In Memory of G. S. Gorelik

S. M. Rytov

On June 27, 1957, an accident cut short the life of Gabriel Semenovich Gorelik, one of the most outstanding Soviet physicists, widely known for his research in the theory of oscillations, radiophysics, optics, and acoustics, as well as for his many years of brilliant pedagogical activity.

G. S. Gorelik was born on December 8, 1906, in Paris, where his father, forced to leave Russia in order to obtain a higher education, was then studying at the university. Later, G. S. Gorelik’s father, having graduated from a medical institute in Geneva, returned to his homeland in 1917 and, throughout the civil war, served as a physician in the ranks of the Red Army. After demobilization (in 1921) he summoned to him his family, which until then had been living in Geneva on an allowance from the Soviet Red Cross. In Geneva G. S. Gorelik completed three grades of secondary school. After moving to Moscow he began to prepare independently for admission to an institution of higher education and, at the same time, having a perfect command of French, supported the family as a translator. In 1923 G. S. Gorelik entered the Faculty of Physics and Mathematics of Moscow State University.

Very soon G. S. Gorelik’s interest in physics became clear. For some time he studied in the faculty in the specialty of electrical measurements, but, attracted by the lectures and seminars of L. I. Mandelstam, who headed the specialty of theoretical physics, he transferred to that specialty and graduated from the university in it in 1929. Even before completing the university, G. S. Gorelik was assigned as a trainee to the All-Union Electrotechnical Institute. Working on a topic proposed to him by B. A. Vvedenskii, he carried out there (together with G. Gints) his first, mainly experimental, scientific investigation, devoted to the superregenerative receiver. Meter and decimeter radio waves were then the “front line” of radio engineering, and the superregenerator was the most advanced receiver for this range. In the crudest approximation it is a circuit whose damping periodically oscillates about the zero value. This interpretation made it possible to explain the phenomenon of “multiple resonance” observed under the action of an external harmonic electromotive force.

G. S. Gorelik’s outstanding abilities attracted the attention of L. I. Mandelstam. In 1930 G. S. Gorelik was enrolled in postgraduate study at the Research Institute of Physics of Moscow State University, which he completed under the supervision of L. I. Mandelstam. The topic of his candidate dissertation was the question of the action of an external force on linear systems with periodically varying parameters. In such a broad formulation this question was a natural generalization of the concrete problem of the superregenerative receiver, more precisely, of those aspects of this problem for which

nonlinearity of the system does not play a fundamental role. Several guiding remarks by L. I. Mandelstam opened before G. S. Gorelik the enticing prospect of a new and profound rethinking of the whole spectral approach of the classical theory of oscillations. He carried out this task not as a student, but as a mature scientist, giving in his work a general theory of nonautonomous parametric systems, generalizing the concepts of resonance, selectivity, and detuning.

The customary notion of the special role of harmonic oscillations, connected with the selective properties of linear systems with constant parameters, had become so firmly rooted that it had come to seem something a priori, following from some inherent “simplicity” of the harmonic functions themselves. In his dissertation G. S. Gorelik showed that systems with periodically varying parameters, which include ordinary systems with constant parameters as a very special case, possess far more varied and interesting properties. For them the “simple” oscillations are no longer harmonic ones, but other periodic processes described by Hill functions. It is precisely with these that such systems resonate; they single them out from the composition of the external force, which therefore proves mathematically expedient to represent in the form of an expansion not in harmonic functions, but in Hill functions. At the same time, the variable parameters substantially enrich the possibilities for varying the system itself. If the “detuning” of a harmonic system consists in changing the values of one or several of its parameters, then the “detuning” of a parametric system is in the general case effected by changing the form of those functions of time which describe the modulation of the system parameters. Thus, for “escape from resonance” a functional space is opened here, and not the ordinary parameter space. The periodic change of parameters already in itself means the nonautonomy of the system and may lead to its regeneration and even excitation (parametric resonance). In parallel, the resonance properties of the system with respect to the external force also change, revealing here too a great diversity of possibilities, comprehensively investigated by G. S. Gorelik. The results he obtained were so valuable and significant that, on the basis of the defense of his dissertation in November 1934, the Physics Faculty of Moscow State University awarded him the degree of Doctor of Physico-Mathematical Sciences, and the Higher Attestation Commission of the People’s Commissariat for Education approved this decision.

G. S. Gorelik began his teaching activity simultaneously with his postgraduate studies, in 1930. For several years (1934–1938) he lectured on the theory of oscillations, took part in conducting L. I. Mandelstam’s seminars, and supervised diploma students and postgraduate students, three of whom successfully defended their candidate dissertations during this period. In 1935 the Higher Attestation Commission awarded G. S. Gorelik the title of professor in the Department of the Physics of Oscillations. Both in his student years and later as a lecturer and then professor at Moscow State University, G. S. Gorelik did not confine himself to a circle of purely scientific interests. He took the liveliest and most direct part in the public life of the institute and the faculty, in organizational and methodological work. He was, in particular, one of the organizers of the All-Union Conference on Oscillations in 1931.

During his work at Moscow State University, in addition to his dissertation, G. S. Gorelik carried out seven more scientific investigations on questions of the theory of oscillations. Among them special mention should be made of the study, conducted jointly with A. A. Vitt, of parametrically coupled oscillatory systems (1933), in which the very concept of parametric coupling was introduced for the first time; this concept was subsequently applied by G. S. Gorelik to acoustic waves (1935), as well as a work generalizing the method of the small parameter to nonli—

linear systems close to linear systems with periodically varying parameters (1938). In general, this entire first period of his scientific work was permeated by an interest in parametric systems. Having begun while still a student with the investigation of a superregenerator, G. S. Gorelik subsequently thought through in depth and developed the whole complex of questions connected with the periodic variation of parameters. This gave him grounds once again, already on the basis of the general theory he had developed, to return to the phenomena of resonance in a superregenerative receiver (1939).

From 1935 to 1937, at the invitation of A. A. Andronov, G. S. Gorelik regularly visited the city of Gorky for scientific consultations at the Gorky Research Physico-Technical Institute (GIFTI). In those same years a number of very serious events occurred in his personal life. In 1936, as the result of a severe heart disease, his wife, E. M. Galikhina, died, leaving him with a small son, Andrei. A. A. Andronov insistently called G. S. Gorelik to Gorky, where he was already known not only for his works but also personally. At the beginning of 1938 G. S. Gorelik accepted the proposal of Gorky State University (GGU) to take there the position of professor, head of the chair of general physics, moved to Gorky and, together with his family—his second wife, N. K. Kozhina, and his son—lived there until 1953.

The fifteen years spent in the city of Gorky were filled with intensive work, which led G. S. Gorelik to new scientific achievements and to the maturity of his pedagogical mastery. Meetings with Academician L. I. Mandelstam became, although richer in content, much rarer. On the other hand, G. S. Gorelik acquired constant contact and friendship with a remarkable person and scientist, A. A. Andronov, and this played a great and beneficial role in his work and life.

More than twenty scientific works of G. S. Gorelik on various questions of the theory of oscillations, magnetism, the theory of automatic control, radiophysics, and optics belong to the Gorky period. Before the Great Patriotic War he published only three works [including one on delayed feedback (1933) and one on phase selection in parametric systems (1941)], since initially he devoted a large part of his efforts to creating a course of general physics. This course was very far from what is usually understood as a good standard university course, and constituted a work of pedagogical art quite exceptional in the depth of its approach and the originality of its form.

G. S. Gorelik did not separate “established” physics from what students would “learn later,” in special courses, i.e. from the most pressing physical problems of the present day. On the contrary, he strove for the “classics” in his lectures to be intertwined with modernity just as it is in reality, without any artificial boundary intended only to lighten the lecturer’s task. At the same time he achieved a sharp captivating quality of exposition; he gave not merely a qualified retelling of the facts, theories, and history of physics, but knew how to strike the listeners’ imagination and kindle their interest. In this respect G. S. Gorelik’s lectures continued and developed the remarkable traditions of teaching of L. I. Mandelstam. G. S. Gorelik’s course instilled in students the need and the skill for independent physical thinking, gave them a genuine, deep understanding of physical phenomena and theories. Parts of this course were published at various times.*)

*) “Inertial and Non-inertial Systems in Mechanics” and “Lectures on Optics,” GGU Press, 1941; (jointly with A. G. Lyubina) “Thermodynamics and Molecular Physics” in Course of Physics, ed. N. D. Papaleksi, vol. I, Gostekhizdat, 1948.

and received a deservedly high appraisal from the scientific and teaching community. There is every reason to speak of a special, Gorelik style of teaching physics in higher education—a style that still calls for thoughtful analysis.

Perhaps the best explanation of this assertion, which cannot be developed within the limits of this brief article, is the following short quotation from G. S. Gorelik’s introductory lecture to the course “Electricity,” delivered by him in the 1956/57 academic year.

“The material from which I must draw is colossal, immense. The lecturer’s first task is to select and ruthlessly discard. One might try to compile a card index of all the facts and quantitative relations, arrange them according to degree of importance, and select, in descending order of importance, what can be fitted into 30 lectures. But such an approach is ambiguous and unreasonable. Therefore I set myself the task of constructing a course of electricity*) as follows.

Given is an audience of second-year students, consisting entirely of intelligent, inquisitive, thinking young people who do a great deal of independent work (the conditions of any problem are an idealization of reality...). How can I be of the greatest use to them?

Such a problem, it seems to me, has an unambiguous answer.

Allow me to begin with a small digression.

In order to become a physicist, one must live through a great deal; one must experience certain fundamental ideas with the intensity with which a person experiences what is most important and personally concerns him, with the intensity with which, in particular, you will experience your personal achievements in science, your own discoveries, great ones (if you have them) or small ones.”

And then there followed a preliminary, but masterly, account of the fundamental ideas of the electromagnetic theory of Faraday—Maxwell—Hertz and of that revolution in physics which is connected with these ideas.

G. S. Gorelik’s pedagogical talent was manifested not only in his lectures, but also in his supervision of students and graduate students, in his ability to cultivate scientific workers and to create friendly scientific collectives. During his work in the city of Gorky, where, in addition to heading a department at Gorky State University, he headed the radio-physics division at GIFTI (from 1942), nine candidate dissertations were defended under his supervision. A large group of talented young researchers—his co-workers and pupils—was formed, working together with him on varied and interesting problems.

During the years of the Great Patriotic War G. S. Gorelik carried out important assignments for special design bureaus working at that time in the city of Gorky. In particular, together with his co-workers he conducted a cycle of studies of alloys of high magnetic permeability, which made it possible to create a magnetometer of a new type, possessing a number of advantages. These investigations gave impetus to further work in the field of magnetism, which yielded many interesting results concerning magnetic transformation spectra and statistical phenomena in the remagnetization of ferromagnets.

In the postwar years G. S. Gorelik also took some part in a new stage in the development of the theory of nonlinear oscillations, connected with the achievements of A. A. Andronov and A. G. Maier in the development of the method of point transformations and its applications to problems of the theory of automatic regulation. This participation was expressed in three works. Together with

*) A term as yet rarely used, notes G. S. Gorelik, but shorter and of the same type as mechanics.

With A. A. Andronov he constructed an extremely elegant “ferroresonance” theory of acceleration (“resonance”) of a relativistic particle in a cyclotron (1945). This topic was suggested by the widely known successes in the acceleration of charged particles achieved at the P. N. Lebedev Physical Institute of the Academy of Sciences of the USSR, where for several years G. S. Gorelik and A. A. Andronov worked concurrently as senior researchers of the Oscillations Laboratory. Further, together with A. A. Andronov and N. N. Bautin, G. S. Gorelik wrote two papers on automatic control: on self-oscillations of a system containing an aircraft propeller with automatically varying pitch (1945), and on the theory of indirect control taking into account dry friction in the sensing element (1946). Somewhat later G. S. Gorelik, together with A. A. Andronov, began preparing a monograph on nonlinear oscillations and the general dynamics of machines and wrote his part of the monograph, but as a whole this work was not destined to be completed because of A. A. Andronov’s untimely death.

Undoubtedly, the profound ideas of A. A. Andronov, on which the edifice of a new science—the general dynamics of machines—was being built, keenly attracted G. S. Gorelik; but in these ideas, as in the theory of oscillations in general, what predominated was that side of physical theory which deals with the mathematical expression of the laws governing physical phenomena. G. S. Gorelik was always closer to another side of physical theory—the one that connects theoretical concepts with real phenomena. Of course, such a characterization of the direction of his scientific interests is just as schematic as the very singling out of the two indicated sides in physical theory, outlined by L. I. Mandelstam precisely with such a reservation*). And yet, reflecting on G. S. Gorelik’s scientific work, one cannot fail to recognize that the mathematical ideas of the theory of oscillations never became dominant in it. At the center of his scientific interests there always remained the extension of the oscillatory approach to phenomena far beyond the usual range of applications of the theory of oscillations. This characteristic feature of his gift permeates the above-mentioned works on magnetism as well, and the method he proposed for determining the rate of energy exchange between the degrees of freedom of gas molecules (1946), and the idea he advanced of demodulation analysis of light (1947), which anticipated the appearance of analogous considerations in the American literature.

The following years led to an even more vivid and fruitful development of this tendency of his thought; moreover, a variety of statistical questions quite naturally entered the circle of his interests, greatly aided by the work on fluctuations in self-oscillatory systems (I. L. Bershtein) begun at GIFTI even before the war under the direction of A. A. Andronov. As a result G. S. Gorelik created his own original line of work, which may be characterized as the study of the properties of matter and radiation by oscillatory, primarily radiophysical, methods.

This line was most vividly and engagingly outlined by him himself in the report “Nonlinear Oscillations, Interference, and Fluctuations” (1949), which he delivered at a meeting of the Scientific Council of FIAN devoted to the memory of L. I. Mandelstam. Summarizing the investigations of the nonmonochromaticity of a tube generator carried out by I. L. Bershtein and his own contribution to this problem**), he advanced in this

*) See L. I. Mandelstam, Complete Collected Works, vol. V, Publishing House of the Academy of Sciences of the USSR, 1950, p. 349.

**) It was precisely G. S. Gorelik who made the clear distinction between the concepts of the natural and technical linewidth of a self-oscillator and introduced these terms themselves (published in 1950).

reported a number of interesting and unexpected ideas concerning applications of I. L. Berstein’s phase-measuring method. The realization of these ideas constituted a significant part of the subsequent scientific activity of G. S. Gorelik, his collaborators, and his students. These include the transfer of Sagnac’s vortex experiment into the radio range, the application of the modulation method in optical interferometry, the measurement of amplitudes of mechanical oscillations that are very small in comparison with the wavelength of light, the measurement of small angular diameters of light sources (first of all, stars), and a number of other applications of “fine phasometry.”

Alongside this fruitful and vivid research activity, the last years spent by G. S. Gorelik in Gorky were, as always, filled with persistent work in a whole series of other directions.

The material and experience he had accumulated in the course of teaching were used by him in his remarkable book Oscillations and Waves (an introduction to acoustics, radiophysics, and optics), which he pondered and worked on for several years. This book, published in 1950, is an outstanding work in our physics literature, wholly original in conception and execution. This is attested also by the numerous reviews sent to G. S. Gorelik, both by individual scientists and by entire groups. In particular, the conclusion of a conference held to discuss this book at the N. E. Zhukovsky Air Force Academy states: “This is perhaps the only book in which a very broad range of questions is considered from a unified physical point of view. On the one hand, it is accessible to students; on the other, it is sufficiently profound, interesting, and serious to captivate the student... All who spoke recognized your book as very interesting, very necessary, and valuable. It is widely used in their practice by teachers; they often find in it new and interesting ideas, which are fruitfully refracted in their practical activity.”

G. S. Gorelik was one of the most active organizers of the radiophysics faculty of Gorky State University, where he subsequently directed the specialization in radiophysics and created a new course in statistical radiophysics. As a member of the Society for the Dissemination of Political and Scientific Knowledge, he repeatedly delivered popular lectures at Gorky factories, and in 1952–1953 headed the city section of the Society. He devoted much effort to work in scientific popularization. His articles devoted to the life and work of our greatest scientists—L. I. Mandelstam, N. D. Papaleksi, A. A. Andronov—like, indeed, everything that came from his pen, are genuinely artistic works. He possessed true literary talent, his own distinctive, refined style, and the ability to clothe his thoughts in brilliant literary form.

In June 1953 G. S. Gorelik was elected by competition as professor and head of the Department of General Physics at the Moscow Institute of Physics and Technology (MIPT). By the beginning of the academic year the Ministry of Culture transferred him from Gorky State University to MIPT, and he moved from Gorky to Moscow. Soon he took upon himself, in addition to heading the department, also the duties of dean of the radiophysics faculty. Under G. S. Gorelik’s direction, research work at MIPT was conducted by assistant N. N. Kolachevsky and graduate students S. M. Kozel (these two moved from Gorky), L. A. Pep, and P. A. Pereshetnik. N. N. Kolachevsky studied the noises of cyclic remagnetization of ferromagnets, while S. M. Kozel developed the theory of a modulation optical interferometer intended for measuring the angular diameters of stars,

IN MEMORY OF G. S. GORELIK

and brought its development to a working model. This work constituted the candidate dissertation of S. M. Kozel, which he defended with great success two days before the death of his supervisor.

In addition to his work at MIPT, G. S. Gorelik, from the very founding of the Institute of Radio Engineering and Electronics of the Academy of Sciences of the USSR (IREAS), was appointed a member of the Institute’s Academic Council (in December 1953), and then head of the statistical radiophysics laboratory organized by him. A new stage of his activity began.

While lecturing on general physics at MIPT, G. S. Gorelik still did not confine himself to repeating a course he had thought through many times. Each time he again began to lecture on one or another part of the general physics course, he fundamentally reworked his lectures. This is what he did in Gorky, and he continued to work on the lectures in the same way in Moscow. Here he was especially absorbed by the search for a new approach to the section “Electricity,” that part of the course whose previous presentations satisfied him least of all and, in his opinion, required a radical revision. This great work is reflected in the existing notes: from year to year (from the 1954/55 to the 1956/57 academic years) he subjected the section “Electricity” to a thorough reworking.

G. S. Gorelik considered it fundamentally wrong to begin the exposition of “Electricity” with electrostatics, i.e., with matters most remote from the everyday experience of students and by no means simpler or more comprehensible than the flow of electrons in a vacuum. At the same time, he disliked the somewhat amateurish manner adopted in R. Pohl’s textbook. In his final version G. S. Gorelik formulated the task of the lectures on “Electricity” as follows. First, they had to enable the audience to become aware of (“live through”) the discovery of the electromagnetic field as a revolution in natural science. Second, from the very beginning they had to equip students for work in a modern electrical laboratory. The lectures begin with the introduction of the concepts of voltage and current (for which an electronic oscilloscope is used at once), then there follows a natural transition to the study of two-terminal networks and their characteristics (impedance and its elements), the analysis of which then makes it possible to introduce the concepts of charge and field. There is no doubt that completion of the work on the section “Electricity” would have led G. S. Gorelik to a new exposition of it, as original and vivid as those he had achieved for thermodynamics, molecular physics, oscillations, and optics. He intended to prepare this course for publication and had already entered into negotiations on this matter with Gostekhizdat.

In addition to lecturing on the general physics course, G. S. Gorelik organized for senior students and graduate students of MIPT a seminar on statistical radiophysics, which he directed for a year.

G. S. Gorelik treated his duties as dean with the utmost seriousness. Numerous current affairs did not obscure for him the main questions of improving the organization of the radiophysics and radio-engineering faculties of MIPT, attracting major scientists to the Institute, organizing new specialties and departments, and raising the level of teaching and methodological work. In a short time he won the deep respect of the entire Institute staff, who had known him earlier as a major scientist, but now saw in him one of the most energetic, principled, and devoted workers.

At the department at MIPT and in the laboratory of IREAS, G. S. Gorelik undertook further scientific investigations, which proceeded in the direction that had previously interested him, but broadened in subject matter.

Alongside questions connected with fluctuations in self-oscillating systems, he became deeply interested in the scattering of waves by chaotic—

moving inhomogeneities, and more recently—self-oscillatory systems with delayed feedback, which had already attracted his attention in the past. In the development of these problems, the pressing tasks of the present day are closely intertwined with ideas that arose in the course of earlier investigations.

Modern measuring apparatus, including and perhaps first of all radio-engineering apparatus, is ever more broadly and more frequently approaching the fluctuation limit of sensitivity and accuracy. This fundamental limit was of lively interest to G. S. Gorelik—not only because its discovery in many cases reveals still existing great possibilities for further improvement of apparatus, but also because with it are connected the limits of applicability of ordinary determinations given to physical quantities, including length and intervals of time. Not long before his death G. S. Gorelik began to write for Uspekhi fizicheskikh nauk an article entitled “On the Fluctuation Limit of Accuracy in Chronometry and Interferometry,” the very subject of which speaks of a broad approach to this question.

In principle any self-oscillatory system may serve as a time meter. A tube generator of electrical oscillations can be used as a clock, and to an even greater extent a much more stable molecular generator. The question lies precisely in the magnitude of the fluctuation limit of measurement accuracy, which raises the task of detecting this limit in a real system that is not free from technical drifts caused by slow changes of its parameters. The ingenious method of I. L. Bershtein, which made it possible to solve this problem for ordinary tube generators and was successfully applied by V. S. Troitskii and V. V. Khrulev for measuring fluctuations of the klystron phase, proves to be practically unrealizable for a molecular generator. A theoretical analysis of the question, carried out in the laboratory of IREAN directed by G. S. Gorelik, made it possible to establish that technical drifts do not affect the “wings” of the spectral line of the generator and that the most suitable experimental method for revealing the fluctuation limit, when it is very small, is comparison of two independent generators.

Another feature of the molecular generator—its extremely small power—makes urgent the question of its use for stabilizing a more powerful system. Here it was shown that the best solution is given by the method of automatic tuning of a powerful generator to the molecular frequency. Since there was no satisfactory treatment of frequency and amplitude fluctuations in systems with automatic tuning, a corresponding theory was developed, taking into account the finite setting time of the discriminator. This last question—of how the fluctuations of the amplitude and phase of a quasi-monochromatic oscillation are transformed in passing through resonant systems—is also of independent interest. Its theory is given in one of G. S. Gorelik’s last works, done jointly with G. A. Elkin.

Having concentrated his attention on statistical problems of radiophysics, G. S. Gorelik showed here as well his masterly command of the oscillatory approach. It would seem that there is nothing in common between fluctuations in a generator and the scattering of radio waves by wandering inhomogeneities, apart from the radio-engineering origin of both problems. Nevertheless, in his very first article on scattering (1956) G. S. Gorelik revealed a far-reaching analogy between these phenomena. Of course, this point does not determine the principal significance of the article named. It became the starting point for a whole series of studies on the theory of scattering by chaotic-

MEMORY OF G. S. GORELIK

... moving discrete inhomogeneities (scatterers), carried out by G. S. Gorelik and his co-workers and extending the original (but leading) formulation of the question in various directions. The case of a statistical connection between the slowly varying translational velocities of the scatterers was considered; the influence of the rotation of the scatterers, when they possess anisotropy, was clarified; irradiation not by a monochromatic wave but by a signal having a discrete or continuous spectrum was investigated, including irradiation of a cloud of scatterers by stationary noise. Finally, a connection was established between the statistical characteristics of the scattered field and the theory of local turbulence of the atmosphere. Here lies one of the most interesting applications of this cycle of theoretical works, since use of the indicated connection gives a new method for studying atmospheric turbulence.

Systems with delayed feedback, which play a major role in a number of radio-engineering and other devices, had been considered in many works, but in doing so substantial simplifying assumptions were made. Linearization of the problem was allowed, or only a weak nonlinearity (this includes S. G. Gorelik’s work of 1939) was admitted; in the case of strong nonlinearity, dispersion in the linear element was not taken into account, or else the delay time was assumed to be small in comparison with the period. The general case of a strongly nonlinear system, in which dispersion may occur and the delay time is large in comparison with the time constants of the linear element and therefore plays an essential role, although it had been considered in some works of recent times, was considered with the introduction of suggestive physical arguments. At the initiative of G. S. Gorelik, members of his laboratory took part in work in which, for the case of a Z-characteristic of the nonlinear element, one of the co-authors (Yu. I. Neimark) gave a complete and rigorous theoretical solution of the problem, and also carried out some qualitative experiments.

It is hard to say what further development of the work in this direction in G. S. Gorelik’s hands might have led to: his special oscillatory intuition more than once led to unexpected prospects. As one more illustration of this, the following fact may be mentioned.

Having become interested, in connection with the super-long-distance propagation of ultrashort waves and wave scattering, in questions of turbulence, he began to study its theory. In one of the conversations he stated that turbulence, with its boundary of “self-excitation,” with the characteristic hysteresis of its appearance and disappearance upon increase and decrease of the velocity of the generating flow, with the primary role of nonlinearity for its developed (stationary) state—these are self-oscillations. Their specificity lies in the fact that these are self-oscillations in a continuous medium, i.e. in a system with an extraordinarily large number of degrees of freedom...

G. S. Gorelik always eagerly caught everything new; to the last day he was on the front-line positions of the rapidly advancing scientific front. A few days before his death he spoke at the Scientific Council of IREAN with a fervent and vividly argued appeal to develop work on molecular amplifiers in every way.

Among the other numerous works of G. S. Gorelik, carried out in addition to scientific research and teaching, mention should be made of his editing of L. I. Mandelstam’s lectures on oscillations, completed in 1954.

For outstanding services in the field of science and teaching, G. S. Gorelik was awarded the Order of the “Badge of Honor” (1944), the medal “For ...

...“For Valiant Labor in the Great Patriotic War” (1946) and the Order of the Red Banner of Labor (1951), which marked twenty years of his work in higher education.

G. S. Gorelik was a broadly educated person, possessing wide-ranging knowledge and interests. In his scientific work and in his teaching he was always driven by a passionate enthusiasm, which infected others and created around him a true scientific atmosphere. He knew how to teach without instructing and to educate without moralizing. He loved young people, and they responded to him in kind. His striving for truth and honesty knew no compromise either in life or in science. Falsehood and dishonesty aroused in him an organic revulsion. But, while making high demands both on himself and on others, he always remained a sensitive, caring, and responsive person.

A senseless accident carried him off in the prime of life, at a time of new and interesting undertakings. The distinctive features of his creative work—the freshness of his thought, the clarity and brilliance of his exposition, to some degree absorbed by his many pupils and close collaborators—must be continued and developed by them as one of the finest traditions of Soviet physics.

LIST OF WORKS BY G. S. GORELIK *)

1931

1. Investigation of a superregenerative receiver (preliminary communication, jointly with G. Ginzton). Vestnik Elektrotekhniki, No. 8, 267 (1931).
2. Investigation of a decimeter-wave generator (collective work under the signature “Collective of Decimeter Waves of VEI”). Vestnik Elektrotekhniki, No. 9, 297 (1931).
3. Über die Wirkung des Pendelrückkoplers (jointly with G. Ginzton). Zeitschr. für Hochfrequenztechnik, 38, 222 (1931).

1932

1. Investigation of discontinuous generation (jointly with V. Kuzovkin and E. Sekerskaya). Tekhnika radio i slabogo toka, No. 11, 629 (1932).
2. Investigation of a superregenerative meter-wave receiver (jointly with G. Ginzton). Tekhnika radio i slabogo toka, No. 12, 645 (1932).

1933

1. On the theory of the superregenerative receiver. ZhTF 3, 110 (1933).
2. Oscillations of a resilient pendulum as an example of two parametrically coupled linear systems (jointly with A. A. Witt). ZhTF 3, 294 (1933).
3. Résonance et stabilisation des électrons dans les tubes à vide. Phys. Zeitschr. der Sowjetunion, 4, 569 (1933).

1934

1. Resonance phenomena in systems with periodically varying parameters, I. ZhTF 4, 1783 (1934).

1935

1. Application of the Braun tube to the investigation of the motion of a representative point in the Van der Pol plane of variables (jointly with G. A. Bendrikov). ZhTF 5, 620 (1935).
2. Resonance phenomena in systems with periodically varying parameters. II. ZhTF 5, 495 (1935).
3. Resonance phenomena in systems with periodically varying parameters. III. ZhTF 5, 489 (1935).
4. Phénomènes de résonance dans les systèmes linéaires à paramètres périodiques. Techn. Phys. USSR 2, 135 (1935).
5. On parametric coupling between standing acoustic waves. ZhTF 5, 1436 (1935). Translated into French in Techn. Phys. USSR 2, 248 (1935).

*) This list does not include articles in abstracting journals and encyclopedias, popular articles, translations, editing, etc.

IN MEMORY OF G. S. GORELIK

1936

1. New research in the field of nonlinear oscillations. Moscow, State Publishing House for Problems of Radio, 1936, 96 pp. (with L. I. Mandelstam, N. D. Papaleksi, A. A. Andronov, A. A. Witt, and S. E. Khaikin).

1938

1. Oscillations of nonlinear systems close to linear systems with periodically varying parameters. ZhTF 8, 435 (1938). [Translated into French in Techn. Phys. USSR 5, 320 (1938).]

1939

1. Linear resonance phenomena in a superregenerative receiver. Elektrosvyaz’, No. 6, 29 (1939).

2. On the theory of delayed feedback. ZhTF 9, 450 (1939). [Translated into French in Journ. of Phys. USSR 1, 465 (1939).]

1941

1. Is sharp phase selection possible? ZhTF 11, 69 (1941). [Translated into French in Journ. of Phys. USSR 4, 57 (1941).]

2. Inertial and non-inertial frames of reference in mechanics (with A. G. Lyubina). Gorky State University Press, 1941.

3. Lectures on optics (with A. G. Lyubina). Gorky State University Press, 1941.

1944

1. On transverse magnetic permeability. DAN SSSR 43, 204 (1944).

2. On certain nonlinear phenomena occurring under the superposition of mutually perpendicular magnetic fields. Izv. AN SSSR (Physical Series) 8, 172 (1944).

3. On the change in the curves of longitudinal magnetization of a ferromagnetic wire under the action of a constant current flowing through it (with K. A. Gorodnaya and I. S. Zhukova). DAN SSSR 44, 257 (1944).

1945

1. Experimental study of the impedance of ferromagnetic wires (with I. I. Bershtein, G. N. Kuteinikov, A. G. Lyubina, K. A. Gorodnaya, and I. S. Zhukova). ZhTF 15, 505 (1945).

2. On resonance phenomena in the motion of a relativistic particle in a cyclotron (with A. A. Andronov). DAN SSSR 49, 664 (1945). [Brief exposition in French in C. R. 221, 696 (1946).]

3. Automatic tracking system containing an automatic variable-pitch screw (with A. A. Andronov and N. N. Bautin). DAN SSSR 47, 265 (1945).

4. L. I. Mandelstam and the doctrine of resonance. Izv. AN SSSR (Physical Series) 9, 61 (1945).

1946

1. On one possible method for studying the rate of energy exchange between the degrees of freedom of gas molecules. DAN SSSR 54, 783 (1946).

2. Theory of indirect regulation taking account of Coulomb friction in the sensitive element (with A. A. Andronov and N. N. Bautin). Avtomatika i Telemekhanika 7, 15 (1946).

1947

1. On the possibility of low-inertia photometry and demodulation analysis of light. DAN SSSR 58, 45 (1947).

2. L. I. Mandelstam and the teaching of physics. Izv. AN SSSR (Physical Series) 10, 135 (1947).

3. Radiophysics and the theory of automatic regulation. Izv. AN SSSR (Physical Series) 11, 103 (1947).

4. Some investigations in the theory of nonlinear oscillations carried out in the USSR beginning in 1935 (with N. D. Papaleksi, A. A. Andronov, and S. M. Rytov). UFN 33, 335 (1947).

1948

1. Some remarks on the style of scientific creativity of N. D. Papaleksi. Izv. AN SSSR (Physical Series) 12, 22 (1948).

2. On demodulation analysis of light. UFN 34, 321 (1948).

3. Interference, diffraction, spectral decomposition in optics and radio. UFN 36, 407 (1948).

4. Supplement to N. D. Papaleksi, “Leonid Isaakovich Mandelstam (a brief sketch of his life and scientific activity)” (with G. S. Lands-

berg, M. A. Leontovich, S. M. Rytov, and I. E. Tamm). Complete Collected Works of L. I. Mandelstam, vol. I, Publishing House of the Academy of Sciences of the USSR, 1948.
39. Thermodynamics and Molecular Physics. Part of the “Course of Physics,” ed. by N. D. Papaleksi, vol. I, Gostekhizdat, 1948.

1949

1. On the interpretation of the first law of thermodynamics. Vestn. Vyssh. Shkoly, No. 1, 21 (1949).

1950

1. On the question of the technical and natural linewidth of a tube generator. ZhETF 20, 351 (1950).
2. On certain magnetic transformation spectra. Izv. AN SSSR (physical series) 14, 174 (1950).
3. Nonlinear oscillations, interference, and fluctuations. Izv. AN SSSR (physical series) 14, 187 (1950).
4. Report of GIFTI for 1950 (together with a group of collaborators).
5. Oscillations and Waves. Introduction to Acoustics, Radiophysics, and Optics, Gostekhizdat, 1950, p. 551.

1951

1. Some applications of the second law of thermodynamics to electrical fluctuations. UFN 44, 34 (1951).
2. On the scientific works of Academician A. A. Andronov. Avtomatika i Telemekhanika 12, 195 (1951).

1952

1. On the application of the modulation method in optical interferometry. DAN SSSR 83, 549 (1952).
2. Investigation of oscillations very small in comparison with the wavelength of light by harmonic analysis of a modulated interference pattern (together with I. Ya. Brusin and S. A. Pikovsky). DAN SSSR 83, 553 (1952).
3. On the theory of the stellar Michelson interferometer (together with I. L. Berstein). DAN SSSR 86, 47 (1952).
4. Report of GIFTI for 1952 (together with a group of collaborators).

1953

1. In memory of A. A. Andronov. UFN 49, 449 (1953).
2. Works of Academician A. A. Andronov on the theory of automatic control. Report at the All-Union Conference on the Theory of Automatic Control. (Published in the collected proceedings of the Conference, vol. I, Publishing House of the Academy of Sciences of the USSR, 1955.)

1954

1. Statistical phenomena in a tube generator. Report read at the section of general radio engineering of the A. S. Popov Society (manuscript, 1954).

1955

1. Some microphasometric methods in radiophysics and optics. Izmer. tekhnika, No. 3, 10 (1955).
2. The life and works of A. A. Andronov. Collected articles in memory of A. A. Andronov, Publishing House of the Academy of Sciences of the USSR, 1955, pp. 3–19.
3. L. I. Mandelstam. Lectures on oscillations (editing of lecture notes). Publishing House of the Academy of Sciences of the USSR, 1955.

1956

1. On the theory of scattering of radio waves by wandering inhomogeneities. Radiotekhnika i elektronika 1, 695 (1956).
2. Heterodyne mixing of light (together with S. I. Borovitsky). UFN 59, 543 (1956).
3. On the scattering of nonmonochromatic radiation by wandering inhomogeneities (together with M. Yu. Gadzhiev and M. I. Rodak). Report of IREAN, 1956.

1957

1. On the transformation of fluctuations of the amplitude and phase of self-oscillations by resonant systems (together with G. A. Elkin). Radiotekhnika i elektronika 2, 28 (1957).
2. Frequency Modulation Noise in Oscillators (together with I. L. Berstein). Pr. Inst. Rad. Eng. 45, 94 (1957).
3. On the influence of correlation of scatterer velocities on the statistical properties of scattered radiation. Radiotekhnika i elektronika (in press).
4. On fluctuations of phase and amplitude in self-oscillating systems (theory and methods of measurement) (together with G. A. Elkin). Report at the XII General Assembly of URSI (manuscript).