UROP Research Mentor Project Submission Portal: Submission #1117

serial: '1117'
sid: '20181'
uuid: 81ef839b-078e-4603-bbf1-b80361048ec0
uri: /urop-research-mentor-project-submission-portal
created: '1755044354'
completed: '1755044354'
changed: '1758819185'
in_draft: '0'
current_page: ''
remote_addr: 217.180.196.112
uid: '0'
langcode: en
webform_id: urop_project_proposal_portal
entity_type: node
entity_id: '1116'
locked: '0'
sticky: '0'
notes: ''
metatag: meta
data:
  roundtable_info: {  }
  approximately_how_many_hours_a_week_would_the_research_assistant: '7'
  are_you_currently_looking_for_students_: 'Yes'
  confirmation_1: '1'
  contact_email_fsu_email: ''
  contact_email_fsu_email2: ''
  contact_email_fsu_email_if_affiliated_: areznikov@fsu.edu
  faculty_advisor_confirmation: ''
  faculty_advisor_name: ''
  faculty_advisor_s_fsu_email: ''
  fsu_college: 'Arts and Sciences'
  fsu_department_if_applicable_: Mathematics
  headshot_optional_: ''
  if_the_project_location_is_off_campus_does_the_student_need_to_p: ''
  mentoring_philosophy: 'The main point in my mentoring philosophy is fostering independent work of a student and teaching the student to come up with ideas, problems, and their solutions on their own.'
  mentor_handbook_and_faqs: '1'
  name_of_other_faculty_collaborator_if_applicable_: ''
  number_of_assistants_needed_faculty_postdoc_max_6_graduate_stude: '1'
  other_faculty_collaborator_s_preferred_pronouns: ''
  overall_research_project_description: |-
    Imagine placing four electrons on the sphere of radius 1 (a common beast in a Calculus class). They will repel each other, and therefore move along the sphere. They will stop moving when they reach an "equilibrium state"; mathematically speaking, when their potential energy is minimized. Unfortunately, the word "minimized" has different meanings in pure math vs the real life. In reality, this stable state can be reached at a critical point of the potential energy (the difference between a critical point, a local minimum and a global minimum is a common Calculus 3 problem). 

    For the project, I propose to collect numerical evidence for the following conjecture: unless the four electrons were placed in a very unfortunate locations, they will reach the stable state at the global minimum of the potential energy. Specifically, they will arrange themselves in the vertices of a regular pyramid. 
  please_add_any_additional_information_here: ''
  please_provide_a_link_to_your_publications_a_video_clip_or_a_web: 'https://scholar.google.com/citations?user=x5-srkIAAAAJ&hl=en&oi=sra'
  please_select_the_choice_that_most_accurately_describes_your_exp: 'Partially Remote'
  please_select_the_location_of_your_project_: 'On FSU Main Campus'
  position_availability_for_student_research: 'Flexible schedule'
  position_title: Faculty
  primary_research_mentor_name: 'Alexander Reznikov'
  project_keywords: 'Potential theory, real analysis, optimization'
  relevant_student_major_s_: 'Mathematics, statistics, physics, computer science, engineering'
  research_mentor_preferred_pronoun2: ''
  research_mentor_pronouns: He/His
  research_mentor_supervisor_if_different_from_above_: ''
  research_tasks_for_student_research_assistant_s_: |-
    The main task will be to develop an efficient script implementing the gradient descent method for a specific "potential energy" function. 

    The efficiency of the script can be evaluated as follows: the same question can be asked in a more general setting (for example, in higher dimensions), when the number of variables grows. The script is expected to be adaptable to those settings.
  roundtable_times_and_zoom_links: N/A
  skills_that_research_assistants_may_need_: |-
    Required: good knowledge of the first half of Calculus 3
    Recommended: knowledge of a common programming language, such as C or Python. 

    The project can be viewed as a learning opportunity to better learn such a language.
  title_of_the_project: '*** Gradient descent method for potential energy of four equal charges'
  update_url: 'https://cre.fsu.edu/urop-research-mentor-project-submission-portal?token=91ayh55k6hUAgb7uGp4sioFocPyLCV7b3u0_eibv3H8'
  urop_performance_evaluation: '1'
  urop_poster_presentation: '1'
  when_potential_research_assistants_are_reaching_out_via_email_2: ''
  when_potential_research_assistants_are_reaching_out_via_email_wh: ''
  when_students_are_reaching_out_via_email_what_is_your_preferreda: 'Dr. '
  would_you_like_to_participate_in_the_urop_research_mentor_round2: 'No'
  would_you_like_to_participate_in_the_urop_research_mentor_roundt: ''
  year: '2025'