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We use a semiclassical three-fluid thermodynamic model to evaluate thephenomena of spatial demixing in mesoscopic clouds of fermionic and bosonicatoms at high dilution under harmonic confinement, assuming repulsiveboson-boson and boson-fermion interactions and including account of a bosonicthermal cloud at finite temperature T. The finite system size allows threedifferent regimes for the equilibrium density profiles at T=0: a fully mixedstate, a partially mixed state in which the overlap between the boson andfermion clouds is decreasing, and a fully demixed state where the two cloudshave zero overlap. We propose simple analytical rules for the two cross-oversbetween the three regimes as functions of the physical system parameters andsupport these rules by extensive numerical calculations. A universal ``phasediagram'' expressed in terms of simple scaling parameters is shown to be validfor the transition to the regime of full demixing, inside which we identifyseveral exotic configurations for the two phase-separated clouds in addition tosimple ones consisting of a core of bosons enveloped by fermions and "viceversa". With increasing temperature the main role of the growing thermal cloudof bosons is to transform some exotic configurations into more symmetric ones,until demixing is ultimately lost. For very high values of boson-fermionrepulsive coupling we also report demixing between the fermions and thethermally excited bosons.Comment: 11 pages, 8 figure

Demixing in mesoscopic boson-fermion clouds inside cylindrical harmonic traps: Quantum phase diagram and role of temperature