  In an effort to better understand the evolution of composite supernova
remnants (SNRs) and the eventual fate of relativistic particles injected by
their pulsars, we present a multifaceted investigation of the interaction
between a pulsar wind nebula (PWN) and its host SNR G327.1-1.1. Our 350 ks
Chandra X-ray observations of SNR G327.1-1.1 reveal a highly complex
morphology; a cometary structure resembling a bow shock, prong-like features
extending into large arcs in the SNR interior, and thermal emission from the
SNR shell. Spectral analysis of the non-thermal emission offers clues about the
origin of the PWN structures, while enhanced abundances in the PWN region
provide evidence for mixing of supernova ejecta with PWN material. The overall
morphology and spectral properties of the SNR suggest that the PWN has
undergone an asymmetric interaction with the SNR reverse shock (RS) that can
occur as a result of a density gradient in the ambient medium and/or a moving
pulsar that displaces the PWN from the center of the remnant. We present
hydrodynamical simulations of G327.1-1.1 that show that its morphology and
evolution can be described by a ~ 17,000 yr old composite SNR that expanded
into a density gradient with an orientation perpendicular to the pulsar's
motion. We also show that the RS/PWN interaction scenario can reproduce the
broadband spectrum of the PWN from radio to gamma-ray wavelengths. The analysis
and modeling presented in this work have important implications for our general
understanding of the structure and evolution of composite SNRs.
