Shocks are physical phenomenon that occur quite often around us. In this thesis we examine the occurrence of shocks in finite amplitude acoustic waves from a numerical perspective. These waves, or jump discontinuities, yield ill-behaved solutions when solved numerically. This study takes on the challenge of finding both single- and multi-valued solutions.
The previously unsolved problem in this study is the representation of the Equation of Motion (EoM) in the form of the Darcy-Jordan model (DJM) and expressed as a dimensionless IVP Cauchy problem. Prior attempts to solve have resulted only in implicit solutions or explicit solutions with certain initial conditions.
The approach taken in this study is the development of a hybrid algorithm combining the reliability of the Bisection Method and the efficiency of the Secant method. The developed algorithm is coded in MATLAB.
","abstract_html":"<p>Shocks are physical phenomenon that occur quite often around us. In this thesis we examine the occurrence of shocks in finite amplitude acoustic waves from a numerical perspective. These waves, or jump discontinuities, yield ill-behaved solutions when solved numerically. This study takes on the challenge of finding both single- and multi-valued solutions.</p> <p>The previously unsolved problem in this study is the representation of the Equation of Motion (EoM) in the form of the Darcy-Jordan model (DJM) and expressed as a dimensionless IVP Cauchy problem. Prior attempts to solve have resulted only in implicit solutions or explicit solutions with certain initial conditions.</p> <p>The approach taken in this study is the development of a hybrid algorithm combining the reliability of the Bisection Method and the efficiency of the Secant method. The developed algorithm is coded in MATLAB.</p>","abstract_has_math":false,"creators":["Shimp, Chandler"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["James Lambers","C. S. Chen","Haiyan Tian"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-10-27T07:00:00Z","date_published":"2021-10-27T07:00:00Z","updated_at":"2026-07-24T05:45:33Z","subjects":["Shock waves","Equation of Motion","Darcy-Jordan Model","Poroacoustics","Numerical Analysis","Numerical Analysis and Computation","Other Applied Mathematics","Partial Differential Equations","Theory and Algorithms"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/866","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["James Lambers","C. S. Chen","Haiyan Tian"]},{"key":"dc:creator","label":"Author","values":["Shimp, Chandler"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2021-12-14T08:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Shock waves","Equation of Motion","Darcy-Jordan Model","Poroacoustics","Numerical Analysis","Numerical Analysis and Computation","Other Applied Mathematics","Partial Differential Equations","Theory and Algorithms"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/866"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Shocks are physical phenomenon that occur quite often around us. In this thesis we examine the occurrence of shocks in finite amplitude acoustic waves from a numerical perspective. These waves, or jump discontinuities, yield ill-behaved solutions when solved numerically. This study takes on the challenge of finding both single- and multi-valued solutions.
The previously unsolved problem in this study is the representation of the Equation of Motion (EoM) in the form of the Darcy-Jordan model (DJM) and expressed as a dimensionless IVP Cauchy problem. Prior attempts to solve have resulted only in implicit solutions or explicit solutions with certain initial conditions.
The approach taken in this study is the development of a hybrid algorithm combining the reliability of the Bisection Method and the efficiency of the Secant method. The developed algorithm is coded in MATLAB.
"]},{"key":"dc:title","label":"Title","values":["Multi-valued Solutions for the Equation of Motion, Darcy-Jordan Model, as a Cauchy Problem: A Shocking Event"]}]}],"canonical_facts":{"dc:contributor":["James Lambers","C. S. Chen","Haiyan Tian"],"dc:creator":["Shimp, Chandler"],"dc:date.available":["2021-12-14T08:00:00Z"],"dc:description.abstract":["Shocks are physical phenomenon that occur quite often around us. In this thesis we examine the occurrence of shocks in finite amplitude acoustic waves from a numerical perspective. These waves, or jump discontinuities, yield ill-behaved solutions when solved numerically. This study takes on the challenge of finding both single- and multi-valued solutions.
The previously unsolved problem in this study is the representation of the Equation of Motion (EoM) in the form of the Darcy-Jordan model (DJM) and expressed as a dimensionless IVP Cauchy problem. Prior attempts to solve have resulted only in implicit solutions or explicit solutions with certain initial conditions.
The approach taken in this study is the development of a hybrid algorithm combining the reliability of the Bisection Method and the efficiency of the Secant method. The developed algorithm is coded in MATLAB.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/866"],"dc:subject":["Shock waves","Equation of Motion","Darcy-Jordan Model","Poroacoustics","Numerical Analysis","Numerical Analysis and Computation","Other Applied Mathematics","Partial Differential Equations","Theory and Algorithms"],"dc:title":["Multi-valued Solutions for the Equation of Motion, Darcy-Jordan Model, as a Cauchy Problem: A Shocking Event"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:45:33Z"}