Works (120)
Updated: April 4th, 2024 01:25
2023 journal article
Traveling Wave Solutions of the Kawahara Equation Joining Distinct Periodic Waves
JOURNAL OF NONLINEAR SCIENCE, 33(5).
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 21, 2023
2023 journal article
Well-posedness and ill-posedness of single-phase models for suspensions
JOURNAL OF FLUID MECHANICS, 954.
author keywords: suspensions; particle/fluid flow
open access via www.cambridge.org (publisher PDF)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: January 4, 2023
2021 article
Dispersive Riemann problems for the Benjamin-Bona-Mahony equation
Congy, T., El, G. A., Hoefer, M. A., & Shearer, M. (2021, August 24). STUDIES IN APPLIED MATHEMATICS, Vol. 8.
author keywords: asymptotic analysis; nonlinear waves; partial differential equations
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: August 25, 2021
2020 journal article
Gradient-induced droplet motion over soft solids
IMA Journal of Applied Mathematics, 85(3), 495–512.
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
7. Affordable and Clean Energy
(OpenAlex)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: June 22, 2020
2019 journal article
Constitutive relations for compressible granular flow in the inertial regime
JOURNAL OF FLUID MECHANICS, 874, 926–951.
author keywords: granular media; rheology
Sources: Web Of Science, NC State University Libraries
Added: August 12, 2019
2019 journal article
Distinguishing deformation mechanisms in elastocapillary experiments
Soft Matter, 15(46), 9426–9436.
TL;DR:
This paper derives a model capable of explaining the observed data and uses it to determine the force law at the three-phase contact line, and shows that the measured forces are consistent with the expected Young-Dupré equation.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
Sources: ORCID, Crossref
Added: November 20, 2019
2018 journal article
A SCALAR CONSERVATION LAW FOR PLUME MIGRATION IN CARBON SEQUESTRATION
SIAM JOURNAL ON APPLIED MATHEMATICS, 78(3), 1823–1841.
author keywords: hyperbolic PDE; discontinuous flux; method of characteristics; shocks and rarefactions; residual trapping
TL;DR:
A quasi-linear hyperbolic partial differential equation with a discontinuous flux models geologic carbon dioxide migration and storage and shows good agreement with prior work on this topic.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
13. Climate Action
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2018 journal article
Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure
Studies in Applied Mathematics, 142(3), 241–268.
author keywords: asymptotic analysis; nonlinear waves; partial differential equations
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
Sources: Web Of Science, NC State University Libraries, ORCID, Crossref
Added: April 2, 2019
2018 journal article
Nonlocal rheology of dense granular flow in annular shear experiments
Soft Matter, 14(16), 3040–3048.
TL;DR:
The authors' measurements confirm the prediction that there is a growing lengthscale at a finite value μs, associated with a frictional yield criterion and identify the physical mechanism behind this transition at μs by observing that it corresponds to a drop in the susceptibility to force chain fluctuations.
(via Semantic Scholar)
Sources: Web Of Science, Crossref, NC State University Libraries, ORCID
Added: August 6, 2018
2017 journal article
Deformation of an elastic substrate due to a resting sessile droplet
European Journal of Applied Mathematics, 29(2), 281–300.
author keywords: PDEs in Connection with Mechanics of Deformable Solids; Transform Methods; Classical Linear Elasticity; Numerical Approximation of Solutions; Fluid-Solid Interactions
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, Crossref, NC State University Libraries, ORCID
Added: August 6, 2018
2017 journal article
Dispersive and Diffusive-Dispersive ShockWaves for Nonconvex Conservation Laws
SIAM REVIEW, 59(1), 3–61.
author keywords: shock waves; conservation laws; partial differential equations; dispersive equations; traveling waves
TL;DR:
This review compares the structure of solutions of Riemann problems for a conservation law with nonconvex, cubic flux regularized by two different mechanisms: (1) dispersion in the modified Korteweg--de Vries (mKdV) equation; and (2) a combination of diffusion and disp immersion in the mKDV--Burgers equation.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2017 journal article
Stationary Expansion Shocks for a Regularized Boussinesq System
Studies in Applied Mathematics, 139(4), 1–22.
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries, Crossref
Added: August 6, 2018
2017 journal article
Well-posed continuum equations for granular flow with compressibility and μ ( I )-rheology
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2201), 20160846.
author keywords: granular flow; continuum modelling; rheology
TL;DR:
The results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ(I) satisfies certain minimal, physically natural, inequalities.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries, Crossref
Added: August 6, 2018
2017 journal article
Wetting dynamics of a collapsing fluid hole
PHYSICAL REVIEW FLUIDS, 2(1).
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2016 journal article
Expansion shock waves in regularized shallow-water theory
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 472(2189), 20160141.
author keywords: Lax entropy condition; non-local dispersion; Benjamin-Bona-Mahony equation; Boussinesq equations
TL;DR:
A new type of shock wave is identified by constructing a stationary expansion shock solution of a class of regularized shallow-water equations that include the Benjamin–Bona–Mahony and Boussinesq equations that exhibits divergent characteristics, thereby contravening the classical Lax entropy condition.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(OpenAlex)
14. Life Below Water
(Web of Science)
Sources: Web Of Science, Crossref, NC State University Libraries
Added: August 6, 2018
2015 book
Partial differential equations: An introduction to theory and applications
Princeton: Princeton University Press.
Source: NC State University Libraries
Added: August 6, 2018
2015 journal article
Spatiotemporal measurement of surfactant distribution on gravity-capillary waves
JOURNAL OF FLUID MECHANICS, 777.
author keywords: capillary waves; Faraday waves; waves/free-surface flows
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 6, 2018
2015 journal article
Traveling waves for conservation laws with cubic nonlinearity and BBM type dispersion
JOURNAL OF DIFFERENTIAL EQUATIONS, 259(7), 3216–3232.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2014 journal article
Elastocapillary deformations on partially-wetting substrates: rival contact-line models
Soft Matter, 10(37), 7361.
TL;DR:
A general solution using a displacement potential function for the elastic deformations within a finite elastic substrate associated with these wetting forces, and compares the results to relevant experiments and concludes that the generalization of solid surface tension Σls ≠ Σsg is an essential feature in any model of partial-wetting.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Crossref, NC State University Libraries, ORCID, NC State University Libraries
Added: August 6, 2018
2014 article
Surfactant spreading on a thin liquid film: reconciling models and experiments
Swanson, E. R., Strickland, S. L., Shearer, M., & Daniels, K. E. (2015, October). JOURNAL OF ENGINEERING MATHEMATICS, Vol. 94, pp. 63–79.
author keywords: Experiment; Model; Surfactant; Thin liquid film
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 6, 2018
2014 chapter book
Two Fluid Flow in a Capillary Tube
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, NC State University Libraries, Crossref
Added: August 6, 2018
2013 journal article
Smooth Periodic Solutions of a 2x2 System of Nonlinear Hyperbolic Conservation Laws
Applied Mathematics Research EXpress, 7.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: June 30, 2019
2013 conference paper
Two Fluid Flow in Porous Media
Proceedings of HYP2012, 8, 212–232. American Institute of Mathematical Sciences.
Source: NC State University Libraries
Added: July 28, 2019
2011 journal article
Simulation of spreading surfactant on a thin liquid film
Applied Mathematics and Computation, 218(9), 5157–5167.
author keywords: Thin liquid films; Surfactant; Hyperbolic-parabolic PDE; Numerical method
TL;DR:
It is shown how the tracking method applies to the full equations with realistic gravity and capillarity terms included, even though the disturbance in the height of the free surface extends beyond the support of the surfactant concentration.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Crossref, NC State University Libraries
Added: June 30, 2019
2011 journal article
Stability of plane waves in two-phase porous media flow
APPLICABLE ANALYSIS, 91(2), 295–308.
author keywords: two-phase flow; linear stability; shock waves
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(OpenAlex)
13. Climate Action
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2011 journal article
THE BUCKLEY-LEVERETT EQUATION WITH DYNAMIC CAPILLARY PRESSURE
SIAM JOURNAL ON APPLIED MATHEMATICS, 71(4), 1088–1108.
author keywords: undercompressive shock; two-phase flow; porous medium; conservation law
TL;DR:
The Buckley–Leverett equation for two-phase flow in a porous medium is modified by including dependence of the capillary pressure on the rate of change of saturation, resulting in a nonlinear pseudoparabolic partial differential equation.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
13. Climate Action
(Web of Science)
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2010 journal article
FINITE TIME EMERGENCE OF A SHOCK WAVE FOR SCALAR CONSERVATION LAWS
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 7(1), 107–116.
author keywords: Shock waves; conservation laws
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2010 journal article
Radial Spreading of a Surfactant on a Thin Liquid Film
Applied Mathematics Research EXpress, 9.
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Crossref, NC State University Libraries
Added: June 30, 2019
2010 journal article
SHOCK FORMATION AND BREAKING IN GRANULAR AVALANCHES
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 27(2), 693–714.
author keywords: avalanches; conservation laws; granular materials; segregation; shock waves
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2010 journal article
Scalar Conservation Laws with Nonconstant Coefficients with Application to Particle Size Segregation in Granular Flow
Journal of Nonlinear Science, 20(6), 689–707.
Contributors: L. May n, n & K. Daniels n
author keywords: Conservation laws; First order partial differential equations; Granular flow; Particle segregation
TL;DR:
A velocity profile is measured from experimental data and initial value problems that mimic the segregation observed in the experiment are solved, thereby verifying the value of the continuum model.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries, Crossref, ORCID
Added: August 6, 2018
2010 journal article
Shear-driven size segregation of granular materials: Modeling and experiment
PHYSICAL REVIEW E, 81(5).
TL;DR:
The Gray-Thornton model of segregation is applied to a granular flow with an exponential shear profile, and the model successfully captures the presence of a fast mixing process and relatively slower resegregation process, but the model predicts a finite resegregation time, while in the experiment resegregation occurs only exponentially in time.
(via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 6, 2018
2010 conference paper
The Gray-Thornton Model of Granular Segregation
Presented at the IUTAM-ISIMM SYMPOSIUM ON MATHEMATICAL MODELING AND PHYSICAL INSTANCES OF GRANULAR FLOWS.
Event: IUTAM-ISIMM SYMPOSIUM ON MATHEMATICAL MODELING AND PHYSICAL INSTANCES OF GRANULAR FLOWS
author keywords: Segregation; granular materials; shock waves; hyperbolic conservation laws
UN Sustainable Development Goal Categories
10. Reduced Inequalities
(OpenAlex)
Sources: Crossref, NC State University Libraries, ORCID
Added: January 8, 2019
2009 journal article
Periodic motion of a mass-spring system
IMA JOURNAL OF APPLIED MATHEMATICS, 74(6), 807–826.
author keywords: mass-spring system; Hamiltonian system; periodic solutions
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2009 other
Stability of traveling waves in thin liquid films driven by gravity and surfactant
Sources: NC State University Libraries, NC State University Libraries, Crossref
Added: August 6, 2018
2008 journal article
Evolution of a Mixing Zone in Granular Avalanches
Applied Mathematics Research EXpress, 7.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: June 30, 2019
2008 journal article
Stable solutions of a scalar conservation law for particle-size segregation in dense granular avalanches
EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 19, 61–86.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2007 journal article
Automated Review of Prerequisite Material for Intermediate-Level Undergraduate Mathematics
PRIMUS, 17(2), 167–180.
UN Sustainable Development Goal Categories
4. Quality Education
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: June 30, 2019
2007 journal article
Gravity-driven thin liquid films with insoluble surfactant: smooth traveling waves
European Journal of Applied Mathematics, 18(6), 679–708.
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, NC State University Libraries, Crossref
Added: August 6, 2018
2006 journal article
Boundary-value problems for hyperbolic equations related to steady granular flow
MATHEMATICS AND MECHANICS OF SOLIDS, 12(6), 665–699.
author keywords: granular materials; nonlinear hyperbolic partial differential equations
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2006 journal article
Growing surfactant waves in thin liquid films driven by gravity
Applied Mathematics Research EXpress, 1.
Sources: Crossref, NC State University Libraries
Added: June 30, 2019
2006 journal article
The Motion of a Thin Liquid Film Driven by Surfactant and Gravity
SIAM Journal on Applied Mathematics, 66(5), 1588–1609.
author keywords: PDE; surfactants; hyperbolic; parabolic system
TL;DR:
Wave solutions of a lubrication model for surfactant-driven flow of a thin liquid film down an inclined plane with system of nonlinear PDEs of mixed hyperbolic-parabolic type in which the effects of capillarity and surface diffusion are neglected are investigated.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, NC State University Libraries, Crossref
Added: August 6, 2018
2006 journal article
Time-dependent solutions for particle-size segregation in shallow granular avalanches
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 462(2067), 947–972.
author keywords: particle-size segregation; kinetic sieving; inverse-grading; shocks
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2005 journal article
Kinetics and nucleation for driven thin film flow
Physica D: Nonlinear Phenomena, 209(1-4), 145–163.
author keywords: kinetics; nucleation; Marangoni; Riemann solver; thin films; hyperbolic conservation laws; traveling waves
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries, Crossref
Added: August 6, 2018
2005 article
Non-linear dynamics of thin films and fluid interfaces - Preface
Behringer, R. P., & Shearer, M. (2005, September 15). PHYSICA D-NONLINEAR PHENOMENA, Vol. 209, pp. VII-VIII.
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2005 chapter
Riemann problems involving undercompressive shocks
In M. Rascle, D. Serre, & M. Slemrod) (Eds.), PDEs and Continuum Models of Phase Transitions (pp. 187–200).
Ed(s): M. Rascle, D. Serre & M. Slemrod)
Sources: Crossref, NC State University Libraries
Added: March 20, 2021
2004 journal article
Comparison of two dynamic contact line models for driven thin liquid films
European Journal of Applied Mathematics, 15(6), 625–642.
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries, Crossref
Added: August 6, 2018
2004 journal article
Non-classical Riemann solvers with nucleation
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 134(2004), 961–984.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2003 journal article
Stability of shear bands in an elastoplastic model for granular flow: The role of discreteness
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 13(11), 1629–1671.
author keywords: shear band; stability; granular; discrete model
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2003 journal article
Thin film traveling waves and the Navier slip condition
SIAM Journal on Applied Mathematics, 63(2), 722–744.
TL;DR:
This work considers the lubrication model for a thin film driven by competing gravitational forces and thermal gradients on an inclined plane and shows that for all three problems there is a finite range of admissible contact angles for which traveling wave solutions exist.
(via Semantic Scholar)
Sources: NC State University Libraries, NC State University Libraries
Added: August 6, 2018
2002 journal article
Computer simulations of particle deposition in the lungs of chronic obstructive pulmonary disease patients
INHALATION TOXICOLOGY, 14(7), 705–720.
MeSH headings : Aerosols; Air Pollutants / pharmacokinetics; Airway Resistance; Bronchitis, Chronic / metabolism; Computer Simulation; Emphysema / metabolism; Humans; Lung / metabolism; Models, Biological; Particle Size; Pulmonary Disease, Chronic Obstructive / metabolism
TL;DR:
Airway obstructions are the main cause for increased deposition in the COPD lung, and a computer model successfully depicts PM deposition patterns and their dependence on the severity of disease.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science; OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2001 journal article
A discrete model for an ill-posed nonlinear parabolic PDE
PHYSICA D-NONLINEAR PHENOMENA, 160(3-4), 189–221.
author keywords: nonlinear PDE; ill-posed equations; nonlinear diffusion; granular medium; shear bands
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2001 journal article
A nonconvex scalar conservation law with trilinear flux
QUARTERLY OF APPLIED MATHEMATICS, 59(4), 615–635.
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2001 journal article
Stability of compressive and undercompressive thin film travelling waves
EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 12(2001 June), 253–291.
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2000 journal article
Existence of undercompressive traveling waves in thin film equations
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 32(1), 194–213.
author keywords: undercompressive shocks; traveling waves; heteroclinic orbit; existence
TL;DR:
Undercompressive traveling wave solutions of the partial differential equation ∂th + ∂xf (h )= −∂x(h 3 ∂ 3h )+ D ∂x (h 3xh), when the flux function f has the nonconvex form f (h)= h2 − h3 are considered.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2000 journal article
Numerical determination of flow corrective inserts for granular materials in conical hoppers
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 35(5), 869–882.
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
2000 other
Similarity solutions for granular flows in hoppers
Sources: Crossref, NC State University Libraries
Added: June 30, 2019
1999 journal article
Mathematical Model of Airflow in the Lungs of Children I: Effects of Tumor Sizes and Locations
Journal of Theoretical Medicine, 2(3), 199–213.
TL;DR:
Analysis of airflow patterns in the lung of a four-year-old child and the effects of tumors indicated that tumors have a pronounced affect on both localized velocity profiles in airways and bulk flow distribution within the lung.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: June 30, 2019
1999 journal article
Mathematical Model of Airflow in the Lungs of Children II: Effects of Ventilatory Parameters
Journal of Theoretical Medicine, 3(1), 51–62.
TL;DR:
The results of simulations show the extent to which changing ventilatory parameters can affect flow patterns in the neighborhood of the tumors as well as drug distribution throughout the lung.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: June 30, 2019
1999 journal article
Undercompressive shocks and Riemann problems for scalar conservation laws with non-convex fluxes
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 129(1999), 733–754.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
1999 journal article
Undercompressive shocks for a system of hyperbolic conservation laws with cubic nonlinearity
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 229(1), 344–362.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
1999 journal article
Undercompressive shocks in thin film flows
PHYSICA D-NONLINEAR PHENOMENA, 134(4), 431–464.
author keywords: undercompressive shock; capillarity; thin films; Marangoni stress; fourth order diffusion; numerical simulation; hyperbolic conservation law
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(Web of Science)
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
1999 chapter
Undercompressive waves in driven thin film flow: Theory, computation, and experiment
In V. Alexiades & G. Siopsis (Eds.), Trends in Mathematical Physics (Vol. 13, pp. 43–68).
Ed(s): V. Alexiades * & G. Siopsis *
Sources: Crossref, NC State University Libraries
Added: July 10, 2019
1998 journal article
A simple model for stress fluctuations in plasticity with application to granular materials
SIAM JOURNAL ON APPLIED MATHEMATICS, 58(6), 1791–1807.
author keywords: plasticity; stress fluctuations; granular material
TL;DR:
This paper discusses a first generation of discrete models for stress ∞uctuations, which consist of many spring-slider elements in parallel and shows that the magnitude of ∞UCTuations is governed by the system size and the roughness, the latter dened as the ratio of particle contact length to particle size.
(via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
1998 journal article
An elastoplasticity model for antiplane shearing with a non-associative flow rule: Genuine nonlinearity of plastic waves
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 219(2), 344–363.
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
1998 journal article
Discrete element investigation of stress fluctuation in granular flow at high strain rates
PHYSICAL REVIEW E, 57(2), 2053–2061.
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
1998 journal article
Lithotripsy: The treatment of kidney stones with shock waves
SIAM REVIEW, 40(2), 356–371.
author keywords: shock waves; bubble dynamics; asymptotic methods
TL;DR:
This paper discusses mathematical models for the response of a small air bubble in water to an ultrasound pulse, a context that arises in the modern treatment for kidney stones, and applies asymptotics to describe large-amplitude solutions of Rayleigh's equations.
(via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
1997 chapter
Formation of Shear Bands in Models of Granular Materials
In IUTAM Symposium on Mechanics of Granular and Porous Materials (pp. 343–352).
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1997 conference paper
Models for stress fluctuations in plasticity
In R. P. Behringer & J. Jenkins (Eds.), Powders & grains 97 : proceedings of the third International Conference on Powders & Grains, Durham, North Carolina, 18-23 May 1997 (pp. 325–328). Rotterdam, Netherlands: Balkema.
Ed(s): R. Behringer & J. Jenkins
Event: International Conference on Powders & Grains at Durham, North Carolina on May 18-23, 1997
Source: NC State University Libraries
Added: April 4, 2021
1997 journal article
Plane shear waves in a fully saturated granular medium with velocity and stress controlled boundary conditions
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 32(3), 489–503.
author keywords: plane shear waves; saturated granular material; hypoplastic flow rule; scale-invariant problem; characteristic wave; shock wave; rarefaction wave; wave curve; state space; kinetic energy
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
1997 conference paper
Stress fluctuations in granular materials
In C. S. Chang, A. Misra, R. Y. Liang, & M. Babic (Eds.), Mechanics of deformation and flow of particulate materials : proceedings of a symposium, Evanston, Illinois, June 29-July 2, 1997. New York: ASCE Publications.
Ed(s): C. Chang, A. Misra, R. Liang & M. Babic
Source: NC State University Libraries
Added: April 4, 2021
1997 journal article
The influence of material non-uniformity preceding shear-band formation in a model for granular flow
EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 8(1997 Oct.), 457–483.
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018
1996 conference paper
Fully nonlinear hyperbolic systems related to hypoplasticity
In J. Glimm, M. J. Graham, J. W. Grove, & B. J. Plohr (Eds.), Proceedings of the Fifth International Conference on Hyperbolic problems: Theory, numerics, applications (pp. 440–446). River Edge, New Jersey: World Scientific.
Ed(s): J. Glimm, M. Graham, J. Grove & B. Plohr
Event: Fifth International Conference on Hyperbolic Problems at University of Stony Brook, New York on June 13-17, 1994
Source: NC State University Libraries
Added: November 24, 2021
1996 journal article
Riemann Problems for 5×5 Systems of Fully Non-linear Equations Related to Hypoplasticity
Mathematical Methods in the Applied Sciences, 19(18), 1433–1444.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: January 24, 2021
1995 journal article
A class of fully nonlinear 2×2 systems of partial differential equations
Communications in Partial Differential Equations, 20(7-8), 1105–1131.
Sources: Crossref, NC State University Libraries
Added: September 7, 2020
1995 journal article
Fully nonlinear hyperbolic systems of partial differential equations related to plasticity
Communications in Partial Differential Equations, 20(7-8), 1133–1153.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1995 journal article
The Riemann problem for a system of conservation laws of mixed type with a cubic nonlinearity
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 125(4), 675–699.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1995 journal article
Traveling Wave Solutions of the Modified Korteweg-deVries-Burgers Equation
Journal of Differential Equations, 116(2), 448–467.
Sources: Crossref, NC State University Libraries
Added: March 20, 2021
1994 conference paper
Formation and development of shear bands in granular material
Transactions of the 11th Army Conference on Applied Mathematics and Computing, 15–28. Research Triangle, North Carolina: Army Research Office.
Source: NC State University Libraries
Added: November 24, 2021
1994 journal article
Unloading near a shear band in granular material
Quarterly of Applied Mathematics, 52(3), 579–600.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1993 journal article
Nonstrictly Hyperbolic Conservation Laws with a Parabolic Line
Journal of Differential Equations, 103(1), 94–126.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1993 journal article
The Initial Value Problem for a System Modelling Unidirectional Longitudinal Elastic-Plastic Waves
SIAM Journal on Mathematical Analysis, 24(5), 1111–1144.
author keywords: ELASTOPLASTICITY; HYPERBOLIC EQUATIONS; FULLY NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; INITIAL VALUE PROBLEM; WEAK SOLUTIONS
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1993 journal article
Unloading near a shear band: a free boundary problem for the wave equation
Communications in Partial Differential Equations, 18(7-8), 1271–1298.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1992 journal article
Scale-invariant initial value problems in one-dimensional dynamic elastoplasticity, with consequences for multidimensional nonassociative plasticity
European Journal of Applied Mathematics, 3(3), 225–254.
Sources: Crossref, NC State University Libraries
Added: February 24, 2020
1991 journal article
Undercompressive shocks for nonstrictly hyperbolic conservation laws
Journal of Dynamics and Differential Equations, 3(2), 199–271.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: March 20, 2021
1991 report
Viscous Profiles and Numerical Methods for Shock Waves
UN Sustainable Development Goal Categories
13. Climate Action
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1990 journal article
Instability in Critical State Theories of Granular Flow
SIAM Journal on Applied Mathematics, 50(1), 33–47.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1990 chapter
Loss of Hyperbolicity in Yield Vertex Plasticity Models under Nonproportional Loading
In The IMA Volumes in Mathematics and Its Applications (pp. 192–217).
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1990 chapter
Undercompressive Shocks in Systems of Conservation Laws
In The IMA Volumes in Mathematics and Its Applications (pp. 218–231).
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1989 journal article
Approximately periodic solutions of the elastic string equations
Applicable Analysis, 32(1), 1–14.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1989 journal article
Loss of real characteristics for models of three-phase flow in a porous medium
Transport in Porous Media, 4(5).
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1989 journal article
The Riemann problem for 2 × 2 systems of hyperbolic conservation laws with case I quadratic nonlinearities
Journal of Differential Equations, 80(2), 343–363.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: March 20, 2021
1989 journal article
The quasidynamic approximation in critical state plasticity
Archive for Rational Mechanics and Analysis, 108(4), 267–280.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1988 journal article
Dynamic phase transitions in a van der Waals gas
Quarterly of Applied Mathematics, 46(4), 631–636.
UN Sustainable Development Goal Categories
13. Climate Action
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1988 chapter
Loss of strict hyperbolicity for the Buckley-Leverett equations of three phase flow in a porous medium
In M. Wheeler (Ed.), Numerical simulation in oil recovery. New York: Springer.
Ed(s): M. Wheeler
Event: Symposium on Numerical Simulation in Oil Recovery at University of Minnesota
Source: NC State University Libraries
Added: November 24, 2021
1987 other
Phase jumps near the Maxwell line
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1987 journal article
Riemann problems for nonstrictly hyperbolic 2x2 systems of conservation laws
Transactions of the American Mathematical Society, 304(1), 267–306.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: March 20, 2021
1987 journal article
Solution of the riemann problem for a prototype 2x2 system of non-strictly hyperbolic conservation laws
Archive for Rational Mechanics and Analysis, 97(4), 299–320.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: March 20, 2021
1987 journal article
The classification of 2 × 2 systems of non-strictly hyperbolic conservation laws, with application to oil recovery
Communications on Pure and Applied Mathematics, 40(2), 141–178.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: March 20, 2021
1987 report
The elastic string equations: numerical results using Glimm’s method, and two new exact solutions
[CRSC Report]. Raleigh, North Carolina: NC State University.
Source: NC State University Libraries
Added: November 24, 2021
1986 journal article
Nonuniqueness of admissible solutions of Riemann initial value problems for a system of conservation laws of mixed type
Archive for Rational Mechanics and Analysis, 93(1), 45–59.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1986 conference paper
Recent developments in nonstrictly hyperbolic conservation laws
Transactions of the Fourth Army Conference on Applied Mathematics and Computing. Presented at the 4th Army Conference on Applied Mathematics and Computing, Cornell University, Ithaca, New York.
Event: 4th Army Conference on Applied Mathematics and Computing at Cornell University, Ithaca, New York on May 27-31, 1986
Source: NC State University Libraries
Added: November 24, 2021
1986 conference paper
Shock waves and bifurcation
In L. Gama (Ed.), Proceedings of the Brazilian National Colloquium.
Ed(s): L. Gama
Source: NC State University Libraries
Added: November 24, 2021
1986 journal article
The Riemann problem for the planar motion of an elastic string
Journal of Differential Equations, 61(2), 149–163.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1986 chapter
Three phase flow in porous media-recent developments in nonstrictly hyperbolic conservation laws
In G. Papanicolaou (Ed.), Advances in Multiphase Flow and Related Problems (pp. 210–218). Philadelphia, Pennsylvania: SIAM.
Ed(s): G. Papanicolaou
Source: NC State University Libraries
Added: November 24, 2021
1985 journal article
Elementary Wave Solutions of the Equations Describing the Motion of an Elastic String
SIAM Journal on Mathematical Analysis, 16(3), 447–459.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1985 chapter
The interaction of transverse waves for the vibrating string
In J. H. Lightbourne & S. M. Rankin (Eds.), Physical Mathematics and Nonlinear Partial Differential Equations (pp. 229–238). New York: Marcel Dekker.
Ed(s): J. Lightbourne & S. Rankin
Source: NC State University Libraries
Added: November 24, 2021
1985 journal article
The nonlinear interaction of smooth travelling waves in an elastic string
Wave Motion, 7(2), 169–175.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1985 conference paper
Three phase flow in a porous medium and the classification of non-strictly hyperbolic conservation laws
Transactions of the third Army Conference on Applied Mathematics and Computing, 509–518. Research Triangle, North Carolina: U.S. Army Research Office.
Event: Third Army Conference on Applied Mathematics and Computing at Atlanta, Georgia on May 13-16, 1985
Source: NC State University Libraries
Added: November 24, 2021
1983 journal article
Admissibility criteria for shock wave solutions of a system of conservation laws of mixed type
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 93(3-4), 233–244.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1982 journal article
The Riemann problem for a class of conservation laws of mixed type
Journal of Differential Equations, 46(3), 426–443.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1981 journal article
Coincident bifurcation of equilibrium and periodic solutions of evolution equations
Journal of Mathematical Analysis and Applications, 84(1), 113–132.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1981 journal article
On Bifurcation and Symmetry in Benard Convection and Taylor Vortices
Studies in Applied Mathematics, 65(1), 85–93.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1980 journal article
Bifurcation of axisymmetric buckled states of a thin spherical shell
Nonlinear Analysis: Theory, Methods & Applications, 4(4), 699–713.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1980 journal article
One-parameter perturbations of bifurcation from a simple eigenvalue
Mathematical Proceedings of the Cambridge Philosophical Society, 88(1), 111–123.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1980 journal article
Secondary Bifurcation Near a Double Eigenvalue
SIAM Journal on Mathematical Analysis, 11(2), 365–389.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1978 journal article
Bifurcation in the neighbourhood of a non-isolated singular point
Israel Journal of Mathematics, 30(4), 363–381.
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: March 20, 2021
1978 journal article
On the null spaces of linear Fredholm operators depending on several parameters
Mathematical Proceedings of the Cambridge Philosophical Society, 84(1), 131–142.
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
1978 report
Secondary bifurcation for one-parameter families of bifurcation problems
(Report No. 97). Colchester, England: University of Essex.
Source: NC State University Libraries
Added: November 24, 2021
1977 journal article
Small solutions of a non-linear equation in Banach space for a degenerate case
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 79(1-2), 35–49.
Sources: Crossref, NC State University Libraries
Added: January 24, 2021
1976 chapter
Bifurcation from a multiple eigenvalue
In Ordinary and Partial Differential Equations (pp. 417–424).
Sources: Crossref, NC State University Libraries
Added: September 14, 2020
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