Normal forms and averaging in an acceleration problem in nonholonomic mechanics.

This paper investigates nonholonomic systems (the Chaplygin sleigh and the Suslov system) with periodically varying mass distribution. In these examples, the behavior of velocities is described by a system of the form dvdτ=f2(τ)u2+f1(τ)u+f0(τ),dudτ=-uv+g(τ), where the coefficients are periodic functions of time τ with the same period. A detailed analysis is made of the problem of the existence of modes of motion for which the system speeds up indefinitely (an analog of Fermi's acceleration). It is proved that, depending on the choice of coefficients, variable v has the asymptotics t1k,k=1,2,3. In addition, we show regions of the phase space for which the system, when the trajectories are started from them, is observed to speed up. The proof uses normal forms and averaging in a slightly unusual form since unusual form averaging is performed over a variable that is not fast.

Low-Field Electron Emission Capability of Thin Films on Flat Silicon Substrates: Experiments with Mo and General Model for Refractory Metals and Carbon.

Herein, we describe a study of the phenomenon of field-induced electron emission from thin films deposited on flat Si substrates. Films of Mo with an effective thickness of 6-10 nm showed room-temperature low-field emissivity; a 100 nA current was extracted at macroscopic field magnitudes as low as 1.4-3.7 V/µm. This result was achieved after formation treatment of the samples by combined action of elevated temperatures (100-600 °C) and the electric field. Morphology of the films was assessed by AFM, SEM, and STM/STS methods before and after the emission tests. The images showed that forming treatment and emission experiments resulted in the appearance of numerous defects at the initially continuous and smooth films; in some regions, the Mo layer was found to consist of separate nanosized islets. Film structure reconstruction (dewetting) was apparently induced by emission-related factors, such as local heating and/or ion irradiation. These results were compared with our previous data obtained in experiments with carbon islet films of similar average thickness deposited onto identical substrates. On this basis, we suggest a novel model of emission mechanism that might be common for thin films of carbon and refractory metals. The model combines elements of the well-known patch field, multiple barriers, and thermoelectric models of low-macroscopic-field electron emission from electrically nanostructured heterogeneous materials.