Controlled manipulation of atoms in insulating surfaces with the virtual atomic force microscope

We predict how single oxygen ions can be manipulated on the MgO (100) surface and demonstrate the possibility of detecting a single-atom event using a noncontact atomic force microscope. The manipulation process is simulated explicitly in real time with a virtual dynamic atomic force microscope including the full response of the instrumentation and demonstrates a strong dependence on temperature. The proposed new atomistic mechanism and protocols for the controlled manipulation of single atoms and vacancies on insulating surfaces may be relevant for anchoring molecules and metal clusters at these surfaces and controlling their electronic properties.     

Nonequilibrium statistical mechanics of mixed quantum classical ensembles: application to noncontact atomic force microscopy

Using the nonequilibrium statistical operator method, we suggest a new general method of treating dynamics of a combined system consisting of interacting classical and quantum parts. The method is illustrated on the tip dynamics in the noncontact atomic force microscopy (NC-AFM) where a macroscopic tip interacts with a quantum microscopic system (the surface and the nanotip). The derived general equation of motion for the tip and the Fokker-Planck equation, applicable even at low temperatures, contain memory effects and a friction term which should (at least partially) be responsible for the observed energy dissipation in NC-AFM experiments.     

Mathematics in economics: Achievements,difficulties, perspectives

I am deeply moved by this high honor which has fallen my lot to receive and I am happy to have the opportunity to appear here as a participant in this honorable series of lectures.In our time mathematics has penetrated into economics so solidly and widely and my theme is connected with such a variety of facts and problems that it brings me to cite the words of Kozma Prutkov, which are very popular in my country: One cannot embrace the unembraceable. The appropriateness of this wise sentence is not diminished by the fact that that great thinker is only a pen name.So, I want to restrict my theme to topics which are nearer to me, mainly to optimization models and their use in the control of the economy in order to best use resources for obtaining best results. I shall touch mainly on the problems and experiences of a planned economy, especially of the Soviet economy. Even within these limits I will succeed to consider only a few problems.Copyright © the Nobel Foundation 1975.     

Prospects of large-block approach in applied mathematics,programming, and computer technology

The direction of the research is examined dealing with the technical realization and the mathematical foundations of the solution of large-scale problems involving mass operations. In predicting the trends of development of computational methods and computer technology, a set of problems are presented and also a systems approach to solving them.Report presented at coordination conference on Mathematical Foundations and Technical Realization of Large-Block Computational Processes, Leningrad, May 28–29, 1973.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 48, pp. 5–11, 1974.     

Derivation of atomistic models for lattices consisting of weakly overlapping structural elements

A theoretical approach based on the arrow diagram technique within the group function theory is applied to an infinite crystal consisting of weakly overlapping structural elements (SE: ions, atoms, and molecules). A perturbation method is used to derive the lattice energy in terms of two‐body, three‐body, etc. types of interactions accompanied by electronic polarization of SEs for the system which is slightly away from some reference configuration. It is demonstrated how an atomistic model for the particular material can be derived from the general theory. A general approach to obtain a parametrization scheme is suggested which is based on a representation of transition and ground‐state reduced density matrices (RDM) of various orders via a finite set of basis functions. Using group theory and necessary conditions for N‐representability of the RDMs, the representation containing the least possible number of the fitting parameters is worked out. The method is illustrated on a special case of spherical SEs (e.g., atoms/ions in atomic/ionic solids) and it is discussed whether existing models are in accord with the ideas developed. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 306–330, 2000     

Structure of Chain Aggregates in Ferrocolloids

The structure of chain aggregates in polydisperse ferrocolloids is considered. The chain distribution over the number of constituent particles is investigated on the basis of the method of heterophase fluctuations. The polydispersity of ferrofluids is taken into account within the frameworks of two-fraction model suggesting the presence of a large number of small particles and a small number of large particles. The sorting algorithm of chain structures with various energies is presented. It is shown that, in real ferrofluids, the most probable are the chains composed of large particles with one or two small particles at the edges. The model predicts that the most of large particles are bonded into short chain aggregates whose average length consists of two or three particles at room temperature.     

An Endergonic Synthesis of Single Sondheimer–Wong Diyne by Local Probe Chemistry

Recent advances in scanning probe microscopy on surface enable not only direct observation of molecular structures but also local probe reactions, in which unstable short-lived products have been synthesized and analyzed. Now, an endergonic reaction to synthesize a single Sondheimer–Wong diyne from 6,13-dibromopentaleno[1,2-b:4,5-b′]dinaphthalene by local probe chemistry on a ultra-thin film of NaCl formed on a Cu(111) surface at 4.3 K is presented. The structures of the precursor, two intermediates, and the final product were directly identified by the differential conductance imaging with a CO functionalized tip. DFT calculations revealed that the multiple-step reaction, being endergonic overall, is facilitated by temporal charging and discharging of the molecule placed in the nanometric junction between the Cu tip and the Cu substrate underneath the ultra-thin NaCl film. This local probe reaction expands possibilities to synthesize nanocarbon materials in a bottom-up manner.