Description of Exam Subjects
The written preliminary examination is the first step for students wishing to pursue their doctorate in AEM. Five exam subjects are offered and original problems are written by AEM faculty each year. The questions are be open-ended and require creative application of the subject matter. The exam subjects are:
- The WPE in Computational Fluid Mechanics covers topics presented in AEM 4253/5253 (Computational Fluid Mechanics). The exam has an emphasis on introductory concepts in finite difference and finite volume methods as applied to various ordinary and partial differential model equations in fluid mechanics. Fundamentals of spatial discretization and numerical integration; character of equations; finite difference approximations; convergence, consistency, and stability; methods for the solution of parabolic, elliptic and hyperbolic equations; numerical linear algebra; solution of nonlinear equations; solution of systems of equations.
- The WPE in Continuum Mechanics aims to evaluate a student’s potential for success in conducting original research and draws from concepts presented in AEM 5501 (Continuum Mechanics). This includes topics such as the kinematics of motion, forces and stresses, thermodynamics, balance laws or constitutive equations. A typical question poses a particular physical problem relevant to science and engineering in which students must demonstrate knowledge of one or more of these concepts and the ability to synthesize ideas and techniques in ways not explicitly demonstrated in their course work.
- The WPE in Controls aims to evaluate a student’s potential for success in conducting original research and draws from concepts presented in AEM 5321 (Modern Feedback Control) related to the modeling, analysis, and design of finite-dimensional linear systems in continuous and discrete time. This includes (but is not limited to) input-output and state-space modeling; linearization of nonlinear systems; fundamental solution matrices and state transition matrices; controllability, observability, and related analyses; Lyapunov and input-output stability; realization theory; state feedback; pole placement; observer design; observer-based control; linear quadratic regulation; and Lyapunov and Riccati equations.
- The WPE in Dynamics covers topics in the course AEM 5401 (Intermediate Dynamics). In particular, the following topics are of importance: Kinematics and kinetics of particles in non-inertial frames; Analytical mechanics including Lagrange’s equations with holonomic and non-holonomic constraints; Rigid body dynamics in three dimensions including Euler angles, inertia matrix, equations of motion.
- The WPE in Fluid Mechanics is based mainly on application of fundamental equations and concepts considered in introductory fluids courses such as AEM 8201 (Fluid Mechanics I). Problems may require application of fundamental conservation equations in integral or differential forms (e.g. mass, momentum, and energy), fluid kinematics concepts including mapping of pathlines, streaklines, streamlines, deformation, rotation, and volumetric expansion, understanding of vorticity transport, vortex dynamics, basic concepts of potential flow, viscous flow, and laminar vs. turbulent flow. Exam problems may include multiple parts where some require direct application of equations while others ask for physical interpretations and estimates based on scaling of relevant parameters.
Policies for the WPE
- In determining whether a student has passed or failed the WPE, faculty will consider the student's overall performance in the AEM graduate program including the WPE subject exam results, but also other information such as performance in course work, progress toward degree, etc.
- The WPE cannot be taken after the second year of study.
- Students are given two attempts to pass, provided they take the exam for the first time during their first year. Students who take the exam for the first time their second year of study are only given one opportunity to pass.
- Students must pass two of the five WPE subjects exams and should pre-register for the specific subjects in which they will participate.
- Students must select at least one of the following subjects: Fluid Mechanics, Continuum Mechanics, or Dynamics.
- The WPE is held during spring semester each year on a Friday evening and Saturday morning, typically the first weekend in April. Students complete one subject exam per day.
- Exams are 3 hours long.
- Students are allowed a calculator and one notebook containing their notes on the subject for each session. The notes can be typed and contained in a 3-ring binder.
- Practice exams are provided for students' preparation. However, solved problems from previous exams cannot be included in the notebook during the exam
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All assigned committee members must be present. The absence of any assigned member results in an invalid examination.
Immediately before the preliminary oral examination, the committee chair stipulates the objectives of the examination and, in consultation with other members of the examining committee, determines how the examination is to be conducted. Immediately after the examination, the candidate is excused from the room and a written secret ballot is taken before discussing the examination. Following the discussion, a second and final vote is taken. Note: If the exam result is PASS WITH RESERVATIONS, the committee is permitted one week to return the Preliminary Oral Examination Form along with a copy of the letter or email outlining the steps the student must take to remove the reservations.
The outcome of the examination, with all committee members present and voting, is recorded in one of three ways: pass, pass with reservations, or fail. The voting proportions necessary for these decisions are as follows: if the committee consists of four members, a favorable verdict for passing consists of either a unanimous vote or a vote of 3-1; if the committee consists of five members, a favorable verdict for passing consists of either a unanimous vote or a vote of 4-1; if the committee consists of six members, a unanimous vote or a vote of 5-1 or 4-2 is needed; and if there are seven members, a unanimous vote or a vote of 6-1 or 5-2 is needed. Candidates who do not earn committee votes in these proportions fail the examination. If, in order to achieve the minimum number of votes to reach a verdict of pass, any vote of pass with reservations is included, then the outcome is recorded as a pass with reservations. A vote to pass the student with reservations still constitutes a passing vote.
If the student passes the examination with reservations, the student is informed immediately, but the committee is permitted one week in which to convey its reservations to the student in writing, informing the student of the steps that must be taken to remove them, as well as a deadline by which the committee expects the reservations to be removed. A copy of this letter must be sent to the GSSP along with the Preliminary Oral Examination Form. When the student has satisfied the committee's reservations, a second letter or email informing the student and GSSP that the reservations have been removed and that the student may proceed toward the degree is also required. The committee chair should write both letters. The final oral examination may not be scheduled until GSSP has received a copy of the letter indicating that the reservations have been removed.
If the committee members disagree as to whether the reservations have been satisfactorily removed, the committee chair asks for another vote, the results of which are subject to the same voting proportions as the initial vote.
A student who is unable to satisfy the committee's reservations may be terminated from doctoral candidacy and from the graduate program.
Students who fail the examination may be excluded from candidacy for the degree (i.e. dismissed from the doctoral program). The student may retake the examination, provided that all committee members, or all committee members save one must approve the re-take. The original preliminary oral examining committee conducts the reexamination.
If the preliminary oral examining committee recesses without having determined whether a student has passed the examination, the chair of the committee must send a letter to the Dean of the Graduate School explaining the reasons for the recess and noting the date on which the examining committee will reconvene. If the recess will be longer than one week, the examination report form must be returned to GSSP, 160 Williamson Hall. The student must schedule the Preliminary Oral Examination at least one week before the rescheduled exam. A new examination report form will be mailed to the chair of the committee before the date on which the committee will reconvene. The reconvened committee must comprise of the same members as the original preliminary oral examining committee.
Please ensure that all assigned committee members are present. The absence of any assigned member results in an invalid examination.
Step One - The Public Seminar: The final examination begins with a seminar to which the scholarly community is invited and which includes a presentation of the dissertation by the candidate.
Step Two - The Closed Examination: A closed meeting between the candidate and the appointed examining committee immediately follows the public seminar. The examination is limited to the candidate's dissertation subject and relevant areas. The entire examination (i.e., public seminar and closed examination) is not to exceed three hours.
Step Three - The Vote: At the end of the closed examination the candidate is excused from the room. A written, secret ballot is taken before discussion of the examination begins. Following the committee's discussion, a second and final vote is taken on whether the student passed the examination.
To be recommended for the award of the doctoral degree, candidates must receive a vote with no more than one member of the total examining committee dissenting.
If the committee recommends revisions to the dissertation, the student's adviser is responsible for ensuring that the student includes the appropriate modifications and required revisions in the final dissertation.
Retakes and "Pass with reservations"
According to the rules defined by the graduate faculty, the student either passes or fails the final doctoral examination. Retakes are not permitted, and (unlike the preliminary oral examination) there is no provision for a "pass with reservations." The faculty examining committee has both the authority and the responsibility to fail a student whose dissertation or performance in the oral defense does not meet the standards for award of the doctoral degree.
Recessing the examination
Occasionally there are instances in which the final examination does not proceed well, but in which the faculty feel that the student has an acceptable dissertation that she or he is capable of adequately defending. While such instances should be rare, it is in both the student's and the faculty's interest to follow clearly defined procedures (see below) for recessing and reconvening the final oral examination.
Note: Suggestions for minor revisions in the dissertation are common and do not require that the faculty or the student follow the procedures outlined below. Such minor revisions need only be made in the text of the dissertation before the final copy is submitted.
Circumstances that might prompt a recess of the final oral examination would fall into two broad categories involving 1) primarily non-substantive matters or 2) cases in which the faculty have a serious concern about either the dissertation itself or the student's ability to defend it, but in which they believe that the situation can be remedied if the student is given additional time to revise the dissertation or prepare for the examination.
1) Primarily non-substantive matters: Cases in this category include, but are not limited to, those in which the student's nervousness prevents him or her from adequately defending the dissertation. In such circumstances, the examining committee may decide informally to recess for up to one week. The committee and the student should select a date and time for reconvening that is agreeable to all parties. No written notice need be given to the student, although the faculty should give him or her advice and assurance, as they deem important.
2) More serious concerns: When the faculty has serious concerns about the dissertation or the student's ability to defend it, but feels the student has the potential to improve the dissertation or his/her examination performance, the faculty should stop the examination, inform the student of their intent to recess, and discuss with the student the deficiencies that prompted the recess.