Edward Bormashenko
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View article: Advanced Ramsey Dimensional Analysis
Advanced Ramsey Dimensional Analysis Open
We propose a Ramsey approach to the dimensional analysis of physical systems, which complements the seminal Buckingham theorem. Dimensionless constants describing a given physical system are represented as vertices of a graph, referred to …
View article: Probabilistic Measure of Symmetry Stability
Probabilistic Measure of Symmetry Stability Open
Symmetry is a fundamental principle in mathematics, physics, and biology, where it governs structure and invariance. Classical symmetry analysis focuses on exact group-theoretic descriptions, but rarely addresses how robust a symmetric con…
View article: Probabilistic Geometry Based on the Fuzzy Playfair Axiom
Probabilistic Geometry Based on the Fuzzy Playfair Axiom Open
A probabilistic version of geometry is introduced. The fifth postulate of Euclid (Playfair’s axiom) is adopted in the following probabilistic form: consider a line and a point not on the line—there is exactly one line through the point wit…
View article: Probabilistic Measure of Symmetry Stability
Probabilistic Measure of Symmetry Stability Open
Symmetry is a fundamental principle in mathematics, physics, and biology, where it governs structure and invariance. Classical symmetry analysis focuses on exact group-theoretic descriptions, but rarely addresses how robust a symmetric con…
View article: The Three-Body Problem: The Ramsey Approach and Symmetry Considerations in the Classical and Quantum Field Theories
The Three-Body Problem: The Ramsey Approach and Symmetry Considerations in the Classical and Quantum Field Theories Open
The graph theory-based approach to the three-body problem is introduced. Vectors of linear and angular momenta of the particles form the vertices of the graph. Scalar products of the vectors of the linear and angular momenta define the col…
View article: Probabilistic Geometry Based on the Fuzzy Playfair Axiom
Probabilistic Geometry Based on the Fuzzy Playfair Axiom Open
Probabilistic version of geometry is introduced. The fifth postulate of Euclid (Playfair’s axiom) is adopted in the following probabilistic form: consider a line and a point not an line, there is exactly one line through the point with pro…
View article: Symmetry Breaking: One-Point Theorem
Symmetry Breaking: One-Point Theorem Open
Symmetry breaking is crucial in many areas of physics, mathematics, biology, and engineering. We investigate the symmetry of regular convex polygons, non-convex regular polygons (stars), and symmetric Jordan curves/domains. We demonstrate …
View article: Negative Mass in the Systems Driven by Entropic Forces
Negative Mass in the Systems Driven by Entropic Forces Open
The paper addresses the phenomena of negative effective mass and negative effective density emerging in systems driven by entropic elastic forces. The elasticity of polymers is, at least partially, of entropic origin, and it represents the…
View article: Fuzzy Geometry
Fuzzy Geometry Open
Probabilistic version of geometry, labeled the “fuzzy” geometry, is introduced. The fifth postulate of Euclid (Playfair’s axiom) is adopted in the following probabilistic form: consider a line and a point not an line, there is exactly one …
View article: Negative Mass in the Systems Driven by Entropic Forces
Negative Mass in the Systems Driven by Entropic Forces Open
The paper addresses the phenomena of the negative effective mass and negative effective density emerging in the systems driven by the entropic elastic forces. The elasticity of polymers is, at least partially, of entropic origin, and it re…
View article: Breaking Symmetry. One Point Theorem
Breaking Symmetry. One Point Theorem Open
Breaking symmetry is crucial in many areas of physics, mathematics, biology and engineering. We address symmetry of regular convex polygons, non-convex regular polygons (stars) and symmetric Jordan curves/domains. We demonstrate that remov…
View article: Ramsey Approach to Vector Fields
Ramsey Approach to Vector Fields Open
Ramsey approach to the vectors fields is introduced. Set of vectors defined on R^3, taken as the generators of the bi-colored complete graph, is introduced. Vectors are considered as the vertices of the graph. Following coloring procedure …
View article: Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach
Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach Open
We introduce a synchronization procedure for clocks based on the Einstein–Landauer framework. Clocks are modeled as discrete, macroscopic devices operating at a thermal equilibrium temperature T. Synchronization is achieved by transmitting…
View article: Advanced Ramsey Dimensional Analysis
Advanced Ramsey Dimensional Analysis Open
We propose the Ramsey approach for the dimensional analysis of physical systems, which is complementary to the seminal Buckingham theorem. Dimensionless constants describing the given physical systems are seen as the vertices of the graph,…
View article: Landauer Principle and Einstein Synchronization of Clocks: the Ramsey Approach
Landauer Principle and Einstein Synchronization of Clocks: the Ramsey Approach Open
We introduce a synchronization procedure for clocks based on the Einstein–Landauer framework. Clocks are modeled as discrete, macroscopic devices operating at a thermal equilibrium temperature ?. Synchronization is achieved by transmitting…
View article: Negative Mass in the Systems Driven by Entropic Forces
Negative Mass in the Systems Driven by Entropic Forces Open
The paper addresses the phenomena of the negative effective mass and negative effective density emerging in the systems driven by the entropic elastic forces. The elasticity of polymers is, at least partially, of entropic origin, and it re…
View article: The Three-Body Problem: the Ramsey Approach and Symmetry Considerations in the Classical and Quantum Field Theories
The Three-Body Problem: the Ramsey Approach and Symmetry Considerations in the Classical and Quantum Field Theories Open
The graph theory based approach to the three-body problem is introduced. Vectors of linear and angular momenta of the particles form the vertices of the graph. Scalar products of the vectors of the linear and angular momenta define the col…
View article: Landauer Principle and Einstein Synchronization of Clocks: The Ramsey Approach
Landauer Principle and Einstein Synchronization of Clocks: The Ramsey Approach Open
We introduce a synchronization procedure for clocks based on the Einstein–Landauer framework. Clocks are modeled as discrete, macroscopic devices operating at a thermal equilibrium temperature
View article: Negative Mass in the Systems Driven by Entropic Forces
Negative Mass in the Systems Driven by Entropic Forces Open
The paper addresses the phenomena of the negative effective mass and negative effective density emerging in the systems driven by the entropic elastic forces. The elasticity of polymers is, at least partially, of entropic origin, and it re…
View article: Physical and Logical Synchronization of Clocks: The Ramsey Approach
Physical and Logical Synchronization of Clocks: The Ramsey Approach Open
Ramsey analysis is applied to the problem of the relativistic and quantum synchronization of clocks. Various protocols of synchronization are addressed. Einstein and Eddington special relativity synchronization procedures are considered, a…
View article: Landauer’s Principle: Past, Present and Future
Landauer’s Principle: Past, Present and Future Open
“Thermodynamics is only physical theory of universal content, which I am convinced will never be overthrown, within the framework of applicability of its basic concepts [...]
View article: Temporal Ramsey Graphs: The Ramsey Kinematic Approach to the Motion of Systems of Material Points
Temporal Ramsey Graphs: The Ramsey Kinematic Approach to the Motion of Systems of Material Points Open
The Ramsey approach is applied to analyses of the kinematics of systems built of non-relativistic, motile point masses/particles. This approach is based on colored graph theory. Point masses/particles serve as the vertices of the graph. Th…
View article: Negative-Viscosity Materials: Exploiting the Effect of Negative Mass
Negative-Viscosity Materials: Exploiting the Effect of Negative Mass Open
The research is motivated by the search for materials with negative viscosity to exploit the effect of negative mass. We introduce media (gaseous and liquid) that demonstrate negative viscosity. Consider the vibrated plate, which is vertic…
View article: Physical and Logical Synchronization of Clocks. The Ramsey Approach
Physical and Logical Synchronization of Clocks. The Ramsey Approach Open
Ramsey analysis is applied for the problem of relativistic and quantum synchronization of clocks. Various protocols of synchronization are addressed. Einstein and Eddington special relativity synchronization procedures are considered; quan…
View article: Temporal Ramsey Graphs: Ramsey Kinematic Approach to the Motion of Systems of Material Points
Temporal Ramsey Graphs: Ramsey Kinematic Approach to the Motion of Systems of Material Points Open
We propose the Ramsey approach for the analysis of the kinematics of the systems built of non-relativistic, motile point masses/particles. The approach is based on the colored graphs theory. Point masses/particles serve as the vertices of …
View article: Mathematical Duality: The Ramsey Approach
Mathematical Duality: The Ramsey Approach Open
The meta-mathematic approach to the mathematical duality is introduced. Systems of mathematical theorems/propositions related each to other by the mutually exclusive relations of “duality” and “non-duality” are addr…
View article: Negative Viscosity Materials Exploiting the Effect of Negative Mass
Negative Viscosity Materials Exploiting the Effect of Negative Mass Open
We introduce the media (gaseous and liquid) demonstrating the negative viscosity. Consider the vibrated plate (ω is the frequency of vibrations), which is vertically pulled through the gas, built of the core-shell ”meta-molecules”: the mas…
View article: Operators in the Hilbert Space: the Ramsey Approach
Operators in the Hilbert Space: the Ramsey Approach Open
Ramsey theory is applied to the analysis of operators acting on the functions belonging to the L^2 Hilbert space. The operators form the vertices of the bi-colored graph. If the operators commute, they are connected by a red link; if the o…
View article: A Ramsey-Theory-Based Approach to the Dynamics of Systems of Material Points
A Ramsey-Theory-Based Approach to the Dynamics of Systems of Material Points Open
We propose a Ramsey-theory-based approach for the analysis of the behavior of isolated mechanical systems containing interacting particles. The total momentum of the system in the frame of the center of masses is zero. The mechanical syste…
View article: Ramsey Approach to Quantum Mechanics
Ramsey Approach to Quantum Mechanics Open
Ramsey theory enables re-shaping of the basic ideas of quantum mechanics. Quantum observables represented by linear Hermitian operators are seen as the vertices of a graph. Relations of commutation define the coloring of edges linking the …