Blow-up Mode Research Articles

Loop blow-up inflation

We present a new model of string inflation driven by a blow-up Kähler modulus of type IIb compactifications with a potential generated by string loops. Slow-roll is naturally realized thanks to the fact that the blow-up mode is a leading-order flat direction lifted by string loops which are unavoidable and generate a plateau at large field values. We check that throughout the whole inflationary dynamics the effective field theory is under control. We perform a phenomenological analysis determining the exact number of efoldings by studying the post-inflationary evolution. We determine the values of the microscopic parameters which lead to agreement with CMB data, together with the prediction of a tensor-to-scalar ratio of order r ∼ 10−5.

Two-Sided Estimates of Solutions with a Blow-Up Mode for a Nonlinear Heat Equation with a Quadratic Source

Two-Sided Estimates of Solutions with a Blow-Up Mode for a Nonlinear Heat Equation with a Quadratic Source

VIBRATION PREDICTION BASED ON PRESENTING IT PREPARATION PERIOD AS A BLUE-UP PROCESS

The method of forecasting vibrations is considered. The technique is based on the assumption that the vibration preparation process can be attributed to the processes developing in the blowup mode. The properties of the technique are demonstrated on the example of a retro forecast of vibrations that took place in Turkey on February 6 and 20, 2023. The results of testing the methodology confirmed the assumptions underlying it. Approbation of the methodology made it possible to predict the time of exacerbation of the seismic situation in the region of the globe, which is very remote from the control point of the initial seismic information for forecasting.

FORECASTING THE CUTTING TOOL LIFE CONSIDERING AS A BLOW-UP MODE ITS OPERATION

The article considers а method for real-time forecasting the cutting tool life, considering as a blow-up mode its operation. The method based on the selection of a log-periodic component in the audio signal accompanying the cutting process. The model of this component contains as the main parameter the time taken as the tool life. To ensure the process control efficiency, when making a decision to stop the cutting process, the residual tool life is determined, which is equal to the difference between the tool life prediction and the current part processing duration.

Energy efficiency of the high-current diode under the blow-up mode evolution in the anode

The results of experimental studies of energy fluxes released during the diode target blow-up initiated by a high-current relativistic electron beam are presented in the paper. The energy of target explosion products required for realization of the observed diode structural elements deformation is being estimated. Measurements of the target explosion products parameters and finite-element modeling of the mechanical deformation of the cathode system elements show an energy release during the target explosion that far exceeds the energy input.

On the Formation of Filamentary Structures in the Early Phase of Solar Flares

A model describing the initial phase of the heating of a flare in the solar corona is proposed. The energy equation for a flare plasma in a magnetic tube is reduced to the two-dimensional equation of thermal conductivity with a nonlinear volume source that ensures the heating of the plasma in the blowup mode and nonlinear anisotropic thermal conductivity. Explosive plasma heating is shown to be accompanied by the formation of high-temperature filamentary structures elongated along the magnetic tube.

Analytic–Numerical Investigation of Combustion in a Nonlinear Medium

Sufficient conditions of the onset of the blow-up mode for the parabolic equation with double nonlinearity that describes the combustion process in a nonlinear medium are analyzed. A sufficient condition for the initial function under which the time of the solution blow-up of the corresponding initial–boundary value problem for this equation is finite is obtained. An analytical upper bound on the solution existence time is derived. This a priori bound on the solution blow-up time is used for the numerical refinement of the blow-up process. It is shown that the numerical diagnostics of the solution blow-up makes it possible to obtained a better estimate of the solution blow-up time and detect the fact of local blow-up with respect to the spatial variable.

Blow-up Modes in Fracture of Rock Samples and Earth’s Crust Elements

It is well known that the final stage of macroscopic fracture develops as a catastrophe in a superfast blow-up mode. However, the specific features of this stage are well studied only on large scales of earthquakes. Of particular interest for fracture prediction are both the stage of superfast catastrophic fracture and the mechanical behavior of the medium in the state of self-organized criticality prior to transition of fracture to the blow-up mode in order to reveal precursors of fracture transition to the catastrophic stage. This paper studies experimentally and theoretically the mechanical behavior of the medium prior to the catastrophic stage and transition to the blow-up mode. Rock samples (marble and artificial marble) were tested in three-point bending and uniaxial compression tests. The lateral surface velocities of loaded samples were recorded using a laser Doppler vibrometer. The recording frequency in measurements was 48 kHz, and the determination accuracy of the velocity amplitude was 0.1 μm/s. The estimated duration of the blow-up fracture stage is 10–20 ms. The mechanical behavior of samples in the experimental conditions, including the catastrophic fracture stage, is simulated numerically. The damage accumulation model parameters are determined from a comparison with the experimental data. Certain features of the mechanical response prior to catastrophic fracture are revealed which can be interpreted as fracture precursors.

A Non-local Damage Model for Brittle Fracture in Metallic Structures with Stress Concentrators

This work is devoted to the development of the constitutive relations for the description of the defect evolution near the stress concentrators. A structural sensitive parameter is introduced as an averaging of the symmetrical tensor characterizing unit defect with the Boltzmann-Gibbs distribution function. Constitutive equation for structural parameter was derived under an assumption of the local thermodynamic equilibrium. The application of the developed approach is illustrated by the numerical simulation of a nonlocal fracture process occurring in a Grade-2 titanium specimen with a stress concentrator under uniaxial tension condition. Nonlocal character of the fracture near the stress concentrator was shown and physical explanation of the critical distance theory as a length of a dissipative structure growing in blow-up mode kinetics in the defect ensemble was proposed.

α′ Inflation: moduli stabilisation and observable tensors from higher derivatives

The leading order dynamics of the type IIB Large Volume Scenario is characterised by the interplay between $\alpha'$ and non-perturbative effects which fix the overall volume and all local blow-up modes leaving (in general) several flat directions. In this paper we show that, in an arbitrary Calabi-Yau with at least one blow-up mode resolving a point-like singularity, any remaining flat directions can be lifted at subleading order by the inclusions of higher derivative $\alpha'$ corrections. We then focus on simple fibred cases with one remaining flat direction which can behave as an inflaton if its potential is generated by both higher derivative $\alpha'$ and winding loop corrections. Natural values of the underlying parameters give a spectral index in agreement with observational data and a tensor-to-scalar ratio of order $r=0.01$ which could be observed by forthcoming CMB experiments. Dangerous corrections from higher dimensional operators are suppressed due to the presence of an approximate non-compact shift symmetry.

Prefracture time of gabbro specimens in a damage accumulation model

In the work, we experimentally determined the characteristic prefracture time of gabbro specimens in three-point bending. The obtained prefracture time was used to estimate the parameters in a model of brittle and quasibrittle material. Based on the verified model, numerical modeling was performed to describe the stress-strain evolution in gabbro specimens under three-point bending. The experiment and numerical calculations show that the final deformation stage involves beam deflection in blowup mode.

Fracture model of brittle and quasibrittle materials and geomedia

A general model and a unified mathematical formalism are proposed for description of inelastic deformation and fracture of any solids, where brittle or plastic, as their evolution in effective force fields. Loaded solids and media are considered as nonlinear dynamic systems. One of the main tasks of the work is to show that if deformation and fracture of a strong medium is treated as its evolution in effective force fields, numerical solutions of equations of solid mechanics do demonstrate the fundamental properties of nonlinear dynamic systems—self-organized criticality and two-stage evolution (a rather slow quasistationary stage and a superfast catastrophic stage or a blowup mode). The model is tested by simulation of fracture of quasibrittle composites under axial compression. Calculations are also presented for the now developing tectonic flows and seismic processes in Central Asia, including the Baikal rift zone and the Altai-Sayany folded region. It is shown that numerical solutions of all examined problems of inelastic deformation and fracture demonstrate self-organized criticality of loaded media, including peculiarities of slow dynamics and spatial-temporal migration of deformation activity, and as well as two-stage fracture: comparatively slow quasi-equilibrium damage accumulation and superfast catastrophic fracture. The predicted seismic events obey the Gutenberg-Richter law.

Modulated reheating and large non-gaussianity in string cosmology

A generic feature of the known string inflationary models is that the same physics that makes the inflaton lighter than the Hubble scale during inflation often also makes other scalars this light. These scalars can acquire isocurvature fluctuations during inflation, and given that their VEVs determine the mass spectrum and the coupling constants of the effective low-energy field theory, these fluctuations give rise to couplings and masses that are modulated from one Hubble patch to another. These seem just what is required to obtain primordial adiabatic fluctuations through conversion into density perturbations through the `modulation mechanism', wherein reheating takes place with different efficiency in different regions of our Universe. Fluctuations generated in this way can generically produce non-gaussianity larger than obtained in single-field slow-roll inflation; potentially observable in the near future. We provide here the first explicit example of the modulation mechanism at work in string cosmology, within the framework of LARGE Volume Type-IIB string flux compactifications. The inflationary dynamics involves two light Kähler moduli: a fibre divisor plays the rôle of the inflaton whose decay rate to visible sector degrees of freedom is modulated by the primordial fluctuations of a blow-up mode (which is made light by the use of poly-instanton corrections). We find the challenges of embedding the mechanism into a concrete UV completion constrains the properties of the non-gaussianity that is found, since for generic values of the underlying parameters, the model predicts a local bi-spectrum with fNL of order `a few'. However, a moderate tuning of the parameters gives also rise to explicit examples with fNL ∼ \U0001d4aa(20) potentially observable by the Planck satellite.

On a class of nonlocal parabolic equations

We consider a boundary value problem for parabolic equations with nonlocal nonlinearity of such a form that favorably differs from other equations in that it leads to partial differential equations that have important properties of ordinary differential equations. Local solvability and uniqueness theorems are proved, and an analog of the Painleve singular nonfixed points theorem is proved. In this case, there is an alternative—either a solution exists for all t ≥ 0 or it goes to infinity in a finite time t = T (blowup mode). Sufficient conditions for the existence of a blowup mode are given.

A spin chain for the symmetric product CFT2

We consider “gauge invariant” operators in SymN T 4, the symmetric product orbifold of N copies of the 2d supersymmetric sigma model with T 4 target. We discuss a spin chain representation for single-cycle operators and study their two point functions at large N. We perform systematic calculations at the orbifold point (“tree level”), where non-trivial mixing is already present, and some sample calculations to first order in the blow-up mode of the orbifold (“one loop”).

General analysis of LARGE Volume Scenarios with string loop moduli stabilisation

We study the topological conditions for general Calabi-Yaus to get a non-supersymmetric AdS exponentially large volume minimum of the scalar potential in flux compactifications of IIB string theory. We show that negative Euler number and the existence of at least one blow-up mode resolving point-like singularities are necessary and sufficient conditions for moduli stabilisation with exponentially large volumes. We also analyse the general effects of string loop corrections on this scenario. While the combination of α' and nonperturbative corrections are sufficient to stabilise blow-up modes and the overall volume, quantum corrections are needed to stabilise other directions transverse to the overall volume. This allows exponentially large volume minima to be realised for fibration Calabi-Yaus, with the various moduli of the fibration all being stabilised at exponentially large values. String loop corrections may also play a role in stabilising 4-cycles which support chiral matter and cannot enter directly into the non-perturbative superpotential. We illustrate these ideas by studying the scalar potential for various Calabi-Yau three-folds including K3 fibrations and briefly discuss the potential phenomenological and cosmological implications of our results.

Dynamical supersymmetry breaking from simple quivers

We construct a simple local model of dynamical supersymmetry breaking. The model is a one-generation $SU(5)$ that arises from a IIB ${\mathbb{Z}}_{N}$ orientifold. It does not admit a runaway direction and is argued to stabilize the blowup mode related to the corresponding $U(1)$ factor. The theory demonstrates the existence of a new class of ``blowup'' fractional branes

An Additive, High-Speed, Step-Reduction Printer

An additive printer for higher production rate of reduction printing of 16mm from 35mm negatives has scene-to-scene color correction, density modulation and a steadier print with increased sharpness. It is readily convertible to a blow-up mode from 16mm negative to 35mm positive; film movements are of the registration pin type. Printing is done at 120 ft/min on the 35mm side, with the capability of going faster; negatives of various shrinkages can be accommodated. The machine has a multiple-length selective-fade shutter which is tape-controlled, and provides A & B printing capability, with intermixed lengths of fades and/or dissolves. A number of features provide simpler operation and greater safety measures, such as air-actuated trips which automatically stop the machine in the event of a film break, separate drive or synchronized drive for the negative and positive heads, built-in air-vacuum squeegees on both negative and positive films and multiple-speed selection.