Cristian Toma

Dynamical Aspects of Macroscopic and Quantum Transitions due to Coherence Function and Time Series Events

This study presents the application of dynamical equations able to generate alternating ndeformations with increasing amplitude and delayed pulses in a certain material medium. It is considered that an external force acts at certain time interval (similar to a time series) upon the material medium in the same area. Using a specific differential equation (considering nnonzero initial values and using a function similar to the coherence function between the external force and the deformations inside the material), it results that modulated amplitude oscillations appear inside the material. If the order of the differential dynamical equation is higher, supplementary aspects as different delayed pulses and multiscale behaviour can be noticed. These features are similar to non-Markov aspects of quantum transitions, and for this reason the mathematical model is suitable for describing both quantum phenomena nand macroscopic aspects generated by sequence of pulses. An example of a quantum system, namely, the Hydrogen atom, is discussed.

Specific Mathematical Aspects of Dynamics Generated by Coherence Functions

This study presents specific aspects of dynamics generated by the coherence function (acting in an integral manner). It is considered that an oscillating system starting to work from initial nonzero conditions is commanded by the coherence function between the output of the system and an alternating function of a certain frequency. For different initial conditions, the evolution of the system is analyzed. The equivalence between integrodifferential equations and integral equations implying the same number of state variables is investigated; it is shown that integro-differential equations of second order are far more restrictive regarding the initial conditions for the state variables. Then, the analysis is extended to equations of evolution where the coherence function is acting under the form of a multiple integral. It is shown that for the coherence function represented under the form of an 𝑛th integral, some specific aspects as multiscale behaviour suitable for modelling transitions in complex systems (e.g., quantum physics) could be noticed when 𝑛 equals 4, 5, or 6.

Mathematical Transform of Traveling-Wave Equations and Phase Aspects of Quantum Interaction

The traveling wave equation is an essential tool in the study of vibrations and oscillating systems. This paper introduces an important extension to the Fourier/Laplace transform that is needed for the analysis of signals that are represented by traveling wave equations. Another objective of the paper is to present a mathematical technique for the simulation of the behavior of large systems of optical oscillators.

Advanced Signal Processing and Command Synthesis for Memory-Limited Complex Systems

This paper presents advanced signal processing methods and command synthesis for memory-limited complex systems. For accurate measurements performed on limited time interval, some specific methods should be added. For signal processing, a robust filtering and sampling procedure performed on a specific working interval is required, so as the influence of low-amplitude and high-frequency fluctuations to be diminished. This study shows that such a signal processing method for the case of memory-limited complex systems requires the use of certain differentiation/integration procedures performed by oscillating systems, so as robust results suitable for efficient command synthesis to be available. A brief comparison with uncertainty aspects in modern physics (where quantum aspects can be considered as features of complex systems) is also presented.

Relativistic Short Range Phenomena and Space-Time Aspects of Pulse Measurements

Particle physics is increasingly being linked to engineering applications via electron microscopy, nuclear instrumentation, and numerous other applications. It is well known that n relativistic particle equations notoriously fail over very short space-time intervals. This paper n introduces new versions of Diracs equation and of the Klein-Gordon equation that are suitable for nshort-range phenomena. Another objective of the paper is to demonstrate nthat pulse measurement methods that are based on the wave nature of matter ndo not necessarily correlate with physical definitions that are based on nthe corpuscular nature of particles.

Transient Aspects of Wave Propagation Connected with Spatial Coherence

This study presents transient aspects of light wave propagation connected with spatial coherence. It is shown that reflection and refraction phenomena involve spatial patterns which are created within a certain transient time interval. After this transient time interval, these patterns act like a memory, determining the wave vector for subsequent sets of reflected/refracted waves. The validity of this model is based on intuitive aspects regarding phase conservation of energy for waves reflected/refracted by multiple centers in a certain material medium.

Wavelets-Computational Aspects of Sterian Realistic Approach to Uncertainty Principle in High Energy Physics: A Transient Approach

This study presents wavelets-computational aspects of Sterian-realistic approach to uncertainty principle in high energy physics. According to this approach, one cannot make a device for the simultaneous measuring of the canonical conjugate variables in reciprocal Fourier spaces. However, such aspects regarding the use of conjugate Fourier spaces can be also noticed in quantum field theory, where the position representation of a quantum wave is replaced by momentum representation before computing the interaction in a certain point of space, at a certain moment of time. For this reason, certain properties regarding the switch from one representation to another in these conjugate Fourier spaces should be established. It is shown that the best results can be obtained using wavelets aspects and support macroscopic functions for computing (i) wave-train nonlinear relativistic transformation, (ii) reflection/refraction with a constant shift, (iii) diffraction considered as interaction with a null phase shift without annihilation of associated wave, (iv) deflection by external electromagnetic fields without phase loss, and (v) annihilation of associated wave-train through fast and spatially extended phenomena according to uncertainty principle.

Modeling Transitions in Complex Systems by Multiplicative Effect of Temporal Patterns Extracted from Signal Flows

This study presents a mathematical model based on Fourier decomposition of a sequence of internal signals generated in a complex system by a sequence of external pulses (time series) nfor characterizing suddenly emerging phenomena as nonlinear transitions. Newly created temporal patterns extracted from internal signal flow (mathematically represented as oscillations with long period) interact as new entities in a multiplicative manner with subsequent pulses from the external time series (already existing entities) in order to generate nonlinear transitions within the system. Such effects are enhanced when the period of external pulses creating new patterns is similar to the settling time of the complex system (this being the condition for an efficient external action). For complex systems where both classical and quantum phenomena generated by external time series are involved, this mathematical model can correctly explain the transition from classical to quantum behaviour (corresponding to a more ordered structure) avoiding typical contradictions generated by analysis performed on transient time intervals or by wave superposition.

Phase detection for vibration measurements based on test-functions

This paper presents special non-linear methods for phase detection for vibration measurements based on laser signals and on test-functions. First are presented mathematical aspects of high-intensity optical pulses (such as the pulse generated by the photonic echo phenomenon), being shown that the only mathematical possibility of simulating such pulses is represented by the use of test-functions (well-known from the mathematical theory of distributions). Then are studied test functions from the generating possibilities point of view, being shown that systems described by differential equations can generate only some functions similar to test-functions, called practical test-functions. The advantages of using them in filtering and sampling procedures is also presented, and further are studied differential equations of first and second order able to generate such functions. Finally are presented possibilities of using systems described by such differential equations for processing the signal generated by photodetectors when laser signals are received, and filtering possibilities in case of detectors placed in a vibrational environment are shown. Due to the existence of non-linear equations, the output of such filtering systems is very sensitive at the phase of an input alternating component, being recommended to use them for phase detection.

Filtering possibilities for processing optoelectronic current for acceleration measurements

This paper presents robust methods for filtering the optoelectronic current generated by laser signals in case of vibration measurements. First is presented a general procedure for obtaining signals corresponding to certain spatial vibrations by using diffracting grating. The diffracting grating is attached to the body supposed to present vibrations, and a set of four photodetectors is placed in the measuring area in symmetrical positions as related to a point of maximum intensity for the received light. The photoelectric current generated by this set is further filtered and processed, so as three electronic signals corresponding to displacements of the body along all three rectangular spatial coordinates axes to be obtained. Then is presented a method for determining the derivative of the spatial coordinates of the body as related to tune, in conditions of low-amplitude vibrations overlapped to a general translation ofthe body along a certain direction, under the influence of an external force. It is shown that such a structure is suitable for controlling the position of material bodies, due to the fact that the derivative of the position as related to time represents the acceleration of the body (proportional to the external force acting upon it).