Davydov Theory Research Articles

Возможности опосредствования решения арифметических задач третьеклассниками: процедура «комплектования»

<p>The purpose of our study was to reveal students’ typical difficulties when performing trivial transformations of several quantities, which are to be coordinated. We have designed two tasks that required to build up the "sets", and to keep their ratio. 97 third-graders from three secondary Moscow schools were recruited for this study. The participants solved the first task individually in the written form, and afterwards there were 25 couples randomly selected to solve the similar task jointly in an oral interview with the experimenter. The analysis of the results revealed the weakness and confusion of most of the surveyed students in solving such problems. The in-depth consideration of the written works and interviews allowed us to characterize the model means, used by students, as formal or meaningful. Among them, only the “portion-by-portion” measurement of two independent quantities, performed through drawing or using the counting material, provided by the experimenter, turned out to be effective. The study showed that the source of difficulties in solving problems related to “assembling sets” is the lack of adequate model mediation, and confirmed the relevance of considering the "assembling sets problem" in the general line of development of the number concept in primary mathematics education within the framework of V.V. Davydov's theory of learning activity.</p>

Вариации на тему развивающего образования

<p>The article raises the problem of developmental teaching (education) from the standpoint of cultural- historical methodology, the origins and scientific foundations of it its basic principles and widespread practical systems. The author’s aim is to discover the general and specific features of existing models of developmental instruction, both theoretical justifications and practical recommendations for the organization of real school education. It is suggested that there is one system of developmental education based on the ideas of L.S.Vygotsky about the correlation between education and mental development and there are various theoretical approaches and practical models based on it. We tried to compare different attitudes to the correlation between education and mental development. We analyzed work made by Galperin, by research teams led by Elkonin and Davydov, and rby esearch teams led by L.V.Zankov. Special attention is paid to Repkin's research on the psychological organization of educational material, it illustrates the interpenetration of two approaches: Galperin's ideas about the developmental effect of instruction and Davydov's theory of learning activity. The author's hypothesis needs a theoretical and experimental verification, which will have not only a narrow scientific value, but also determine the directions of changes in the content of school education in accordance with the psychological laws of assimilation.</p>

Solving the time-independent Schrödinger equation for chains of coupled excitons and phonons using tensor trains.

We demonstrate how to apply the tensor-train format to solve the time-independent Schrödinger equation for quasi-one-dimensional excitonic chain systems with and without periodic boundary conditions. The coupled excitons and phonons are modeled by Fröhlich-Holstein type Hamiltonians with on-site and nearest-neighbor interactions only. We reduce the memory consumption as well as the computational costs significantly by employing efficient decompositions to construct low-rank tensor-train representations, thus mitigating the curse of dimensionality. In order to compute also higher quantum states, we introduce an approach that directly incorporates the Wielandt deflation technique into the alternating linear scheme for the solution of eigenproblems. Besides systems with coupled excitons and phonons, we also investigate uncoupled problems for which (semi-)analytical results exist. There, we find that in the case of homogeneous systems, the tensor-train ranks of state vectors only marginally depend on the chain length, which results in a linear growth of the storage consumption. However, the central processing unit time increases slightly faster with the chain length than the storage consumption because the alternating linear scheme adopted in our work requires more iterations to achieve convergence for longer chains and a given rank. Finally, we demonstrate that the tensor-train approach to the quantum treatment of coupled excitons and phonons makes it possible to directly tackle the phenomenon of mutual self-trapping. We are able to confirm the main results of the Davydov theory, i.e., the dependence of the wave packet width and the corresponding stabilization energy on the exciton-phonon coupling strength, although only for a certain range of that parameter. In future work, our approach will allow calculations also beyond the validity regime of that theory and/or beyond the restrictions of the Fröhlich-Holstein type Hamiltonians.

Perspectiva teórica e histórica da resolução de problemas no ensino de matemática nos anos iniciais

Esta pesquisa constitui parte da Tese de Doutorado em Educação, intitulada “Concepções de Professores sobre a Resolução de Problemas, vinculada institucionalmente ao Programa de Pós-Graduação em Educação (PPGED) pela Universidade Federal de Uberlândia (UFU). O estudo em questão buscou delinear o referencial histórico e teórico sobre a Resolução de Problemas (RP) enquanto uma metodologia, trazendo as principais teorias e também propor a RP a partir da perspectiva davydoviana. A abordagem metodológica foi a pesquisa qualitativa, com os desdobramentos da pesquisa teórica. Após a apresentação das principais teorias da RP, utilizamos a teoria de Davydov, que propõe um processo de ensino-aprendizagem-desenvolvimento dos conteúdos matemáticos pautado na atividade de estudo que marca a formação do pensamento teórico do estudante. A RP, na perspectiva de Davydov, é abordada na atividade de estudo do aluno, que, a partir das situações de dificuldade propostas pelo professor, se envolve com o resolver problemas no desenvolvimento das tarefas. A proposta de Davydov volta-se para a apropriação dos conteúdos matemáticos e o desenvolvimento da RP é fundamentado em aspectos científicos validados para o desenvolvimento do sujeito. A perspectiva de Davydov diverge das outras teorias da RP, por apresentar a preocupação com a apropriação dos conceitos e a formação do pensamento teórico. Elucidamos que a RP no âmbito desta pesquisa, antes de qualquer ação, prioriza a trajetória que é percorrida antes e durante a resolução do problema, visto que essa linha recorre aos conteúdos e aos fundamentos científicos, o que realmente importa para a formação dos estudantes.

Intermediate filaments in the retinal Müller cells as natural light energy guides

In the current study, we investigated transmission spectrum of the intermediate filaments (IFs) extracted from porcine retinal Müller cells (MC). The recorded transmission spectrum is quite similar to that of the entire guinea pig retina, providing direct proof that the quantum mechanism (QM) of light energy transmission through the inverted retina is in fact the main mechanism determining the high-contrast vision of the vertebrate eyes. The recorded transmission spectrum of the IFs was deconvoluted into four bands, which we assign to different types of IFs. We interpret the differences in the transmission band shape and maxima as differences in the effective electron mass, dependent on the IF structure and composition of its constituting proteins. We analyzed model systems containing IFs and dye molecules, and IFs bridging two adjacent cobalt nanofilms on a substrate. The respective results demonstrate that IFs function as waveguides transferring energy from an energy donor and to an energy acceptor, by way of the exchange mechanism. The presently reported results provide direct experimental confirmation of the earlier proposed quantum mechanism for the high-contrast vision of vertebrate eyes. The mechanism proposed in the current study may be generalized, providing a consistent alternative to Davydov's theory of vibrational solitons in enzymes.

Didática desenvolvimental e políticas educacionais para a escola no Brasil

O artigo apresenta a concepção de didática desenvolvimental e discute sua relevância para as práticas de ensino-aprendizagem no contexto brasileiro. A didática desenvolvimental pode constituir-se como referência aos educadores brasileiros para práticas de ensino em contraposição ao modelo de educação escolar baseado em resultados. Inicia-se fazendo referência à constituição e implantação do Sistema de Ensino Elkonin-Davydov na Rússia e em seguida é feita a exposição da teoria de Davydov, em especial seus princípios e elementos que fundamentam uma didática desenvolvimental. Por fim, são apontadas as contribuições da didática desenvolvimental para as práticas de ensino-aprendizagem na educação escolar brasileira em face das políticas educacionais neoliberais em curso no país.

Whatever happened to process theories of learning?

Abstract The article examines strengths and limitations of three examples of well known post-behaviorist process theories of learning: Norman and Rumelhart, Kolb, and Nonaka and Takeuchi. Two central shortcomings are found in these theories, namely universalism and separation of learning from instruction. After that the article analyzes Davydov's theory of learning activity and Engestrom's theory of expansive learning as process theories that may significantly enrich the current landscape of learning theory and research. The strength of the two cultural–historical theories is in their rejection of universalism. The theory of expansive learning also attempts to bring learning and instruction into a dialectical relationship. The conclusion is that in order to revitalize theorizing of learning processes, researchers need to give up explicit and implicit universalism and recognize the intimate relationship between learning and instruction and the gap between them as a source of creative deviation and agency.

THE EFFECTS OF DAMPING AND TEMPERATURE OF MEDIUM ON THE SOLITON EXCITED IN α-HELIX PROTEIN MOLECULES WITH THREE CHANNELS

We studied numerically the influences of damping and temperature of medium on the properties of the soliton transported bio-energy in the α-helix protein molecules with three channels by using the dynamic equations in the improved Davydov theory and fourth-order Runge–Kutta method. From the simulation experiments, we see that the new solitons can move along the molecular chains without dispersion at a constant speed, in which the shape and energy of the soliton can remain in the cases of motion, whether short-time at T=0 or long time at T=300 K. In these motions, the soliton can travel over about 700 amino acid residues, thus its lifetime is, at least, 120 ps at 300 K. When the two solitons undergo a collision, they can also retain themselves forms to transport towards. These results are consistent with the analytic result obtained by quantum perturbed theory in this model. However, the amplitudes of the solitons depress along with increase of temperature of the medium, and it begins to disperse at 320 K. In the meanwhile, the damping of the medium can influence the states and properties of the soliton excited in α-helix protein molecules. The investigation indicates that the amplitude and propagated velocity of the soliton decrease, when the damping of medium increases. The soliton is dispersed at the large damping coefficient Γ=4 Γ0 at 300 K. The results show that the soliton excited in the α-helix protein molecules with three channels is very robust against the damping and thermal perturbation of medium at biological temperature of 300 K. Thus we can conclude that the soliton can play important part in the bio-energy transport and the improved model is possibly a candidate for the mechanism of the energy transport in the α-helix proteins.

Comment on “Improvement of the Davydov theory of bioenergy transport in protein molecular systems”

The validity of the recently proposed tentative improvement of the Davydov theory of intramolecular vibrational transfer is discussed. It is shown that it contains a few principal shortcomings and cannot be a sound ground for studies of the transport processes in molecular systems.

States and properties of the soliton transported bio-energy in nonuniform protein molecules at physiological temperature

We have numerically studied states and properties of the soliton transported bio-energy at physiological temperature 300 K by the Runge–Kutta way and dynamic equations in the improved Davydov theory. We proved that the new solitons can move without dispersion retaining its shape and energy in both uniform and nonuniform protein molecules. If considering further effect of thermal perturbation of heat bath on the soliton in the nonuniform proteins, it is still thermally stable at the biological temperature 300 K and in the longer times of 300 ps and larger spacings of 400 amino acids, which is consistent with the analytic result obtained by a quantum perturbed theory. These results exhibit that the new soliton is a possible carrier of the bio-energy transport and the improved model is possibly a candidate for the mechanism of this transport.

Stabilization of the Soliton Transported Bio-energy in Protein Molecules in the Improved Model**The project supported by National Natural Science Foundation of China under Grant No. 19974034

We study the stabilization of the soliton transported bio-energy by the dynamic equations in the improved Davydov theory from four aspects containing the feature of free motion and states of the soliton at the long-time motion and at biological temperature 300 K and behaviors of collision of the solitons by Runge–Kutta method and physical parameter values appropriate to the α-helix protein molecules. We prove that the new solitons can move without dispersion at a constant speed retaining its shape and energy in free and long-time motions and can go through each other without scattering. If considering further influence of the temperature effect of heat bath on the soliton, it is still thermally stable at biological temperature 300 K and in a time as long as 300 ps and amino acid spacings as large as 400, which shows that the lifetime of the new soliton is at least 300 ps, which is consistent with analytic result obtained by quantum perturbation theory. These results exhibit that the new soliton is a possible carrier of bio-energy transport and the improved model is possibly a candidate for the mechanism of this transport.

Comment on “Improvement of the Davydov theory of bioenergy transport in protein molecular systems”

It is shown that a certain wave function represents a two quanta state of the Davydov-Scott model, contrary to the claims of Pang. Furthermore, Pang's choice of wave function and derivation of equation of motions are criticized. Directions for future work in this area are indicated.

Distribution of Vibrational Energy Levels of Protein Molecular Chains**The project supported by National Natural Science Foundation of China (Grant No. 19774034)

The distributions of the quantum vibrational energy levels of the protein molecular chain are found by the discretely nonlinear Schrödinger equation appropriate to protein obtained from the Davydov theory. The results calculated by this method are basically consistent with the experimental values. Furthermore, the energy spectra at high excited states have also been obtained for the molecular chain which is helpful in researching the properties of infrared absorption and Raman scattering of the protein molecules.

Improvement of the Davydov theory of bioenergy transport in protein molecular systems

The Hamiltonian and the wave function in the Davydov theory have simultaneously been improved and extended, based on some physical and biological grounds and on results from other models. The equations of motion for the improved Davydov model with a quasicoherent two-quanta state and a new interaction term in the Hamiltonian describe bioenergy transport along the molecular chains in protein molecules by a soliton mechanism. Some elementary properties of the soliton, including the nonlinear coupling energy and greatly increased binding energy of the soliton, are also given. The results obtained suggest that the model could be a candidate for a bioenergy transport mechanism in protein molecules.

The role of solitons in charge and energy transfer in 1D molecular chains

The idea that polarons and solitons could play the crucial role in the transport processes in biological structures, has been critically reexamined on the basis of the general theory of self-trapping phenomena. The criteria which enable one to determine conditions for the existence and stability of polarons and solitons and to determine their character, in dependence of the values of the basic physical parameters of the system, were formulated. Validity of the so-called Davydov's soliton model was discussed on the basis of these criteria. It was found that the original Davydov's proposal, based upon the idea of the soliton creation due to the single excitation (particle, vibron, etc.) self-trapping, cannot explain the intramolecular energy transfer in α-helix and acetanilide. However, Davydov theory is flexible enough to describe the single electron transfer in some systems (α-helix and acetanilide for example). In the many-particle systems, dressing effect, due to the quantum nature of phonons, may cause the creation of the bound states of the several excitons in the molecular chain. The possibility of creation of the soliton states of this type is discussed for the simple Fröhlich's one-dimensional model. The regions of the system parameter space where different mechanisms dominate the behaviour of such entities are characterized.

Superconductivity and Temperature Effects on Davydov Model of α-Helix Protein**The project supported by National Natural Science Foundation of China

We study the thermodynamic properties of α-helix protein on the basis of Davydov theory. The Hamiltonian of Davydov theory can be represented as a form of pairing Hamiltonian in the momentum space. We prove that the quasi-classical Davydov theory is essentially a theory with Bose condensation no matter whether the molecular excitations are treated as fermions or bosons. The transition temperature of superconductivity theory gives the existence condition of the Davydov soliton.

On the relevance of self-trapping as the mechanism for charge and energy transfer in biological systems

The concept that polarons and solitons may play a crucial role as the underlying transport agents in biological structures has been critically re-examined on the basis of the general theory of self-trapping (ST) phenomena. The conditions determining the existence and stability of polarons and solitons, and their character as a function of the values of the basic physical parameters of the system, were formulated. It was found that Davydov's soliton model cannot explain the intramolecular energy transfer in the α-helix and acetanilide, and an alternative formulation in terms of the so-called Takeno model is more realistic. However, Davydov's theory is sufficiently flexible to describe electron transfer in the α-helix and acetanilide.

Exciton self-trapping in the Ginzburg–Landau framework

In this paper we reformulate the Davydov theory for exciton self-trapping in the Ginzburg–Landau language of phase transitions. In the parameter range of the Davydov system, where both the nonlinearity–and the dipole–dipole coupling parameters are positive, explicit expressions for the wave-function and energy per pulse, are derived for all possible extended elliptic wave solutions. The corresponding partition function, free energy and specific heat are calculated numerically. It is shown that for small proteins, and at physiological temperatures, these extended waves may play a role thermodynamically.

Quantum-Mechanical Method for the Soliton Transported Bio-energy in Protein

The equations of motion of the soliton transported bio-energy in the protein, were heretofore already obtained by a combination of quantum-mechanical and classical methods, but here have been derived based completely on quantum mechanics. And we point out the shortcoming of no self-consistency of the Davydov theory. Some interesting results have also been got.

Quantum and temperature effects on Davydov soliton dynamics. IV. Lattice with a thermal phonon distribution

For pt.III see ibid. vol.5, p.823 (1993). The author derives equations of motion for a new model to introduce temperature effects into Davydov's mod D1) theory for solitons in proteins. The temperature model used so far suffers from conceptual difficulties, although it can reproduce exact quantum Monte Carlo (QMC) results qualitatively correctly as was shown previously. In their model they populate the lattice with a thermal phonon distribution and derive equations of motion in the presence of these thermal phonons, instead of deriving equations of motion from a thermally averaged Hamiltonian as in Davydov's theory. This procedure seems to be more reliable than Davydov's averaged Hamiltonian approach. For derivation of the equations of motion the Euler-Lagrange method is used. Numerical applications to soliton dynamics at 300 K are reported and comparisons of the results obtained with available exact QMC data are discussed. It is found that Davydov's method agrees better with the QMC results than does the newly derived method, although the latter method seems to be physically more reliable.