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In a unidirectional solidification design problem, the solidification velocity and liquid-side interfacial temperature gradient are of principle interest due to their effect on the morphology of the cast structure. The design challenge is the prediction of the temporal conditions at the boundaries such that the solidification velocity and liquid-side temperature gradient at the solid-liquid interface follow a prescribed scenario. This design problem requires the resolution of two inverse heat conduction problems: one in an expanding solid domain and the second in a shrinking liquid domain. Resolution of the solid domain results in a transient boundary condition that yields the prescribed solidification velocity, while resolution of the liquid domain results in a transient boundary condition that yields the prescribed interfacial temperature gradient. An innovative and robust solution technique is proposed and demonstrated for resolution of the liquid-side temperature gradient design problem during unidirectional solidification. The technique, termed the Function Decomposition Method (FDM), is an innovative combination of function decomposition for the superposition of direct solutions, continuous least squares, and the weighted residual method which transforms the mildly ill-posed inverse heat conduction problem in the shrinking liquid region into a set of well-posed direct problems. To demonstrate its application, a set of test cases are presented which provide illustrative results highlighting the flexibility of the methodology.

Episodic memory, or memory of experienced events, is a critical function of the hippocampus. It is therefore important to understand how hippocampal activity represents specific events in an animal's life. We addressed this question in chickadees — specialist food-caching birds that hide food at scattered locations and use memory to find their caches later in time. We performed high-density neural recordings in the hippocampus of chickadees as they cached and retrieved seeds in a laboratory arena. We found that each caching event was represented by a burst of firing in a unique set of hippocampal neurons. These 'barcode-like' patterns of activity were sparse (<10% of neurons active), uncorrelated even for immediately adjacent caches, and different even for separate caches at the same location. The barcode representing a specific caching event was transiently reactivated whenever a bird later interacted with the same cache — for example, to retrieve food. Barcodes co-occurred with the conventional activity of place cells, as well as with responses to cached seeds. We propose that barcodes are signatures of episodic memories evoked during memory recall. These patterns assign a unique identifier to each event and may be a mechanism for rapid formation and storage of many non-interfering memories.