Quantum Physics

In this paper we explore the decay η b → τ + τ -as a probe for a light pseudoscalar or a light axial vector state. We estimate the standard model branching ratio for this decay to be ∼ 4×10 -9 . We show that considerably larger branching ratios, up to the present experimental limit of ∼ 8%, is possible in models with a light pseudoscalar or a light axial vector state. As we do not include possible mixing effects between the light pseudoscalar and the η b , our results should be reliable when the pseudoscalar mass is away from the η b mass.

We evaluate the decay constants for the B and D mesons and the form factors for the semileptonic decays of the B meson to D and D * mesons in a Bethe-Salpeter model. From data we extract V cb = 0.039 ± 0.002 from B → D * lν and V cb = 0.037 ± 0.004 from B → Dlν decays. The form factors are then used to obtain non-leptonic decay partial widths for B → Dπ(K) and B → DD(D s ) in the factorization approximation.

Adsorption of the methoxy radical on clean and on low oxygen precovered Ru(0 0 0 1) metallic surfaces has been studied by densityfunctional theory cluster calculations. Methoxy is predicted to be preferentially chemisorbed on both hollow sites (hcp and fcc) of such surfaces, and adopts an upright orientation (C 3m local symmetry). Such prediction is supported by the good agreement found between the calculated vibrational frequencies and the experimentally observed RAIRS spectra. Regarding the charge transfer process between the adsorbate and the surface, our results suggest that the bonding is dominantly polar covalent which arises from a charge donation from the ruthenium surface to the radical, and the co-adsorbed electronegative oxygens deplete slightly the surface electron density. However, the major difference is not induced through much O-Ru bonding, but indirectly, by lowering the valence d-band center of the system. This results in a lower adsorption energy for methoxy than on the clean Ru(0 0 0 1) surface, in accordance with experimental data. Further, accordingly to the present calculations, the radical is expected to dissociate or desorb more easily on the modified surface but with no participation from the co-adsorbed oxygen atoms.

A trajectory-preprocessing algorithm has been devised which matches antenna angular position, velocity, and acceleration to those of a target. This eliminates vibrations of the antenna structure caused by discontinuities in velocity and acceleration commands, and improves antenna-pointing performance by constraining antenna motion to a linear regime. The algorithm permits faster acquisition times and preserves antenna-tracking capability in situations where there would otherwise be an unacceptably sudden change in antenna velocity or acceleration. A simulation of DSS 13 shows that this preprocessor would reduce servo error to 1 mdeg during acquisition of a low-Earth-orbiting satellite.

In a recent paper, "Reexamining f (R, T ) gravity", by S. B. Fisher and E. D. Carlson, Phys. Rev. D 100, 064059 (2019), the authors claim that for the particular f (R, T ) modified gravity model, with f (R, T ) = f1(R) + f2(T ), the term f2(T ) must be included in the matter Lagrangian and therefore it does not have any physical significance. We carefully reexamine the line of reasoning presented in the paper, and we show that there are several major conceptual problems related to the author's physical interpretations, as well as in the physical and mathematical approaches used to derive the energy-momentum tensor of the theory. These problems raise some serious concerns about the validity of most of the results presented in the paper.

If dark matter is composed of massive bosons, a Bose-Einstein condensation process must have occurred during the cosmological evolution. Therefore galactic dark matter may be in a form of a condensate, characterized by a strong self-interaction. We consider the effects of rotation on the Bose-Einstein condensate dark matter halos, and we investigate how rotation might influence their astrophysical properties. In order to describe the condensate we use the Gross-Pitaevskii equation, and the Thomas-Fermi approximation, which predicts a polytropic equation of state with polytropic index n = 1. By assuming a rigid body rotation for the halo, with the use of the hydrodynamic representation of the Gross-Pitaevskii equation we obtain the basic equation describing the density distribution of the rotating condensate. We obtain the general solutions for the condensed dark matter density, and we derive the general representations for the mass distribution, boundary (radius), potential energy, velocity dispersion, tangential velocity and for the logarithmic density and velocity slopes, respectively. Explicit expressions for the radius, mass, and tangential velocity are obtained in the first order of approximation, under the assumption of slow rotation. In order to compare our results with the observations we fit the theoretical expressions of the tangential velocity of massive test particles moving in rotata e-mail:

The possibility that dark matter, whose existence is inferred from the study of the galactic rotation curves, and from the mass deficit in galaxy clusters, can be in a form of a Bose-Einstein Condensate, has been extensively investigated lately. In the present work, we consider a detailed analysis of the astrophysical properties of the Bose-Einstein Condensate dark matter halos that could provide clear observational signatures that help discriminate between different dark matter models. In the Bose-Einstein condensation model dark matter can be described as a non-relativistic, gravitationally confined Newtonian gas, whose density and pressure are related by a polytropic equation of state with index n = 1. The mass and gravitational properties of the condensate halos are obtained in a systematic form, including the mean logarithmic slopes of the density and of the tangential velocity. The lensing properties of the condensate dark matter are investigated in detail. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halos, is obtained in the form of series expansions. This enables arbitraryprecision calculations of the surface mass density, deflection angle, deflection potential, and of the magnification factor, thus giving the possibility of the comparison of the predicted lensing properties of the condensate dark matter halos with observations. The stability properties of the condensate halos are also investigated by using the scalar and the tensor virial theorems, respectively, and the virial perturbation equation for condensate dark matter halos is derived. As an application of the scalar virial theorem we consider the problem of the stability of a slowly rotating and slightly disturbed galactic dark matter halo. For such a halo the oscillations frequencies and the stability conditions are obtained in the linear approximation.

The equation of motion for massive particles in f (R) modified theories of gravity is derived. By considering an explicit coupling between an arbitrary function of the scalar curvature, R, and the Lagrangian density of matter, it is shown that an extra force arises. This extra force is orthogonal to the four-velocity and the corresponding acceleration law is obtained in the weak field limit. Connections with MOND and with the Pioneer anomaly are further discussed.

The late-time cosmic acceleration may be due to infra-red modifications of General Relativity. In particular, we consider a maximal extension of the Hilbert-Einstein action and analyze several interesting features of the theory. Generally, the motion is non-geodesic and takes place in the presence of an extra force, which is orthogonal to the four-velocity. These models could lead to some major differences, as compared to the predictions of General Relativity or other modified theories of gravity, in several problems of current interest, such as cosmology, gravitational collapse or the generation of gravitational waves. The study of these phenomena may also provide some specific signatures and effects, which could distinguish and discriminate between the various gravitational models.

Recently, a renormalizable gravity theory with higher spatial derivatives in four dimensions was proposed by Hor ˇava. The theory reduces to Einstein gravity with a nonvanishing cosmological constant in IR, but it has improved UV behaviors. The spherically symmetric black hole solutions for an arbitrary cosmological constant, which represent the generalization of the standard Schwarzschild-(anti) de Sitter solution, have also been obtained for the Hor ˇava-Lifshitz theory. The exact asymptotically flat Schwarzschild-type solution of the gravitational field equations in Hor ˇava gravity contains a quadratic increasing term, as well as the square root of a fourth order polynomial in the radial coordinate, and it depends on one arbitrary integration constant. The IR-modified Hor ˇava gravity seems to be consistent with the current observational data, but in order to test its viability more observational constraints are necessary. In the present paper we consider the possibility of observationally testing Hor ˇava gravity by using the accretion disk properties around black holes. The energy flux, the temperature distribution, the emission spectrum, as well as the energy conversion efficiency are obtained, and compared to the standard general relativistic case. Particular signatures can appear in the electromagnetic spectrum, thus leading to the possibility of directly testing Hor ˇava gravity models by using astrophysical observations of the emission spectra from accretion disks.

The generalized Chaplygin gas, which interpolates between a high density relativistic era and a non-relativistic matter phase, is a popular dark energy candidate. We consider a generalization of the Chaplygin gas model, by assuming the presence of a bulk viscous type dissipative term in the effective thermodynamic pressure of the gas. The dissipative effects are described by using the truncated Israel-Stewart model, with the bulk viscosity coefficient and the relaxation time functions of the energy density only. The corresponding cosmological dynamics of the bulk viscous Chaplygin gas dominated universe is considered in detail for a flat homogeneous isotropic Friedmann-Robertson-Walker geometry. For different values of the model parameters we consider the evolution of the cosmological parameters (scale factor, energy density, Hubble function, deceleration parameter and luminosity distance, respectively), by using both analytical and numerical methods. In the large time limit the model describes an accelerating universe, with the effective negative pressure induced by the Chaplygin gas and the bulk viscous pressure driving the acceleration. The theoretical predictions of the luminosity distance of our model are compared with the observations of the type Ia supernovae. The model fits well the recent supernova data. From the fitting we determine both the equation of state of the Chaplygin gas, and the parameters characterizing the bulk viscosity. The evolution of the scalar field associated to the viscous Chaplygin fluid is also considered, and the corresponding potential is obtained. Hence the viscous Chaplygin gas model offers an effective dynamical possibility for replacing the cosmological constant, and to explain the recent acceleration of the universe.

We investigate the interaction between dark energy and dark matter in the framework of irreversible thermodynamics of open systems with matter creation/annihilation. We consider dark energy and dark matter as an interacting two component (scalar field and "ordinary" dark matter) cosmological fluid in a homogeneous spatially flat and isotropic Friedmann-Robertson-Walker (FRW) Universe. The thermodynamics of open systems as applied together with the gravitational field equations to the two component cosmological fluid leads to a generalisation of the elementary dark energy-dark mater interaction theory, in which the decay (creation) pressures are explicitly considered as parts of the cosmological fluid stress-energy tensor. Specific models describing coherently oscillating scalar waves, leading to a high particle production at the beginning of the oscillatory period, and models with a constant potential energy scalar field are considered. Furthermore, exact and numerical solutions of the gravitational field equations with dark energy-dark matter interaction are also obtained.

We study the low energy string effective action with an exponential type dilaton potential and vanishing torsion in a Bianchi type I space-time geometry. In the Einstein and string frames the general solution of the gravitational field equations can be expressed in an exact parametric form. Depending on the values of the dilaton coupling constant and of the coefficient in the exponential, the obtained cosmological models can be generically divided into three classes, leading to both singular and non-singular behaviors. The effect of the potential on the time evolution of the mean anisotropy parameter is also considered in detail, and it is shown that a Bianchi type I universe isotropizes only in the presence of a dilaton field potential or a central deficit charge.

We rigorously prove that for compact charged general relativistic objects there is a lower bound for the mass-radius ratio. This result follows from the same Buchdahl type inequality for charged objects, which has been extensively used for the proof of the existence of an upper bound for the mass-radius ratio. The effect of the vacuum energy (a cosmological constant) on the minimum mass is also taken into account. Several bounds on the total charge, mass and the vacuum energy for compact charged objects are obtained from the study of the Ricci scalar invariants. The total energy (including the gravitational one) and the stability of the objects with minimum mass-radius ratio is also considered, leading to a representation of the mass and radius of the charged objects with minimum mass-radius ratio in terms of the charge and vacuum energy only.

A fundamental ingredient in wormhole physics is the flaring-out condition at the throat which, in classical general relativity, entails the violation of the null energy condition. In this work, we present the most general conditions in the context of modified gravity, in which the matter threading the wormhole throat satisfies all of the energy conditions, and it is the higher order curvature terms, which may be interpreted as a gravitational fluid, that support these nonstandard wormhole geometries. Thus, we explicitly show that wormhole geometries can be theoretically constructed without the presence of exotic matter, but are sustained in the context of modified gravity.

No presente trabalho nós consideramos um campo escalar real não massivo em um espaço-tempo bidimensional, satisfazendo a condição de fronteira Dirichlet ou Neumann na posição instantânea de uma fronteira em movimento. Para uma lei de movimento relativística, nós mostramos que as condições de fronteira Dirichlet e Neumann produzem a mesma força de radiação sobre um espelho em movimento quando o estado inicial do campo é invariante sobre translações temporais. Obtemos as fórmulas exatas para a densidade de energia do campo e da força de radiação na fronteira para os estados de vácuo, coerente e comprimido. No limite não-relativistico, nossos resultados coincidem com os encontrados na literatura. Nós também investigamos o campo dentro de uma cavidade oscilante. Considerando as condições de fronteira Neumann e Dirichlet, escrevemos a fórmulas exata para a densidade de energia dentro de uma cavidade não-estática, para um estado inicial arbitrário do campo. Tomando como base a equação de Moore, nós calculamos recursivamente a densidade de energia e investigamos a evolução temporal da densidade de energia para o estado coerente do campo.

"Adjunctions" are types of addition or union with another, but they are not essential or permanent. In linear algebra, this is the "adjoint," which is the transpose and conjugate operator of A (or the corresponding square matrix); it is also denoted by adj(A). Here it is used in information theory.

Additional jet activity in dijet events is measured using pp collisions at ATLAS at a centre-of-mass energy of 7 TeV, for jets reconstructed using the anti-k t algorithm with radius parameter R = 0.6. This is done using variables such as the fraction of dijet events without an additional jet in the rapidity interval bounded by the dijet subsystem and correlations between the azimuthal angles of the dijets. They are presented, both with and without a veto on additional jet activity in the rapidity interval, as a function of the scalar average of the transverse momenta of the dijets and of the rapidity interval size. The double differential dijet cross section is also measured as a function of the interval size and the azimuthal angle between the dijets. These variables probe differences in the approach to resummation of large logarithms when performing QCD calculations. The data are compared to powheg, interfaced to the pythia 8 and herwig parton shower generators, as well as to hej with and without interfacing it to the ariadne parton shower generator. None of the theoretical predictions agree with the data across the full phase-space considered; however, powheg+pythia 8 and hej+ariadne are found to provide the best agreement with the data. These measurements use the full data sample collected with the ATLAS detector in 7 TeV pp collisions at the LHC and correspond to integrated luminosities of 36.1 pb -1 and 4.5 fb -1 for data collected during 2010 and 2011, respectively.

ATLAS measurements of the azimuthal anisotropy in lead-lead collisions at √ s NN = 2.76 TeV are shown using a dataset of approximately 7 µb -1 collected at the LHC in 2010. The measurements are performed for charged particles with transverse momenta 0.5 < p T < 20 GeV and in the pseudorapidity range |η| < 2.5. The anisotropy is characterized by the Fourier coefficients, v n , of the charged-particle azimuthal angle distribution for n = 2-4. The Fourier coefficients are evaluated using multi-particle cumulants calculated with the generating function method. Results on the transverse momentum, pseudorapidity and centrality dependence of the v n coefficients are presented. The elliptic flow, v 2 , is obtained from the two-, four-, six-and eight-particle cumulants while higher-order coefficients, v 3 and v 4 , are determined with two-and four-particle cumulants. Flow harmonics v n measured with four-particle cumulants are significantly reduced compared to the measurement involving two-particle cumulants. A comparison to v n measurements obtained using different analysis methods and previously reported by the LHC experiments is also shown. Results of measurements of flow fluctuations evaluated with multiparticle cumulants are shown as a function of transverse momentum and the collision centrality. Models of the initial spatial geometry and its fluctuations fail to describe the flow fluctuations measurements. T distribution showed that the fraction of the total inelastic cross-section sampled by the trigger and event selection requirements is (98 ± 2) %. The E FCal T distribution was divided into centrality intervals, each representing a per-

We present a search for charged massive long-lived particles (CMLLPs) that are pair produced in pp collisions at √ s = 1.96 TeV collected by the D0 experiment at the Fermilab Tevatron collider. Our result is a combination of two searches where either one or both CMLLPs are reconstructed in the detector. We select events with muon-like particles that have both speed and ionization energy loss (dE/dx) different from muons produced in pp collisions. In the absence of evidence for CMLLPs corresponding to 6.3 fb -1 of integrated luminosity, we set limits on the CMLLP masses in several supersymmetric (SUSY) models, excluding masses below 278 GeV for long-lived gaugino-like charginos, and masses below 244 GeV for long-lived higgsino-like charginos at the 95% C.L. We also set limits on the cross section for pair production of long-lived scalar tau leptons that range from 0.04 pb to 0.008 pb for scalar tau lepton masses of 100 to 300 GeV.

Impurities and defects are known to affect the properties of the charge density wave (CDW) state but the influence of impurities on the density of states inside the Peierls gap remains largely unexplored. Here we present an experimental study of the effect of indium impurities on photoconduction spectra of CDW compound orthorhombic TaS 3 . We use the temperature diffusion method to introduce indium into a sample from preliminary attached In contacts. The concentration of In after 23 hours of diffusion is found to be nonuniform and strongly dependent on the distance to the contacts. The diffusion affects the spectral range 0.15-0.25 eV, increasing the photoconduction amplitude linearly with diffusion time. The optical gap value obtained from the measurements is 2∆ = 0.25 eV and the tail of states below 2∆ is associated with the impurities in agreement with the Tüttö-Zawadowski theory. Diffusion-induced modification of current-voltage characteristics and decrease of the Peierls temperature are also observed. Neither changes in photoconduction spectra nor in the Peierls transition temperature of the control sample with Au contacts are found.

A technique for estimating eddy diffusivities in a turbulent atmospheric layer is presented; the scheme adopted is based on an inverse-problem methodology. The inverse problem is formulated as a nonlinear constrained optimization problem, where the objective function is defined through the square differences between experimental and model data. The direct mathematical model is given by the advection-diffusion equation, which is solved by second-order finite-difference method. In the presence of noise it is necessary to use some regularization term; the Tikhonov function and an entropic regularization of zeroth, first and second orders are used in this paper. In addition, two inversion strategies are used: alternate and simultaneous eddy diffusivities estimation. Numerical experiments show a good performance of the proposed methodology.

The argumentary oscillator. Experimental set-up. Modelling. Experimental results. Future work. Receptors. Sensors and generator. Software. Experimental set-up: sensors and generator. Angular-position sensor. This sensor gives the angular position of the pendulum's rod, with respect to the vertical reference. Its resolution is 100 k points/turn. Current sensor. This sensor gives a voltage-image of the current in the coil. It is a necessary sensor, to ensure that the current is maintained to a constant RMS value, and that no distorsion is introduced in the waveform feeded to the coil. This sensor is included inside the generator. Generator. We use a B&K generator which practically generates an harmonic current into the coils. A current generator is necessary, to ensure that no magnetic feedback from the source-receptor interaction gets into the loop. Experimental set-up. Modelling. Experimental results.

Experiments on trapped quantum gases can probe challenging regimes of quantum many-body dynamics, where strong interactions or nonequilibrium states prevent exact solutions. Here we present a different kind of exact result, which applies even in the absence of actual solutions: a class of space-time mappings of different experiments onto each other. Since our result is an identity relating second-quantized field operators in the Heisenberg picture of quantum mechanics, it is extremely general; it applies to arbitrary measurements on any mixtures of Bose or Fermi gases, in arbitrary initial states. It represents a strong prediction of quantum field theory which can be tested in current laboratories, and whose practical applications include perfect simulation of interesting experiments with other experiments which may be easier to perform.

Apurba Biswas, 2, ∗ V . V. Prasad, 4, † O. Raz, ‡ and R. Rajesh 2, § The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India Department of Physics of Complex Systems, Weizmann Institute of Science, 76100 Rehovot, Israel Government Arts and Science College, Nadapuram, Kozhikode 673506, India

The local multiplier algebra Mloc(A) of a C∗-algebra A is the C∗-algebraic direct limit of multiplier algebras M(K) along the downward-directed system E(A) of all (closed) essential ideals K of A. Such algebras first arose in the study of derivations and were formally introduced by ...

By extending the freedom to define spacetime itself as a manifestation of the fundamental energy field, the Source Energy Field Theory (SEFT) provides a unified framework in which all physical phenomena arise from the dynamics of a single nonlinear energy field. While previous work (Part V) demonstrated that the gauge group of the Standard Model and the Higgs mechanism emerge naturally from the internal geometry of the SEFT field, the unresolved issues of neutrino mass, CP violation, and baryogenesis have remained open. In this paper (Part VI), we extend SEFT to address these challenges. First, we show that gradient terms of the SEFT field generate suppressed Dirac-type neutrino masses of order 10 -2 eV, consistent with oscillation experiments and cosmological bounds. Second, we demonstrate that the dynamical evolution of the internal phase provides a natural geometric source of CP violation, coupling to the Chern-Simons number density and inducing an effective baryon chemical potential. Third, by solving the Boltzmann equation with SEFT inputs, we reproduce the observed baryon-to-photon ratio η ≃ 6 × 10 -10 , with freeze-out occurring near the electroweak scale. These results establish SEFT as a framework capable of providing a unified and geometric explanation of phenomena that remain unexplained within the Standard Model, reinforcing its role as a candidate for a unified theory of particle physics and cosmology.

A compact cw Tm,Ho:YLF laser with single-mode tunability over +/-4 GHz has been developed into a modular unit containing an isolator and photomixer for offset tuning of the LO from a master oscillator which controls the frequency of a Doppler lidar transmitter. This and an alternative diode laser LO will be described,

A compact cw Tm,Ho:YLF laser with single-mode tunability over +/-4 GHz has been developed into a modular unit containing an isolator and photomixer for offset tuning of the LO from a master oscillator which controls the frequency of a Doppler lidar transmitter. This and an alternative diode laser LO will be described,

Sarfatti's Post-Quantum Model in Hameroff's Microtubule Networks: A Complete Integration

Yes, Jack Sarfatti's post-quantum mechanics (PQM)—a retrocausal extension of de Broglie-Bohm theory incorporating action-reaction back-flow between ontic pilot waves and beables—seamlessly integrates into Stuart Hameroff's microtubule framework within the Orchestrated Objective Reduction (Orch-OR) model of consciousness. This synthesis, grounded in 2025 updates to Orch-OR emphasizing quantum vibrations and superradiance in microtubules at physiological temperatures, replaces Roger Penrose's gravity-induced objective reduction (OR) for non-random collapse with Sarfatti's nonlocal anyonic braiding mechanism. In this post-Bohmian ontological interpretation, physically real Aharonov-Bohm "destiny" (future-to-past) and "history" (past-to-future) pilot waves compute weak values of neural electromagnetic (EM) field operators. Direct back-reaction from these operators on the destiny-history pilots forms a conscious self-organizing feedback control post-quantum circuit, enabling temporal EPR signaling.

This circuit manifests dual experiential imprints: Back-reaction on the history pilot wave evokes Marcel Proust's In Search of Lost Time—involuntary, sensory-triggered floods of holistic memories (e.g., the madeleine dipped in tea reviving Combray). Conversely, back-reaction on the destiny pilot wave, propagated via Igor Novikov's self-consistent "time loops" (acausal closed timelike curves preserving consistency), generates creative new ideas—intuitions "back from the future" that resolve paradoxes by selecting optimal paths. Note: These loops are bidirectional; past memories can also loop forward as predictive engrams, unifying recollection and foresight in PQM temporal EPR signaling, where nonlocal anyon braiding enforces consistency without superluminal paradoxes

No, Post-Selected Quantum Tomography (PSQT) has not been commercialized in patents for actual devices that reveal hidden correlations. PSQT remains a foundational research technique in quantum information science, primarily explored in academic and experimental contexts for efficient state reconstruction and metrology. While weak measurements (core to PSQT) have inspired patents in quantum sensing (e.g., amplified magnetometers), no direct patents or commercial products explicitly claim PSQT for "hidden correlation" devices as of September 29, 2025. Searches across patent databases yield unrelated acronyms (e.g., PSQT for "Practical Software Quality Techniques" or biotech transposases), confirming its niche status without commercial traction. Future applications in quantum networks may change this, but current evidence points to lab prototypes only.

The given equation describes a classical nonlinear oscillator with time-dependent damping (a(t)), timedependent linear restoring force coefficient (b(t)), cubic nonlinearity 𝛾𝑥 3 , and external forcing (f(t)): 𝑑 2 𝑥 𝑑𝑡 2 + 𝑎(𝑡) 𝑑𝑥 𝑑𝑡 + 𝑏(𝑡)𝑥 + 𝛾𝑥 3 = 𝑓(𝑡). This is a generalization of the Duffing oscillator, which is notoriously difficult to solve analytically due to the nonlinearity and time dependence. No closed-form solution exists in general. However, we can outline standard approaches to "solve" it, meaning to find approximate or numerical solutions. Analytical Approaches (for Special Cases) Undriven, undamped, constant coefficients (𝑎(𝑡) = 0, 𝑓(𝑡) = 0, 𝑏 = constant = 𝜔 0 2 > 0, 𝛾 > 0): The equation reduces to 𝑥 ¨+ 𝜔 0 2 𝑥 + 𝛾𝑥 3 = 0. Multiply by 𝑥 ˙ and integrate to get the energy conservation form: 1 2 𝑥 ˙2 + 1 2 𝜔 0 2 𝑥 2 + 𝛾 4 𝑥 4 = 𝐸, where (E) is a constant. The solution is expressed in terms of Jacobi elliptic functions: 𝑥(𝑡) = 𝐴sn(𝛾𝐴 2 + 𝜔 0 2 2 √ 𝑡 + 𝜙, 𝑘), with modulus (k) determined by the amplitude (A) and phase 𝜙 from initial conditions. For 𝛾 < 0 (softening spring), chaotic solutions can emerge. Small nonlinearity perturbation (|𝛾| ≪ 1): Use multiple-scale perturbation theory or Lindstedt-Poincaré method to find approximate periodic solutions. Assume 𝑥(𝑡) = 𝑥 0 (𝑡) + 𝛾𝑥 1 (𝑡) + 𝑂(𝛾 2), and solve order by order, adjusting frequency for resonance avoidance. For forced cases, apply the method of averaging for slowly varying amplitudes in polar form 𝑥 = 𝑟cos(𝜔𝑡 + 𝜙). Time-dependent coefficients: Transform to a Liouville-Green (WKB) approximation for slowly varying (a(t)), (b(t)), treating the nonlinearity as a perturbation. For parametric excitation (e.g., 𝑏(𝑡) = 𝜔 0 2 (1 + 𝜖cos(2𝜔𝑡))), use Floquet theory to analyze stability. Numerical Solution For general cases, rewrite as a first-order system: 𝑥 ˙= 𝑣, 𝑣 ˙=-𝑎(𝑡)𝑣-𝑏(𝑡)𝑥-𝛾𝑥 3 + 𝑓(𝑡). Integrate using Runge-Kutta methods (e.g., via SciPy's solve_ivp). To demonstrate, assume constants 𝑎 = 0.1, 𝑏 = 1, 𝛾 = 0.15, 𝑓(𝑡) = 1.5cos(𝑡) (resonant drive), initial conditions 𝑥(0) = 0, 𝑣(0) = 0, over 𝑡 ∈ [0, 100]. The solution exhibits chaotic bistability typical of the Duffing oscillator, with amplitude jumping between large and small responses near the resonance. Time Interval Behavior Approximate Amplitude Range 0 ≤ 𝑡 < 20 Transient decay to small oscillation (20 ≤ 𝑡 < 50 Low-amplitude periodic response (50 ≤ 𝑡 < 100 Jump to high-amplitude chaotic orbit (Phase space portraits ((x) vs. (v)) show strange attractors for these parameters, confirming nonlinearityinduced chaos.

Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results indicate two zones in parameter space where the dynamics shows the most complex patterns. These zones are located on the two edges of an absorbent region where the system displays spatio-temporal intermittency.

We study synchrotron polarization in spatially resolved horizon-scale images, such as those produced by the Event Horizon Telescope (EHT). In both general relativistic magnetohydrodynamic (GRMHD) simulations as well as simplified models of the black hole magnetosphere, the polarization angle, quantified by the complex observable ∠β 2 , depends strongly and systematically on the black hole spin. This relationship arises from the coupling between spin and the structure of the magnetic field in the emission region, and it can be computed analytically in the force-free limit. To explore this connection further, we develop a semi-analytic inflow framework that solves the time stationary axisymmetric equations of GRMHD in the black hole's equatorial plane; this model can interpolate between the force-free and inertial regimes by varying the magnetization of the inflow. Our model demonstrates how finite inertia modifies the structure of the electromagnetic field and can be used to quantitatively predict the observed polarization pattern. By comparing reduced models, GRMHD simulations, and analytic limits, we show that the observed synchrotron polarization can serve as a robust diagnostic of spin under assumptions about Faraday rotation and the emission geometry. Applied to EHT data, the model disfavors high-spin configurations for both M87 * and Sgr A * , highlighting the potential of polarimetric imaging as a probe of both black hole spin and near-horizon plasma physics.

It gives me great pleasure to introduce this work on simulation modeling. In this book, Simulation Modeling – Recent Advances, New Perspectives, and Applications, we discuss some fundamental aspects of the theory of numerical methods of simulation and explore their use to solve a large array of problems. Therefore, we cover many topics on deterministic and random techniques.
A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation.
Additionally, simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games. Simulation is also used with scientific modeling of natural systems or human systems to gain insight into their functioning, as in economics.
Simulation can be used to show the eventual real effects of alternative conditions and courses of action. Simulation is also used when the real system cannot be engaged because it may not be accessible, or it may be dangerous or unacceptable to engage, or it is being designed but not yet built, or it may simply not exist.
Moreover, key issues in modeling and simulation include the acquisition of valid sources of information about the relevant selection of key characteristics and behaviors used to build the model, the use of simplifying approximations and assumptions within the model, and fidelity and validity of the simulation outcomes. Procedures and protocols for model verification and validation are an ongoing field of academic
study, refinement, research, and development in simulations technology or practice, particularly in the work of computer simulation.
Finally, this book discusses some important aspects of simulation modeling and explores its use to solve a large set of problems. As such, the book will be of interest to all scholars, researchers, and undergraduate and graduate students in pure and applied mathematics, physical sciences, engineering and technology, computer science, numerical analysis, scientific computing, and science in general.

The paper is an epistemological treatise on what constitutes statements of truths, determination of facts and formation of opinions about them. It is based on a number of prior papers by this author on the “New Epistemology”, and inherent “Imperfections” in Logic and Linguistics. In the determination of evidence, factors which contribute to the embedded impediments in reaching “perfection” are exposed. The specific proposition is put forward that real truths and facts can only be approximated, but never reached. These impediments inevitably mar the foundations of Empiricism. Central to these unavoidable limitations two components are further explored in this paper: (a) the scale factor and the unending scaling process in the description of events and their detailed, forensic anatomy; and (b) the relativity of viewpoints and perceptions in looking at actors and actions and in examining observations obtained about objects and events in Nature, Reality and Society. The fundamental nature of the latter is demonstrated by presenting a schematic Cartesian diagram, on a basic physical element: time; whereby, the actual flow of time is plotted versus the observed flow of time. All propositions set forward are suggested as being applicable to all sciences (natural and social) as well as to all professions.

Small-world architectures may be implicated in a range of phenomena from disease propagation to networks of neurons in the cerebral cortex . While most of the recent attention on small-world networks has focussed on the effect of introducing disorder/randomness into a regular graph, we show that that the fundamental mechanism behind the small-world phenomenon is not disorder/randomness, but the presence of edges of many different length scales. Consequently, in order to explain the small-world phenomenon, we introduce the concept of multiple scale graphs and then state the multiple length scale hypothesis. Multiple scale graphs form a unifying conceptual framework for the study of evolving graphs. Moreover, small-world behavior in randomly rewired graphs is a consequence of features common to all multiple scale graphs. To support the multiple length scale hypothesis, novel graph architectures are introduced that need not be a result of random rewiring of a regular graph. In each case it is shown that whenever the graph exhibits small-world behavior, it also has edges of diverse length scales. We also show that the distribution of the length scales of the new edges is significantly more important than whether the new edges are long range, medium range or short range.

Atomic force microscopy in combination with piezoresponse force microscopy are applied to inspect and manipulate the lamellar ferroelectric domains of a non-continuous polycrystalline PbTiO 3 film. A former study showed such films to exhibit a net integral polarization direction with every grain being randomly oriented. However, the results presented here demonstrate a lamellar domain structure inside most of these single crystalline grains which is attributable to 90°d omain walls. This lamellar domain distribution might be a result of mechanical strain at the surface and the interface to the substrate as predicted from theoretical calculations for epitaxially grown PbTiO 3 films. In a switching experiment, the domains of a single grain were manipulated, showing that the lamellar structure recovers. This indicates that the lamellar domain arrangement is energetically favored in these samples.

It is the purpose of the present paper to outline an introduction in theory of embeddings in the 2-osculator bundle. First, we recall the notion of 2-osculator bundle ([1], ) and the notion of submanifolds in the 2-osculator bundle. A moving frame is constructed. The induced connections and the relative covariant derivation are discussed in third and fourth sections.The Ricci identities for the deflection tensor are present in the next section.

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We propose a structural-physical model in which the fundamental dynamics of the universe solely depend on a local space-structure measure ∆x(x,t). This measure describes the fineness of space-time structure and determines, via the temporal flow pressure PT(x), all energetic, dynamic, and gravitational properties. Particles appear as structure-resonant nodes, gravitation as local structural compression, and cosmic expansion as a consequence of a structural equilibrium offset.

We consider the support of the limit distribution of the Grover walk on crystal lattices with the linear scaling. The orbit of the Grover walk is denoted by the parametric plot of the pseudo-velocity of the Grover walk in the wave space. The region of the orbit is the support of the limit distribution. In this paper, we compute the regions of the orbits for the triangular, hexagonal and kagome lattices. We show every outer frame of the support is described by an ellipse. The shape of the ellipse depends only on the realization of the fundamental lattice of the crystal lattice in R 2 .

We investigate directional couplers in silicon-oninsulator photonic technology. We theoretically and experimentally demonstrate a large coupling-induced phase delay that occurs when nearly all light is coupled from one waveguide to the other, i.e., when the coupler operates as a cross-coupler. We show that even a tiny asymmetry in the two waveguides of the coupler causes a significant additional phase delay. The observed change in the free-spectral-range of ring resonators from 5.0 nm to 6.4 nm is explained by a small 0.1% difference in the propagation constants of the two waveguides. Such a difference can be caused by for example a 1 nm difference in the widths of the two waveguides.

Microscale strain gauges are widely used in micro electro-mechanical systems (MEMS) to measure strains such as those induced by force, acceleration, pressure or sound. We propose all-optical strain sensors based on micro-ring resonators to be integrated with MEMS. We characterized the strain-induced shift of the resonances of such devices. Depending on the width of the waveguide and the orientation of the silicon crystal, the linear wavelength shift per applied strain varies between 0.5 and 0.75 pm/microstrain for infrared light around 1550 nm wavelength. The influence of the increasing ring circumference is about three times larger than the influence of the change in waveguide effective index, and the two effects oppose each other. The strong dispersion in 220 nm high silicon sub-wavelength waveguides accounts for a decrease in sensitivity of a factor 2.2 to 1.4 for waveguide widths of 310 nm to 860 nm. These figures and insights are necessary for the design of strain sensors based on silicon waveguides.

We compute the beta function at one loop for Yang-Mills theory using as regulator the combination of higher covariant derivatives and Pauli-Villars determinants proposed by Faddeev and Slavnov. This regularization prescription has the appealing feature that it is manifestly gauge invariant and essentially four-dimensional. It happens however that the one-loop coefficient in the beta function that it yields is not -11/3, as it should be, but -23/6. The difference is due to unphysical logarithmic radiative corrections generated by the Pauli-Villars determinants on which the regularization method is based. This no-go result discards the prescription as a viable gauge invariant regularization, thus solving a long-standing open question in the literature. We also observe that the prescription can be modified so as to not generate unphysical logarithmic corrections, but at the expense of losing manifest gauge invariance. Comment 1. It is clear that regularization does not require condition (2.21), contrarily to what is claimed in ref. [3] and all papers thereafter. Comment 2. Divergences from isolated Feynman diagrams in σ 1 3 get regularized only after integration at finite R. This is in contrast with what happens for σ 1 and σ 2 , where regularization takes place algebraically prior to integration. Here we have taken dimensional

We apply to the Atiyah-Ward ansMze a systematic procedure locating symmetric monopoles in SU(3) gauge theory broken to U(1) x U(1). In particular we recover the known spherically symmetric monopole as a limit of a cylindrically symmetric separated two monopole solution in SU(3). We also discuss the spherically symmetric monopole in SU(n). This latter is the only instance where we have properly shown the smoothness of the Higgs and gauge fields.