3D die stacking is an exciting new technology that increases transistor density by vertically integrating two or more die with a dense, high-speed interface. The result of 3D die stacking is a significant reduction of interconnect both within a die and across dies in a system. For instance, blocks within a microprocessor can be placed vertically on multiple die to reduce block to block wire distance, latency, and power. Disparate Si technologies can also be combined in a 3D die stack, such as DRAM stacked on a CPU, resulting in lower power higher BW and lower latency interfaces, without concern for technology integration into a single process flow. 3D has the potential to change processor design constraints by providing substantial power and performance benefits. Despite the promising advantages of 3D, there is significant concern for thermal impact. In this research, we study the performance advantages and thermal challenges of two forms of die stacking: Stacking a large DRAM or SRAM cache on a microprocessor and dividing a traditional microarchitecture between two die in a stack.Results: It is shown that a 32MB 3D stacked DRAM cache can reduce the cycles per memory access of a twothreaded RMS benchmark on average by 13% and as much as 55% while increasing the peak temperature by a negligible 0.08ºC. Off-die BW and power are also reduced by 66% on average. It is also shown that a 3D floorplan of a high performance microprocessor can simultaneously reduce power 15% and increase performance 15% with a small 14ºC increase in peak temperature. Voltage scaling can reach neutral thermals with a simultaneous 34% power reduction and 8% performance improvement.

We formulate the statistical dynamics of topological defects in the active nematic phase, formed in two dimensions by a collection of self-driven particles on a substrate. An important consequence of the nonequilibrium drive is the spontaneous motility of strength +1/2 disclinations. Starting from the hydrodynamic equations of active nematics, we derive an interacting particle description of defects that includes active torques. We show that activity, within perturbation theory, lowers the defect-unbinding transition temperature, determining a critical line in the temperature-activity plane that separates the quasi-long-range ordered (nematic) and disordered (isotropic) phases. Below a critical activity, defects remain bound as rotational noise decorrelates the directed dynamics of +1/2 defects, stabilizing the quasi-long-range ordered nematic state. This activity threshold vanishes at low temperature, leading to a reentrant transition. At large enough activity, active forces always exceed thermal ones and the perturbative result fails, suggesting that in this regime activity will always disorder the system. Crucially, rotational diffusion being a two-dimensional phenomenon, defect unbinding cannot be described by a simplified one-dimensional model.

Collections of self-propelled particles that move persistently by continuously consuming free energy are a paradigmatic example of active matter. In these systems, unlike Brownian "hot colloids," the breakdown of detailed balance yields a continuous production of entropy at steady state, even for an ideal active gas. We quantify the irreversibility for a noninteracting active particle in two dimensions by treating both conjugated and time-reversed dynamics. By starting with underdamped dynamics, we identify a hidden rate of entropy production required to maintain persistence and prevent the rapidly relaxing momenta from thermalizing, even in the limit of very large friction. Additionally, comparing two popular models of self-propulsion with identical dissipation on average, we find that the fluctuations and large deviations in work done are markedly different, providing thermodynamic insight into the varying extents to which macroscopically similar active matter systems may depart from equilibrium.

Topological defects play a prominent role in the physics of two-dimensional materials. When driven out of equilibrium in active nematics, disclinations can acquire spontaneous self-propulsion and drive self-sustained flows upon proliferation. Here we construct a general hydrodynamic theory for a two-dimensional active nematic interrupted by a large number of such defects. Our equations describe the flows and spatio-temporal defect chaos characterizing active turbulence, even close to the defect unbinding transition. At high activity, nonequilibrium torques combined with manybody screening cause the active disclinations to spontaneously break rotational symmetry forming a collectively moving defect ordered polar liquid. By recognizing defects as the relevant quasiparticle excitations, we construct a comprehensive phase diagram for two-dimensional active nematics. Using our hydrodynamic approach, we additionally show that activity gradients can act like "electric fields", driving the sorting of topological charge. This demonstrates the versatility of our continuum model and its relevance for quantifying the use of spatially inhomogeneous activity for controlling active flows and for the fabrication of active devices with targeted transport capabilities.