On the Small Squaring and Commutativity

Let G be a group and let k > 2 be an integer, such that (k²– 3)(k – 1) < |G|/15 if G is finite. Supposethat the condition |A²| k(k + 1)/2 + (k – 3)/2 is satisfiedby every it-element subset A G. Then G is abelian. The proofuses the structure of quasi-invariant sets.     

An elementary model for fast detonations in tubular charges

The paper is concerned with the experimentally known phenomenon that the detonation velocity of a tubular charge may markedly exceed that of a homogeneous charge of the same explosive. It is shown that the effect may be successfully reproduced using a simple quasi-one-dimensional two-layer model assuming the gas–solid system to be isothermal and the volumetric fraction of the solid phase to be small. In view of a considerable drop of the burned gas pressure/density, compared to the Chapman–Jouguet case, fast detonation may be perceived as a variety of weak (undercompressed) detonation.     

Measurement of the power density of electromagnetic radiation by the method of microwave nonstationary spectroscopy

We present a new method for measurement of the microwave power based on the analysis of transient signals of gas molecules. These signals arise due to the phase switch of microwave radiation, which interacts with molecular rotational transition with frequency equal to that of the radiation. The method allows one to measure the amplitude of radiation via determination of the Rabi frequency. This approach is especially preferable in the submillimeter wavelength range.     

Precursors in two-phase detonation: An elementary model for the channel effect

The paper is concerned with the channel effect: detonation-propelled shocks occurring in tubular charges. It is shown that some salient aspects of the phenomenon may be successfully reproduced within a simple one-dimensional model assuming the gas–solid system to be isothermal and the volume fraction of the solid phase to be small. Two modes of the channel effect, dependent on the level of the ignition pressure, are identified. Although the emerging detonations appear to be of the Chapman–Jouguet (CJ) type, their velocities are controlled by the system’s gasification kinetics rather than its thermodynamics. The structure of the emerging CJ detonation differs from that of conventional ZND detonation. There is no shock attached to the reaction zone. The precursor shock is the only shock in the event.     

Mechanisms of melt droplets and solid-particle ejection from a target surface by pulsed laser action

We suggest an explanation of the effect of melt droplets and solid particle ejection from a target surface under the impact of laser radiation with intensity 10⁸–10¹⁰ W/cm². We consider the capillary wave instabilities on the evaporating surface of melt, which lead to growth of large-scale surface structures and ejection of macroparticles. The instability increments and characteristic droplet sizes are determined. Conditions are found for droplet-free evaporation in terms of the dynamic pressure of evaporated matter.     

Fingering Instability in Water-Oil Displacement

Following the classical Buckley–Leverett theory for the two-phase immiscible flows in porous media a non-linear evolution equation for the water-oil displacement front is formulated and studied numerically. The numerical simulations yield a physically plausible picture of the fingering instability known to develop in water-oil systems. A way to control the unrestricted growth of fingers is discussed. Distinctions and similarities with dynamically related Saffman–Taylor and Darrieus–Landau problems are outlined.     

Precursors in two-phase detonation: Occurrence of a contact discontinuity

This paper is concerned with detonation-propelled shocks (precursors) occurring in gas-permeable charges. It is shown that the basic aspects of the event may successfully be reproduced within a one-dimensional two-phase picture widely employed in the modelling of porous energetic materials. Precursor shocks are sustained by intense gasification of the solid phase, provided the ignition pressure (P_ign) exceeds a certain critical level. At high enough P_ign, the post-shock flow is found to acquire a contact discontinuity. Although this pattern is compatible with the associated self-similar solution, the question of the mechanism governing its formation remains open.     

Structure of quasi-invariant sets

The content of this paper corresponds to a part of the author's Ph.D. thesis research carried out in Tel-Aviv University under the supervision of Prof. G. Freiman and Prof. M. Herzog.