THE OBJECTIVES OF THIS RESEARCH ARE TO IMPROVE OUR UNDERSTANDING OF THE DYNAMICAL ARCHITECTURES OF PLANETARY SYSTEMS AND THE OVERALL MASS DISTRIBUTION OF PLANETS IN THE GALAXY BY USING AVAILABLE EXOPLANET OBSERVATIONAL DATA SETS IN CONCERT WITH THEORY AND MODELING OF THEIR ORBITAL DYNAMICS. OBSERVATIONAL DATA SETS OF EXOPLANETS ARE EXPANDING RAPIDLY (THANKS TO NASA MISSIONS SUCH AS KEPLER AND THE FORTHCOMING JWST TESS AND WFIRST) BUT THEIR THEORETICAL INTERPRETATION HAS SIGNIFICANTLY LAGGED. EXOPLANET DETECTION AND CONFIRMATION PIPELINES NOW ROUTINELY CHECK WHETHER THE PLANETARY SYSTEMS THEY DISCOVER ARE LIKELY TO BE DYNAMICALLY STABLE. AT THE SAME TIME IT IS INCREASINGLY RECOGNIZED THAT OBSERVED PLANETARY ARCHITECTURES ARE OFTEN QUITE CLOSE TO THE EDGE OF DYNAMICAL STABILITY". IN THE FIRST PROJECT WE WILL APPLY THE TOOLS OF N-BODY NUMERICAL SIMULATIONS TO OBSERVED CLOSE-IN MULTI-PLANET SYSTEMS DISCOVERED BY KEPLER TO ASSESS THEIR DISTRIBUTION OF DYNAMICAL INSTABILITY LIFETIMES. WE WILL IDENTIFY THE COMMON SIGNS OF IMMINENT INSTABILITY AS WELL AS COMMON SIGNS OF LONGEVITY FOR PLANETARY SYSTEMS ON THE EDGE OF DYNAMICAL STABILITY. THIS PROJECT WILL PRODUCE PREDICTIONS OF THE DISTRIBUTION OF STABLE PLANETARY ARCHITECTURES TESTABLE BY FUTURE LARGE SAMPLES OF MULTI-PLANET SYSTEMS SUCH AS THOSE OBSERVED BY THE FORTHCOMING TESS SURVEY. IN THE SECOND PROJECT WE WILL CONTINUE WITH NUMERICAL SIMULATIONS OF UNSTABLE SYSTEMS TO ASSESS POST-INSTABILITY PLANETARY ARCHITECTURES. IT HAS BEEN SUGGESTED THAT MULTI-PLANET SYSTEMS WITH FEWER MORE WIDELY SPACED PLANETS COULD BE THE RESULT OF COLLISIONS BETWEEN PLANETS IN ORIGINALLY MORE TIGHTLY PACKED SYSTEMS. BY MODELING TWO DIFFERENT SCENARIOS OF COLLISION OUTCOMES (THAT COLLISIONS ARE EITHER DESTRUCTIVE OR MOSTLY ACCRETIONAL) WE WILL GENERATE SIMULATED DISTRIBUTIONS OF POST-INSTABILITY PLANETARY SYSTEMS ARISING FROM A VARIETY OF PRE-INSTABILITY PLANETARY ARCHITECTURES; COMPARISON WITH THE OBSERVED KEPLER PLANETARY SYSTEMS WILL TEST THE IDEA THAT A FRACTION OF THE OBSERVED SYSTEMS UNDERWENT PAST INSTABILITIES. THIS PROJECT WILL ALSO PROVIDE PREDICTIONS FOR THE FREQUENCY OF PLANET-PLANET COLLISIONS AROUND DWARF STARS AS A FUNCTION OF SYSTEM AGE TO BE COMPARED WITH THE OBSERVED FREQUENCY OF INFRARED-EXCESSES AROUND DWARF STARS. IN THE THIRD PROJECT WE WILL CONSIDER ANEW THE RELATIONSHIP BETWEEN ORBITAL SEPARATIONS AND PLANETARY MASSES IN MARGINALLY STABLE MULTIPLE PLANET SYSTEMS AND DERIVE AN IMPROVED ESTIMATE OF THE PLANET MASS DISTRIBUTION FUNCTION. WHILE VARIOUS PREVIOUS STUDIES HAVE TAKEN A DETERMINISTIC APPROACH TO COMPUTE DYNAMICAL LIFETIMES AS A FUNCTION OF THE DIMENSIONLESS "DYNAMICAL SEPARATION" (ORBITAL SPACING IN UNITS OF THE MUTUAL HILL RADIUS OF TWO ADJACENT PLANETS) WE PROPOSE A STATISTICAL APPROACH USING THE RESULTS OF OUR FIRST TWO PROJECTS TO CHARACTERIZE THE DISTRIBUTION OF DYNAMICAL SEPARATIONS AS A FUNCTION OF DYNAMICAL LIFETIMES IN DIVERSE PLANETARY SYSTEMS. WITH THESE RESULTS IN HAND WE WILL LEVERAGE THE KEPLER DATASET OF WELL DETERMINED ORBITAL PERIODS IN HUNDREDS OF MULTIPLE PLANET SYSTEMS TO PREDICT THE OVERALL MASS DISTRIBUTION FUNCTION OF CLOSE-IN PLANETS. OUR PREDICTED MASS DISTRIBUTION FUNCTION WILL BE OBSERVATIONALLY TESTABLE BY BOTH THE FORTHCOMING TESS TRANSITING PLANET SAMPLE AND BY THE FUTURE WFIRST MISCROLENSING PLANET SAMPLE. OUR PROPOSED INVESTIGATIONS ARE RELEVANT TO XRP BECAUSE THEY INCORPORATE THEORY AND MODELING TO FACILITATE INTERPRETATION OF OBSERVATIONAL DATA FROM NASA'S KEPLER SPACE MISSION AND THEY WILL MAKE TESTABLE PREDICTIONS FOR FORTHCOMING EXOPLANET SURVEYS AS WELL AS SURVEYS OF INFRARED EXCESSES ASSOCIATED WITH PLANET-PLANET COLLISIONS. OUR PROPOSED STUDIES WILL IMPROVE UNDERSTANDING OF THE ORIGINS OF OBSERVED EXOPLANETARY SYSTEMS BY CHARACTERIZING THEIR ORBITAL DYNAMICS.