplified Ericksen–Leslie (sEL) vector model for nematic liquid crystals, confined in a two-dimensional square domain with tangent boundary conditions. An efficient numerical algorithm is developed to construct the solution landscapes by utilizing the symmetry properties of the model and the domain. Since the sEL model and the reduced Landau–de Gennes (rLdG) models can be viewed as Ginzburg–Landau functionals, we systematically compute the solution landscapes of the sEL model, for different domain sizes, and compare them with the solution landscapes of the corresponding rLdG model. There are many similarities, including the stable diagonal and rotated states, bifurcation behaviours and sub-solution landscapes with low-index saddle solutions. Significant disparities also exist between the two models. The sEL vector model exhibits the stable solution C ± with interior defects, high-index ‘fake defect’ solutions, novel tessellating solutions and certain types of distinctive dynamical pathways. The solution landscape approach provides a comprehensive and efficient way for model comparison and is applicable to a wide range of mathematical models in physics.

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WANG, XIAOHUAN, and GUANGYING LV. "ENTIRE SOLUTIONS FOR LOTKA–VOLTERRA COMPETITION-DIFFUSION MODEL." International Journal of Biomathematics 06, no. 04 (July 2013): 1350020. http://dx.doi.org/10.1142/s1793524513500204.

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This paper is concerned with the existence of entire solutions of Lotka–Volterra competition-diffusion model. Using the comparing argument and sub-super solutions method, we obtain the existence of entire solutions which behave as two wave fronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables.

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ZAIT, R. A. "SOLITON SOLUTIONS IN A MODIFIED ϕ4 MODEL." International Journal of Modern Physics A 17, no. 31 (December 20, 2002): 4749–58. http://dx.doi.org/10.1142/s0217751x02011485.

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We consider a ϕ4 model in 1+1 dimensions modified by the addition of an extra kinetic term similar to the Skyrme term in higher dimensions and a potential term. We generalize the procedures of the leading order method to include elliptic functions and obtain cnoidal wave type solutions of the familiar ϕ4 model. As a limit case, we re-obtain the well-known solitary and travelling wave solutions of this model from the constructed cnoidal wave solutions. A further kink solution of the pure ϕ4 model is also obtained. We obtain soliton solutions of the modified ϕ4 model and show that it possesses two ϕ4 kink solutions, with the same velocity and total energy, as well as a double-kink solution. We study some properties of the modified model. In particular, we see that the two ϕ4 kinks have a definite velocity and this velocity is a critical velocity for the double-kink structures. Finally, we conclude the paper with some features and comments.

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Cieplińska, Jagienka, and Agnieszka Szmelter-Jarosz. "Toward Most Valuable City Logistics Initiatives: Crowd Logistics Solutions’ Assessment Model." Central European Management Journal 28, no. 2 (June 15, 2020): 38–56. http://dx.doi.org/10.7206/cemj.2658-0845.21.

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Introduction: Crowd logistics is a widely accepted concept in times of the growing popularity of sharing economy solutions. The popularity of e-commerce and a tendency to provide same-day delivery are the main reasons for their development. Developing those trends requires new products and services, now available on the market, known in the transport area as crowd logistics solutions. Purpose: The purpose of the paper is to provide a tool for assessing crowd-logistics solutions, taking into consideration customers’ requirements. The text includes groups of environmental, economic, and social criteria to facilitate the choice of the best crowd logistics solution for freight transport. Methodology: The research is based on the critical analysis of different sources (literature, European Commission reports, other reports and analyses) and practical solutions in the field of crowd logistics. The main data analysis method is the Analytic Hierarchy Process, usually used to evaluate variants in decision-making processes. This method was chosen because of the variety of data types (quantitative and qualitative) and formats, its popularity, universality, and replicability. Results: This paper contains ready-to-use weights for the assessment of crowd logistics solutions. The proposed set of criteria and weights can be a useful tool for customers to evaluate the sharing- -economy services landscape in the areas they manage.

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Mishra, Aamlan Saswat. "Social Acceptance Prediction Model for Generative Architectural Spaces in India." Journal of Advanced Research in Construction and Urban Architecture 6, no. 3 (July 23, 2021): 50–57. http://dx.doi.org/10.24321/2456.9925.202109.

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Generative Architectural design is an emerging design process that is evolving due to evolution of computational power of computers and its ability to provide multiple choices of design solutions in architecture. This process, however, has a few drawbacks, some of which are, a high number of solutions which take less time for computers to produce than for their human counterpart to interpret and choose from and the less social acceptance of generative architectural design solutions. Due to the algorithms being unaware of what humans deem as acceptable solutions, these problems persist. A way to bridge such gap is through a survey simulation model, which the computer can apply to simulate acceptance of the created solution if it were put through a survey. A mathematical model has been developed though analysis of a survey such that a computer can predict how acceptable a particular iteration of a Generative Architectural design process is if it were put through a similar survey. Scores obtained in the survey simulation can be used to predict how acceptable a particular design iteration is there by culling less acceptable solutions and reducing the number of iterations provided to humans for review after running Generative Architectural algorithms.

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Li, Jiequan, and Gerald Warnecke. "On measure solutions to the Zero-pressure gas model and their uniqueness." Mathematica Bohemica 127, no. 2 (2002): 265–73. http://dx.doi.org/10.21136/mb.2002.134173.

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Kislenko, Volodymyr, Liliya Oliynyk, and Svyatoslav Ivanyshyn. "The Model of Metal Oxide Particle Formation from Water Solutions of Salts." Chemistry and Chemical Technology 4, no. 2 (June 15, 2010): 95–100. http://dx.doi.org/10.23939/chcht04.02.095.

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The model describing the formation of metal oxide particles from water solutions of salts was suggested. Dependence of instability constants of metal complexes and ionization constants of oxygen containing inorganic acids on the electron density upon the central ion or atom allows to calculate these values for metal hydroxides. Equations describing the number of metal ions in polyion, the concentration of polyions in solution, the number of metal ions in primary metal oxide particles and their concentration in the system were suggested.

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Kang, Juntao, Xueqiang Zhang, Hongyou Cao, and Shiqiang Qin. "Research on Multi-Alternatives Problem of Finite Element Model Updating Based on IAFSA and Kriging Model." Sensors 20, no. 15 (July 31, 2020): 4274. http://dx.doi.org/10.3390/s20154274.

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Due to insufficient test data, insufficient constraint equations and uncertain objective function, the local optimal solution and the global optimal solution of the objective function in finite element model updating may represent the actual parameters of the structure. Based on this, this paper proposes an improved artificial fish school algorithm. By combining the niche technology with the artificial fish school algorithm, the improved algorithm can systematically find multiple global optimal solutions and local optimal solutions of the objective function. Aiming at the difficulty of determining the niche radius, an adaptive niche radius mechanism is proposed. The improved algorithm is used to study the multi-alternatives problem of finite element model updating after verifying its feasibility through numerical simulation analysis. In the case of benchmark framework model updating, it is confirmed that multi-alternative problems exist and the global optimal solution of the objective function does not necessarily represent the true parameters of the structure. In case 2, the improved algorithm combined with the Kriging model is applied to the model updating of a cable-stayed footbridge, and 15 sets of solutions are obtained, in which the error objective function values of the measured and theoretical values of the bridge modes are close but the solutions are completely different. Combining with the actual bridge condition and reanalysis technology, the author takes the suboptimal solution 2 as the most representative solution of the bridge parameters, which reduces the possibility of misjudgment of structural parameters.

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McNaughton, Alastair. "Model Solutions to Quadratic Equations." Mathematics Teacher 79, no. 5 (May 1986): 332–36. http://dx.doi.org/10.5951/mt.79.5.0332.

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Here is a method of representing quadratic functions by three-dimensional wire models. It enables one to form a simple geometric concept of the location of the imaginary zeros. I have been using this material with my students and have been delighted with the ease with which they respond to it. As a result, their confidence in dealing with complex numbers has increased, their concept of functions has shown much improvement, and they are attacking problems with real insight.

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Zhang, Ruifeng, Nan Liu, and Man An. "Analytical solutions of Skyrme model." Discrete and Continuous Dynamical Systems - Series S 9, no. 6 (November 2016): 2201–11. http://dx.doi.org/10.3934/dcdss.2016092.

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Bhadeshia, H. K. D. H. "Quasichemical model for interstitial solutions." Materials Science and Technology 14, no. 4 (April 1998): 273–76. http://dx.doi.org/10.1179/mst.1998.14.4.273.

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Shi, Chang-Guang, and Minoru Hirayama. "Solitonic solutions of Faddeev model." Journal of Mathematical Physics 53, no. 2 (February 2012): 022301. http://dx.doi.org/10.1063/1.3682246.

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Zarea, Sana’a A. "NEW SOLUTIONS FOR BIOLOGICAL MODEL." Advances in Differential Equations and Control Processes 17, no. 3 (September 30, 2016): 213–29. http://dx.doi.org/10.17654/de017030213.

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Bijalwan, Naveen. "Exact solutions: classical electron model." Astrophysics and Space Science 336, no. 2 (September 6, 2011): 485–89. http://dx.doi.org/10.1007/s10509-011-0796-5.

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Han, I. S., and M. Cheryan. "Nanofiltration of model acetate solutions." Journal of Membrane Science 107, no. 1-2 (November 1995): 107–13. http://dx.doi.org/10.1016/0376-7388(95)00107-n.

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Kasperchik, V. P., and A. V. Bil'dyukevich. "Ultrafiltration of model heparin solutions." Pharmaceutical Chemistry Journal 29, no. 4 (April 1995): 294–96. http://dx.doi.org/10.1007/bf02219558.

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Svoboda, Martin. "Numerical Verification of Model Multibody Systems." Applied Mechanics and Materials 486 (December 2013): 239–44. http://dx.doi.org/10.4028/www.scientific.net/amm.486.239.

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The article deals with the influence of manufacturing and geometric asymmetry on the vertical oscillation of symmetric and asymmetric systems consisting of rigid bodies linked flexibly with different kinematic excitation. The solution was performed using experimental and numerical analysis (with application of oscillation of vehicles and flexibly coupled machines). Numerical solutions were carried out by finite element method (FEM) on a simple model and experimental solutions on laboratory model of a mechanical system. The aim of the work was to create a numerical model and its solution using the finite element method. The experimental solution was used to verify the numerical model.

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Fang, Yuanyuan, Ying Zhou, and Zhenxing Yao. "Model Misfit Minimization." Bulletin of the Seismological Society of America 109, no. 5 (July 30, 2019): 1729–37. http://dx.doi.org/10.1785/0120190079.

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Abstract In geophysical applications, solutions to ill‐posed inverse problems Ax=b are often obtained by analyzing the trade‐off between data residue ‖Ax−b‖2 and model norm ‖x‖2. In this study, we show that the traditional L‐curve analysis does not lead to solutions closest to the true models because the maximum curvature (or the corner of the L‐curve) depends on the relative scaling between data residue and model norm. A Bayes approach based on empirical risk function minimization using training datasets may be designed to find a statistically optimal solution, but its success depends on the true realization of the model. To overcome this limitation, we construct training models using eigenvectors of matrix ATA as well as spectral coefficients calculated from the correlation between observations and eigenvector projected data. This approach accounts for data noise level but does not require it as a priori knowledge. Using global tomography as an example, we show that the solutions are closest to true models.

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CASANA, R. "RENORMALIZED NEW SOLUTIONS FOR THE MASSLESS THIRRING MODEL." International Journal of Modern Physics A 20, no. 30 (December 10, 2005): 7129–51. http://dx.doi.org/10.1142/s0217751x0502389x.

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We present a nonperturbative study of the (1+1)-dimensional massless Thirring model by using path integral methods. The regularization ambiguities — coming from the computation of the fermionic determinant — allow to find new solution types for the model. At quantum level the Ward identity for the 1PI 2-point function for the fermionic current separates such solutions in two phases or sectors, the first one has a local gauge symmetry that is implemented at quantum level and the other one without this symmetry. The symmetric phase is a new solution which is unrelated to the previous studies of the model and, in the nonsymmetric phase there are solutions that for some values of the ambiguity parameter are related to well-known solutions of the model. We construct the Schwinger–Dyson equations and the Ward identities. We make a detailed analysis of their UV divergence structure and, after, we perform a nonperturbative regularization and renormalization of the model.

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McCartor, Gary. "Some Lessons from the Schwinger Model." International Journal of Modern Physics A 12, no. 06 (March 10, 1997): 1091–99. http://dx.doi.org/10.1142/s0217751x97000815.

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I shall recall a number of solutions to the Schwinger model in different gauges, having different boundary conditions and using different quantization surfaces. I shall discuss various properties of these solutions emphasizing the degrees of freedom necessary to represent the solution, the way the operator products are defined and the effects these features have on the chiral condensate.

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Lv, Guangying, and Dang Luo. "Entire solutions for some reaction–diffusion systems." International Journal of Biomathematics 08, no. 04 (June 22, 2015): 1550052. http://dx.doi.org/10.1142/s1793524515500527.

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This paper is concerned with the existence of entire solutions of some reaction–diffusion systems. We first consider Belousov–Zhabotinskii reaction model. Then we study a general model. Using the comparing argument and sub-super-solutions method, we obtain the existence of entire solutions which behave as two wavefronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables. At last, we give some examples to explain our results for the general models.

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Dimitrijevic, Ivan, Branko Dragovich, Zoran Rakic, and Jelena Stankovic. "New Cosmological Solutions of a Nonlocal Gravity Model." Symmetry 14, no. 1 (December 21, 2021): 3. http://dx.doi.org/10.3390/sym14010003.

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A nonlocal gravity model (2) was introduced and considered recently, and two exact cosmological solutions in flat space were presented. The first solution is related to some radiation effects generated by nonlocal dynamics on dark energy background, while the second one is a nonsingular time symmetric bounce. In the present paper, we investigate other possible exact cosmological solutions and find some the new ones in nonflat space. Used nonlocal gravity dynamics can change the background topology. To solve the corresponding equations of motion, we first look for a solution of the eigenvalue problem □(R−4Λ)=q(R−4Λ). We also discuss possible extension of this model with a nonlocal operator, symmetric under □⟷□−1, and its connection with another interesting nonlocal gravity model.

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Cheng, Hongjun, and Shiwei Li. "A Deposition Model: Riemann Problem and Flux-Function Limits of Solutions." Abstract and Applied Analysis 2018 (2018): 1–14. http://dx.doi.org/10.1155/2018/8569435.

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The Riemann solutions of a deposition model are shown. A singular flux-function limit of the obtained Riemann solutions is considered. As a result, it is shown that the Riemann solutions of the deposition model just converge to the Riemann solutions of the limit system, the scalar conservation law with a linear flux function involving discontinuous coefficient. Especially, for some initial data, the two-shock Riemann solution of the deposition model tends to the delta-shock Riemann solution of the limit system; by contrast, for some initial data, the two-rarefaction-wave Riemann solution of the deposition model tends to the vacuum Riemann solution of the limit system. Some numerical results exhibiting the formation processes of delta-shocks and vacuum states are presented.

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Winstanley, H. F., M. Chapwanya, M. J. McGuinness, and A. C. Fowler. "A polymer–solvent model of biofilm growth." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2129 (December 2010): 1449–67. http://dx.doi.org/10.1098/rspa.2010.0327.

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We provide and analyse a model for the growth of bacterial biofilms based on the concept of an extracellular polymeric substance as a polymer solution, whose viscoelastic rheology is described by the classical Flory–Huggins theory. We show that one-dimensional solutions exist, which take the form at large times of travelling waves, and we characterize their form and speed in terms of the describing parameters of the problem. Numerical solutions of the time-dependent problem converge to the travelling wave solutions.

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Suárez, Antonio. "Nonnegative solutions for a heterogeneous degenerate competition model." ANZIAM Journal 46, no. 2 (October 2004): 273–97. http://dx.doi.org/10.1017/s1446181100013845.

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AbstractThis paper deals with the existence, uniqueness and qualitative properties of nonnegative and nontrivial solutions of a spatially heterogeneous Lotka-Volterra competition model with nonlinear diffusion. We give conditions in terms of the coefficients involved in the setting of the problem which assure the existence of nonnegative solutions as well as the uniqueness of a positive solution. In order to obtain these results we employ monotonicity methods, singular spectral theory and a fixed point index.

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Storbacka, Kaj. "A solution business model: Capabilities and management practices for integrated solutions." Industrial Marketing Management 40, no. 5 (July 2011): 699–711. http://dx.doi.org/10.1016/j.indmarman.2011.05.003.

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Chilarescu, Constantin. "ON THE SOLUTIONS OF THE LUCAS-UZAWA MODEL." Mathematical Modelling and Analysis 24, no. 1 (January 3, 2019): 127–33. http://dx.doi.org/10.3846/mma.2019.009.

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In a recent paper, Naz and Chaudry provided two solutions for the model of Lucas-Uzawa, via the Partial Hamiltonian Approach. The first one of these solutions coincides exactly with that determined by Chilarescu. For the second one, they claim that this is a new solution, fundamentally different than that obtained by Chilarescu. We will prove in this paper, using the existence and uniqueness theorem of nonlinear differential equations, that this is not at all true.

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Leng, W., L. Ju, M. Gunzburger, and S. Price. "Manufactured solutions and the numerical verification of isothermal, nonlinear, three-dimensional Stokes ice-sheet models." Cryosphere Discussions 6, no. 4 (July 20, 2012): 2689–714. http://dx.doi.org/10.5194/tcd-6-2689-2012.

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Abstract. The technique of manufactured solutions is used for verification of computational models in many fields. In this paper we construct manufactured solutions for models of three-dimensional, isothermal, nonlinear Stokes flow in glaciers and ice sheets. The solution construction procedure starts with kinematic boundary conditions and is mainly based on the solution of a first-order partial differential equation for the ice velocity that satisfies the incompressibility condition. The manufactured solutions depend on the geometry of the ice sheet and other model parameters. Initial conditions are taken from the periodic geometry of a standard problem of the ISMIP-HOM benchmark tests and altered through the manufactured solution procedure to generate an analytic solution for the time-dependent flow problem. We then use this manufactured solution to verify a parallel, high-order accurate, finite element Stokes ice-sheet model. Results from the computational model show excellent agreement with the manufactured analytic solutions.

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Burnside, Craig. "Consistency of a Method of Moments Estimator Based on Numerical Solutions to Asset Pricing Models." Econometric Theory 9, no. 4 (August 1993): 602–32. http://dx.doi.org/10.1017/s0266466600008008.

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This paper considers the properties of estimators based on numerical solutions to a class of economic models. In particular, the numerical methods discussed are those applied in the solution of linear integral equations, specifically Fredholm equations of the second kind. These integral equations arise out of economic models in which endogenous variables appear linearly in the Euler equations, but for which easily characterized solutions do not exist. Tauchen and Hussey [24] have proposed the use of these methods in the solution of the consumption-based asset pricing model. In this paper, these methods are used to construct method of moments estimators where the population moments implied by a model are approximated by the population moments of numerical solutions. These estimators are shown to be consistent if the accuracy of the approximation is increased with the sample size. This result depends on the solution method having the property that the moments of the approximate solutions converge uniformly in the model parameters to the moments of the true solutions.

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BORDAG, L. A., and A. Y. CHMAKOVA. "EXPLICIT SOLUTIONS FOR A NONLINEAR MODEL OF FINANCIAL DERIVATIVES." International Journal of Theoretical and Applied Finance 10, no. 01 (February 2007): 1–21. http://dx.doi.org/10.1142/s021902490700407x.

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Families of explicit solutions are found to a nonlinear Black–Scholes equation which incorporates the feedback-effect of a large trader in case of market illiquidity. The typical solution of these families will have a payoff which approximates a strangle. These solutions were used to test numerical schemes for solving a nonlinear Black–Scholes equation.

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GUIDORZI, M., M. PADULA, and P. I. PLOTNIKOV. "HOPF SOLUTIONS TO A FLUID-ELASTIC INTERACTION MODEL." Mathematical Models and Methods in Applied Sciences 18, no. 02 (February 2008): 215–69. http://dx.doi.org/10.1142/s0218202508002668.

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In this paper, we give a global existence theorem of weak solutions to model equations governing interaction fluid structure in a two-dimensional layer, cf. Refs. 8 and 14. To our knowledge this is the first existence theorem of global in time solutions for such model. The interest of our result is double because, first, we change the original initial value problem by deleting one initial condition, second, we construct a solution through the classical Galerkin method for which several computing codes have been constructed.

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Elboree, M. K. "Studying Lump solutions, Rogue wave solutions and dynamical interaction for new model generating from lax pair." Mathematical Modelling of Natural Phenomena 15 (2020): 67. http://dx.doi.org/10.1051/mmnp/2020029.

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In this paper, we consider the (3 + 1)-dimensional Burgers-like equation which arises in fluid mechanics, which constructed from Lax pair generating technique. The bilinear form for this model is obtained to construct the multiple-kink solutions. Lump solution, rogue wave solutions are constructed via the obtained bilinear form for this model. The physical phenomena for these solution are analyzed by studying the influence of the parameters for these solutions. The phase shifts, propagation directions and amplitudes for these solutions are controlled via these parameters. The collisions between the lump wave and the stripe soliton, which is called lumpoff solution are completely non-elastic interaction. Finally, the figures of the solutions are shown to study the dynamical behavior for the lump, rogue wave and the properties of the interaction phenomena under various parameters for (3 + 1)-dimensional Burgers-like equation. These results can’t be found in the previous scientific papers.

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Roy, Samit, and Yong Wang. "Analytical Solution for Cohesive Layer Model and Model Verification." Polymers and Polymer Composites 13, no. 8 (November 2005): 741–52. http://dx.doi.org/10.1177/096739110501300801.

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The objective of this work was to find an analytical solution to the stresses in the cohesive damage zone and the damage zone length at the interface between a fibre reinforced polymer (FRP) plate and concrete substrate. Analytical solutions have been derived to predict the stress in the cohesive layer when considering the deformation in the stiff substrate. A two-dimensional cohesive layer constitutive model with a prescribed traction-separation (stress-strain) law was constructed using a modified Williams' approach, and analytical solutions derived for the elastic zone as well as the damage zone. Detailed benchmark comparisons of analytical results with finite element predictions for a double cantilever beam specimen were performed for model verification, and issues related to cohesive layer thickness were investigated. It was observed that the assumption of a rigid substrate in analytical modelling can lead to inaccurate analytical prediction of the cohesive damage zone length.

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Lin, Jian-Jhong, and Ting-Hui Yang. "Traveling wave solutions for a diffusive three-species intraguild predation model." International Journal of Biomathematics 11, no. 02 (February 2018): 1850022. http://dx.doi.org/10.1142/s1793524518500225.

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The aim of this work is to investigate the existence and non-existence of traveling wave solutions for a diffusive three-species intraguild predation model which means that one predator can eat its potential resource competitors. The method of upper–lower solution is implemented to show the existence of traveling wave solutions. In order to simplify the construction of an admissible pair of upper–lower solution, the scheme of strictly contracting rectangle is applied. Finally, the minimal speed [Formula: see text] of traveling wave solutions of the model is characterized. If the wave speed is greater than [Formula: see text], we show the existence of traveling wave solutions connecting trivial and positive equilibria by combining the upper and lower solutions with the contracting rectangle. On the other hand, if the wave speed is less than [Formula: see text], the non-existence of such solutions is also established. Furthermore, to illustrate our theoretical results, some numerical simulations are performed and biological meanings are interpreted.

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AKBAR, NOREEN SHER, and S. NADEEM. "ANALYTICAL AND NUMERICAL SOLUTIONS OF PERISTALTIC FLOW OF WILLIAMSON FLUID MODEL IN AN ENDOSCOPE." Journal of Mechanics in Medicine and Biology 11, no. 04 (September 2011): 941–57. http://dx.doi.org/10.1142/s0219519411003910.

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The present studies deal with the peristaltic motion of an incompressible Williamson fluid model in an endoscope. The governing equations of Williamson fluid model are first simplify using the assumptions of long wavelength and low Reynolds number. The four types of solutions have been presented for velocity profile named (i) exact solution, (ii) perturbation solution, (iii) HAM solution, and (iv) numerical solutions. The comparisons of four solutions have been found a very good agreement between all the solutions. In addition, the expressions for pressure rise and velocity against various physical parameters are discussed through graphs.

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Gong, Gui Fen, Ke Yin, and Ming Lan. "Study of Assessment Model of Packaging via AHP Method." Advanced Materials Research 542-543 (June 2012): 403–6. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.403.

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An assessment model of packaging solutions is built based on AHP method in response to diversification of packaging solutions. The assessment is intuitive. The model can be not only used in comprehensive evaluation, but also used in the evaluation of the secondary indicators. Using the model to assess packing solutions, you can make the assessment process operate easier, and the results more intuitive. The model can be widely used in assessment of packaging solution.

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Kim, J. W., K. J. Bai, R. C. Ertekin, and W. C. Webster. "A Strongly-Nonlinear Model for Water Waves in Water of Variable Depth—The Irrotational Green-Naghdi Model." Journal of Offshore Mechanics and Arctic Engineering 125, no. 1 (February 1, 2003): 25–32. http://dx.doi.org/10.1115/1.1537722.

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Recently, the authors have derived a new approximate model for the nonlinear water waves, the Irrotational Green-Naghdi (IGN) model. In this paper, we first derive the IGN equations applicable to variable water depth, and then perform numerical tests to show whether and how fast the solution of the IGN model converges to the true solution as its level increases. The first example given is the steady solution of progressive waves of permanent form, which includes the small-amplitude sinusoidal wave, the solitary wave and the nonlinear Stokes wave. The second example is the run-up of a solitary wave on a vertical wall. The last example is the shoaling of a wave train over a sloping beach. In each numerical test, the self-convergence of the IGN model is shown first. Then the converged solution is compared to the known analytic solutions and/or solutions of other approximate models such as the KdV and the Boussinesq equations.

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Sutcliffe, Paul. "Knots in the Skyrme–Faddeev model." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2087 (August 28, 2007): 3001–20. http://dx.doi.org/10.1098/rspa.2007.0038.

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The Skyrme–Faddeev model is a modified sigma model in three-dimensional space, which has string-like topological solitons classified by the integer-valued Hopf charge. Numerical simulations are performed to compute soliton solutions for Hopf charges up to 16, with initial conditions provided by families of rational maps from the three-sphere into the complex projective line. A large number of new solutions are presented, including a variety of torus knots for a range of Hopf charges. Often these knots are only local energy minima, with the global minimum being a linked solution, but for some values of the Hopf charge they are good candidates for the global minimum energy solution. The computed energies are in agreement with Ward's conjectured energy bound.

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Berdnikov, V. I., and Yu A. Gudim. "THREE-PARAMETER MODEL OF SUBREGULAR SOLUTIONS." Izvestiya Visshikh Uchebnykh Zavedenii. Chernaya Metallurgiya = Izvestiya. Ferrous Metallurgy 58, no. 4 (June 10, 2015): 226. http://dx.doi.org/10.17073/0368-0797-2015-4-226-229.

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Abbott, Steve, and Teunis C. Dorlas. "Statistical Mechanics: Fundamentals and Model Solutions." Mathematical Gazette 84, no. 500 (July 2000): 375. http://dx.doi.org/10.2307/3621734.

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Kučera, V., J. C. Martínez García, and M. Malabre. "Partial Model Matching: Parametrization of Solutions." IFAC Proceedings Volumes 29, no. 1 (June 1996): 1199–204. http://dx.doi.org/10.1016/s1474-6670(17)57828-3.

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CHUAN, LE HUY, TOHRU TSUJIKAWA, and ATSUSHI YAGI. "STATIONARY SOLUTIONS TO FOREST KINEMATIC MODEL." Glasgow Mathematical Journal 51, no. 1 (January 2009): 1–17. http://dx.doi.org/10.1017/s0017089508004485.

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AbstractWe continue the study of a mathematical model for a forest ecosystem which has been presented by Y. A. Kuznetsov, M. Y. Antonovsky, V. N. Biktashev and A. Aponina (A cross-diffusion model of forest boundary dynamics, J. Math. Biol. 32 (1994), 219–232). In the preceding two papers (L. H. Chuan and A. Yagi, Dynamical systemfor forest kinematic model, Adv. Math. Sci. Appl. 16 (2006), 393–409; L. H. Chuan, T. Tsujikawa and A. Yagi, Aysmptotic behavior of solutions for forest kinematic model, Funkcial. Ekvac. 49 (2006), 427–449), the present authors already constructed a dynamical system and investigated asymptotic behaviour of trajectories of the dynamical system. This paper is then devoted to studying not only the structure (including stability and instability) of homogeneous stationary solutions but also the existence of inhomogeneous stationary solutions. Especially it shall be shown that in some cases, one can construct an infinite number of discontinuous stationary solutions.

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Kučera, V., J. C. Martínez García, and M. Malabre. "Partial model matching: Parametrization of solutions." Automatica 33, no. 5 (May 1997): 975–77. http://dx.doi.org/10.1016/s0005-1098(96)00252-x.

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Chen, Ching L. "Analytic Solutions for Tidal Model Testing." Journal of Hydraulic Engineering 115, no. 12 (December 1989): 1707–14. http://dx.doi.org/10.1061/(asce)0733-9429(1989)115:12(1707).

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Xiong, Weiwen. "Solutions: A Mixed-Error Component Model." Econometric Theory 12, no. 2 (June 1996): 401–2. http://dx.doi.org/10.1017/s0266466600006721.

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Pan, Feng, and J. P. Draayer. "Analytical solutions for the LMG model." Physics Letters B 451, no. 1-2 (April 1999): 1–10. http://dx.doi.org/10.1016/s0370-2693(99)00191-4.

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Journal articles on the topic 'Model solutions'

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