Anomalous negative differential thermal resistance in a momentum-conserving lattice

Abstract

A two-segment Fermi-Pasta-Ulam lattices has been investigated by using nonequilibrium molecular dynamics. Here we present an anomalous negative differential thermal resistance (NDTR) that have not been reported in Frenkel-Kontorova and φ 4 lattices up to the present. The NDTR disappears at low temperature region. The region of NDTR shifts from the large to the small temperature difference region as the system size increases. Anomalous dependence of NDTR on the temperature can be explained as the negative effect induced by the nonlinear coupling. The explanation can also cover the phenomenon of NDTR in momentum-nonconserved lattices.

Scaling analysis of negative differential thermal resistance

“…nanotube-based thermal rectifiers [10,11], thermal cloaks [12,13]), there has been much interest in understanding how NDTR can be systematically generated. In particular, studies have been carried out for various nonlinear lattices [14][15][16][17][18][19], namely the Frenkel-Kontorova (FK) model [14][15][16], the φ 4 model [16] and the Fermi-Pasta-Ulam (FPU) model [16,17]. Each of these models is described by a Hamiltonian of the form…”

“…(3) also holds for the FPU-β model (with a β(x i+1 − x i ) 4 /4 in its potential of nearest-neighbour interaction, where β = 1 is the strength of such nonlinear interaction) with γ < 0 and t > 0 within a specific range of T . For the conventional cases of having the value of either T + or T − fixed [14][15][16][17][18][19], NDTR corresponds to…”

“…nanotube-based thermal rectifiers [10,11], thermal cloaks [12,13]), there has been much interest in understanding how NDTR can be systematically generated. In particular, studies have been carried out for various nonlinear lattices [14][15][16][17][18][19], namely the Frenkel-Kontorova (FK) model [14][15][16], the φ 4 model [16] and the Fermi-Pasta-Ulam (FPU) model [16,17]. Each of these models is described by a Hamiltonian of the form where N is the total number of particles (system size) and, for the i th particle, x i is the position, p i is the instantaneous momentum, U (x i ) is the onsite potential, and V (x i+1 − x i ) is the potential of nearest-neighbour interaction.…”

Thermally driven classical Heisenberg chain with a spatially varying magnetic field: thermal rectification and negative differential thermal resistance

“…However, in spite of enormous efforts the underlying physical mechanism that generates NDTR in nonlinear system is still not satisfactorily understood. A lot of mechanisms have been proposed and many unresolved questions regarding the emergence of NDTR, such as the mismatch of the phonon bands [13,14], role of interface [15], ballistic-diffusive transport [16,17], role of momentum conservation [18] presence of a critical system size and a transition from the exhibition to the nonexhibition of NDTR [19] and scaling [20] are still being explored. NDTR is considered to be of immense technological im- * E-mail address: debarshee.bagchi@saha.ac.in portance in the working of recently proposed thermal devices such as the thermal transistors [13], thermal logic gates [14], thermal memory elements [21] etc.…”

“…NDTR is considered to be of immense technological im- * E-mail address: debarshee.bagchi@saha.ac.in portance in the working of recently proposed thermal devices such as the thermal transistors [13], thermal logic gates [14], thermal memory elements [21] etc. Theoretical studies using mostly numerical simulation have been employed extensively to study both these feature in many nonlinear lattice systems, few examples are the Frenkel-Kontorova model [6,19], the φ 4 model [15], the Fermi-Pasta-Ulam chain [7,18], the Morse lattice [5].…”