Thermal metamaterials, designed by transformation thermodynamics are artificial structures that can actively control heat flux at a continuum scale. However, fabrication of them is very challenging because it requires a continuous change of thermal properties in materials, for one specific function. Herein, we introduce tunable thermal metamaterials that use the assembly of unit-cell thermal shifters for a remarkable enhancement in multifunctionality as well as manufacturability. Similar to the digitization of a two-dimensional image, designed thermal metamaterials by transformation thermodynamics are disassembled as unit-cells thermal shifters in tiny areas, representing discretized heat flux lines in local spots. The programmed-reassembly of thermal shifters inspired by LEGO enable the four significant functions of thermal metamaterials-shield, concentrator, diffuser, and rotator-in both simulation and experimental verification using finite element method and fabricated structures made from copper and PDMS. This work paves the way for overcoming the structural and functional limitations of thermal metamaterials.Active control of thermal energy through mediums is a significant subject with applicability in diverse fields, from fundamental physics to practical applications. Understanding thermal energy transport at nano-microscales mainly depends on the phonon distribution and contact interface of layers 1 . Manipulation of thermal energy transport at macroscales has been regarded as equivalent to the control of heat flux through the material, because of its diffusive nature through specific mediums at continuum scales 1,2 . Most research about macroscale thermal transport has focused on the development of bulk materials or mediums that promote thermal transport with superior thermal conductivity or suppress heat transfer with thermal insulation and grain boundaries 3,4 . The progress of micro-nanotechnologies has enabled advanced research into a new class of materials with desirable properties, by means of using embedded fillers in composite structures [5][6][7] . However, such methods have reached the limit for achieving breakthroughs in terms of active control of thermal energy near local spots in macroscales, since they inevitably depend on thermal properties of mediums.The development of metamaterials that are able to manipulate diverse physical properties using artificially designed structures have been introduced as a new approach to overcome previous limitations of transport phenomena through the mediums. Transformation optics was one of general approaches to design cloaking devices or optical waveguides [8][9][10][11][12][13][14] . This method was applicable to microwave frequencies as well 13 , and experimental verifications have been conducted in the visible wavelength region 15 . Furthermore, transformation thermodynamics has been recently extended to design new kinds of thermal metamaterials 16 , which actively control heat flux through diverse mediums in millimeter to centimeter scales, dominated b...

We study the mass fallback rate of tidally disrupted stars on marginally bound and unbound orbits around a supermassive black hole (SMBH) by performing three-dimensional smoothed particle hydrodynamic simulations with three key parameters. The star is modeled by a polytrope with two different indexes (n = 1.5 and 3). The stellar orbital properties are characterized by five orbital eccentricities ranging from e = 0.98 to 1.02, and five different penetration factors ranging from β = 1 to 3, where β represents the ratio of the tidal disruption to pericenter distance radii. We derive analytic formulae for the mass fallback rate as a function of the stellar density profile, orbital eccentricity, and penetration factor. Moreover, two critical eccentricities to classify tidal disruption events (TDEs) into five different types: eccentric ( ), marginally eccentric ( ), purely parabolic (e = 1), marginally hyperbolic ( ), and hyperbolic ( ) TDEs, are reevaluated as and , where q is the ratio of the SMBH to stellar masses and 0 < k ≲ 2. We find the asymptotic slope of the mass fallback rate varies with the TDE type. The asymptotic slope approaches −5/3 for the parabolic TDEs, is steeper for the marginally eccentric TDEs, and is flatter for the marginally hyperbolic TDEs. For the marginally eccentric TDEs, the peak of mass fallback rates can be about one order of magnitude larger than the parabolic TDE case. For marginally hyperbolic TDEs, the mass fallback rates can be much lower than the Eddington accretion rate, which can lead to the formation of a radiatively inefficient accretion flow, while hyperbolic TDEs lead to failed TDEs. Marginally unbound TDEs could be an origin of a very low-density gas disk around a dormant SMBH.

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