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).

By: P. Sprenger n, T. Bridges* & M. Shearer n

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.

By: T. Barker*, J. Gray*, D. Schaeffer* & M. Shearer n

author keywords: suspensions; particle/fluid flow
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.

By: T. Congy*, G. El*, M. Hoefer* & M. Shearer n

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.

By: A. Bardall n, S. Chen n, K. Daniels n & M. Shearer n

UN Sustainable Development Goal Categories
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.

By: D. Schaeffer*, T. Barker*, D. Tsuji*, P. Gremaud n, M. Shearer n & J. Gray*

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.

By: S. Chen n, A. Bardall n, M. Shearer n & K. Daniels n

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)
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.

By: E. Brown* & M. Shearer*

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.

By: T. Congy*, G. El*, M. Hoefer* & M. Shearer n

author keywords: asymptotic analysis; nonlinear waves; partial differential equations
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.

By: Z. Tang n, T. Brzinski*, M. Shearer n & K. Daniels n

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.

By: A. Bardall*, K. Daniels* & M. Shearer*

author keywords: PDEs in Connection with Mechanics of Deformable Solids; Transform Methods; Classical Linear Elasticity; Numerical Approximation of Solutions; Fluid-Solid Interactions
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.

By: G. El*, M. Hoefer* & M. Shearer n

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.

By: M. Shearer n, G. El* & M. Hoefer*

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.

By: T. Barker*, D. Schaeffer*, M. Shearer n & J. Gray*

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).

By: J. Bostwick*, J. Dijksman* & M. Shearer*

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.

By: G. El*, M. Hoefer* & M. Shearer n

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.

By: M. Shearer & R. Levy

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.

By: S. Strickland n, M. Shearer n & K. Daniels n

author keywords: capillary waves; Faraday waves; waves/free-surface flows
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 6, 2018

2015 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.

By: E. Swanson*, S. Strickland n, M. Shearer n & K. Daniels n

author keywords: Experiment; Model; Surfactant; Thin liquid film
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.

By: M. Shearer*, K. Spayd* & E. Swanson*

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.

By: J. Bostwick*, M. Shearer n & K. Daniels n

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)
Sources: Crossref, NC State University Libraries, ORCID, NC State University Libraries
Added: August 6, 2018

2014 chapter book

Two Fluid Flow in a Capillary Tube

By: M. Strait n, M. Shearer n, R. Levy*, L. Cueto-Felgueroso* & R. Juanes*

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.

By: M. Shearer n

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.

By: M. Shearer

Source: NC State University Libraries
Added: July 28, 2019

2012 journal article

Simulation of spreading surfactant on a thin liquid film

Applied Mathematics and Computation, 218(9), 5157–5167.

By: E. Peterson* & M. Shearer*

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
Sources: Crossref, NC State University Libraries
Added: June 30, 2019

2012 journal article

Stability of plane waves in two-phase porous media flow

APPLICABLE ANALYSIS, 91(2), 295–308.

By: K. Spayd n, M. Shearer n & Z. Hu n

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.

By: K. Spayd* & M. Shearer*

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

Evolution of a Mixing Zone in Granular Avalanches

Applied Mathematics Research EXpress, 7.

By: M. McIntyre*, E. Rowe n, M. Shearer n, J. Gray* & A. Thornton*

UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: June 30, 2019

2010 journal article

FINITE TIME EMERGENCE OF A SHOCK WAVE FOR SCALAR CONSERVATION LAWS

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 7(1), 107–116.

By: M. Shearer* & C. Dafermos*

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.

By: E. Peterson* & M. Shearer*

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.

By: M. Shearer* & N. Giffen*

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.

By: L. May n, M. Shearer n & K. Daniels n

Contributors: L. May n, M. Shearer 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).

By: L. May n, L. Golick n, K. Phillips n, M. Shearer n & K. Daniels n

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.

By: M. Shearer*, L. May, N. Giffen, K. Daniels*, J. Goddard, P. Giovine, J. Jenkins

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.

By: M. Shearer n, P. Gremaud n & K. Kleiner n

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

By: E. Peterson, M. Shearer*, T. Witelski & R. Levy*

Sources: NC State University Libraries, NC State University Libraries, Crossref
Added: August 6, 2018

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.

By: M. Shearer n, J. Gray* & A. Thornton*

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.

By: R. Levy*, M. Shearer* & P. Taylor

UN Sustainable Development Goal Categories
4. Quality Education (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: June 30, 2019

2007 journal article

Boundary-value problems for hyperbolic equations related to steady granular flow

MATHEMATICS AND MECHANICS OF SOLIDS, 12(6), 665–699.

By: D. Schaeffer*, M. Shearer n & T. Witelski*

author keywords: granular materials; nonlinear hyperbolic partial differential equations
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2007 journal article

Gravity-driven thin liquid films with insoluble surfactant: smooth traveling waves

European Journal of Applied Mathematics, 18(6), 679–708.

By: R. Levy*, M. Shearer* & T. Witelski*

UN Sustainable Development Goal Categories
Sources: Web Of Science, NC State University Libraries, Crossref
Added: August 6, 2018

2006 journal article

Growing surfactant waves in thin liquid films driven by gravity

Applied Mathematics Research EXpress, 1.

By: T. Witelski, M. Shearer* & R. Levy*

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.

By: R. Levy* & M. Shearer*

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)
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.

By: J. Gray*, M. Shearer n & A. Thornton*

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.

By: R. Levy* & M. Shearer n

author keywords: kinetics; nucleation; Marangoni; Riemann solver; thin films; hyperbolic conservation laws; traveling waves
UN Sustainable Development Goal Categories
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.

By: R. Behringer* & M. Shearer n

UN Sustainable Development Goal Categories
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2004 journal article

Comparison of two dynamic contact line models for driven thin liquid films

European Journal of Applied Mathematics, 15(6), 625–642.

By: R. Levy n & M. Shearer n

UN Sustainable Development Goal Categories
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.

By: P. LeFloch* & M. Shearer*

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.

By: M. Shearer n, D. Schaeffer* & T. Witelski*

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.

By: R. Buckingham, M. Shearer* & A. Bertozzi

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.

By: R. Segal n, T. Martonen*, C. Kim* & M. Shearer n

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.

By: T. Witelski*, D. Schaeffer* & M. Shearer n

author keywords: nonlinear PDE; ill-posed equations; nonlinear diffusion; granular medium; shear bands
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.

By: B. Hayes* & M. Shearer n

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.

By: A. Bertozzi*, A. Munch*, M. Shearer n & K. Zumbrun*

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.

By: A. Bertozzi & M. Shearer*

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
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2000 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.

By: R. Segal n, X. Guan*, M. Shearer n & T. Martonen*

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

2000 journal article

Mathematical Model of Airflow in the Lungs of Children II: Effects of Ventilatory Parameters

Journal of Theoretical Medicine, 3(1), 51–62.

By: X. Guan*, R. Segal n, M. Shearer n & T. Martonen*

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

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.

By: P. Gremaud n, D. Schaeffer* & M. Shearer n

Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2000 other

Similarity solutions for granular flows in hoppers

By: P. Gremaud, J. Matthews & M. Shearer*

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.

By: B. Hayes* & M. Shearer n

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.

By: M. Schulze n & M. Shearer n

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.

By: A. Bertozzi*, A. Munch* & M. Shearer n

author keywords: undercompressive shock; capillarity; thin films; Marangoni stress; fourth order diffusion; numerical simulation; hyperbolic conservation law
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).

By: M. Shearer, A. Bertozzi & A. Munch

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.

By: D. Schaeffer & M. Shearer*

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.

By: F. Garaizar n, M. Gordon n & M. Shearer n

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.

By: O. Schwarz n, Y. Horie n & M. Shearer n

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.

By: L. Howle, D. Schaeffer, M. Shearer* & P. Zhong

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).

By: M. Shearer n, F. Garaizar n & M. Gordon n

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.

By: D. Schaeffer & M. Shearer

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.

By: M. Gordon n, M. Shearer n & D. Schaeffer*

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
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.

By: D. Schaeffer & M. Shearer

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.

By: D. Schaeffer* & M. Shearer n

UN Sustainable Development Goal Categories
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.

By: M. Shearer

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.

By: M. Shearer n & D. Schaeffer*

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.

By: M. Shearer n & D. Schaeffer*

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.

By: M. Shearer n & D. Schaeffer*

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.

By: M. Shearer n & Y. Yang n

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.

By: D. Jacobs n, B. Mckinney n & M. Shearer n

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.

By: M. Shearer, F. Garaizar, D. Schaeffer & J. Trangenstein

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.

By: M. Shearer n & D. Schaeffer*

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.

By: D. Schaeffer n, S. Schecter n & M. Shearer n

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.

By: M. Shearer* & D. Schaeffer

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.

By: D. Schaeffer* & M. Shearer n

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.

By: D. Schaeffer* & M. Shearer n

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.

By: S. Schecter n & M. Shearer n

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

By: M. Shearer*

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.

By: D. Schaeffer, M. Shearer* & E. Pitman

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).

By: D. Schaeffer* & M. Shearer n

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).

By: M. Shearer n & S. Schecter n

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.

By: J. Fehribach* & M. Shearer n

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).

By: M. Shearer n & J. Trangenstein n

Sources: Crossref, NC State University Libraries
Added: September 14, 2020

1989 chapter

Riemann problems involving undercompressive shocks

In M. Rascle, D. Serre, & M. Slemrod) (Eds.), PDEs and Continuum Models of Phase Transitions (pp. 187–200).

By: M. Shearer n & S. Schecter n

Ed(s): M. Rascle, D. Serre & M. Slemrod)

Sources: Crossref, NC State University Libraries
Added: March 20, 2021

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.

By: M. Shearer n

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.

By: M. Shearer n & D. Schaeffer n

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.

By: M. Shearer n

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.

By: M. Shearer

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

By: M. Shearer*

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.

By: D. Schaeffer & M. Shearer*

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.

By: M. Shearer n, D. Schaeffer n, D. Marchesin n & P. Paes-Leme n

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.

By: D. Schaeffer n & M. Shearer n

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.

By: M. Shearer & J. Fehribach

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.

By: M. Shearer n

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.

By: M. Shearer & D. Schaeffer

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.

By: M. Shearer

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.

By: M. Shearer*

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.

By: M. Shearer & D. Schaeffer

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.

By: M. Shearer*

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.

By: M. Shearer

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.

By: M. Shearer*

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.

By: M. Shearer & D. Schaeffer

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.

By: M. Shearer*

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.

By: M. Shearer*

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.

By: M. Shearer*

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.

By: M. Shearer* & I. Walton*

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.

By: M. Shearer*

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.

By: M. Shearer*

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.

By: M. Shearer*

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.

By: M. Shearer*

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.

By: M. Shearer*

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.

By: M. Shearer

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.

By: M. Shearer*

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).

By: M. Shearer*

Sources: Crossref, NC State University Libraries
Added: September 14, 2020

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