The stress and vascular catastrophes in newborn rats: mechanisms preceding and accompanying the brain hemorrhages

In this study, we analyzed the time-depended scenario of stress response cascade preceding and accompanying brain hemorrhages in newborn rats using an interdisciplinary approach based on: a morphological analysis of brain tissues, coherent-domain optical technologies for visualization of the cerebral blood flow, monitoring of the cerebral oxygenation and the deformability of red blood cells (RBCs). Using a model of stress-induced brain hemorrhages (sound stress, 120 dB, 370 Hz), we studied changes in neonatal brain 2, 4, 6, 8 h after stress (the pre-hemorrhage, latent period) and 24 h after stress (the post-hemorrhage period). We found that latent period of brain hemorrhages is accompanied by gradual pathological changes in systemic, metabolic, and cellular levels of stress. The incidence of brain hemorrhages is characterized by a progression of these changes and the irreversible cell death in the brain areas involved in higher mental functions. These processes are realized via a time-depended reduction of cerebral venous blood flow and oxygenation that was accompanied by an increase in RBCs deformability. The significant depletion of the molecular layer of the prefrontal cortex and the pyramidal neurons, which are crucial for associative learning and attention, is developed as a consequence of homeostasis imbalance. Thus, stress-induced processes preceding and accompanying brain hemorrhages in neonatal period contribute to serious injuries of the brain blood circulation, cerebral metabolic activity and structural elements of cognitive function. These results are an informative platform for further studies of mechanisms underlying stress-induced brain hemorrhages during the first days of life that will improve the future generation's health

Fixed energy problem for nonlinear Schrödinger operator

Abstract This work studies the inverse fixed energy scattering problem for the generalised nonlinear Schrödinger operators. We prove that in a three-dimensional case the unknown compactly supported generalised nonlinear potential (with some restriction for this potential) from $L^{2}$ space can be uniquely determined by the scattering data with fixed positive energy (meaning that we have the knowledge of the scattering amplitude with fixed non-zero spectral parameter). The results are based on the new estimates for the Faddeev’s Green function in $L^{∞}$. These results may have applications in nonlinear optics for the saturation model. In particular, the constant coefficients of this model can be uniquely reconstructed by the scattering data with fixed energy

Some inverse scattering problems for perturbations of the biharmonic operator

Abstract Some inverse scattering problems for the three-dimensional biharmonic operator are considered. The operator is perturbed by first and zero order perturbations, which may be complex-valued and singular. We show the existence of the scattering solutions in the Sobolev space $W^1_{\infty }(R^3)$. One of the main result of this paper is the proof of analogue of Saito’s formula (in different form as known before), which can be used to prove a uniqueness theorem for the inverse scattering problem. Another main result is to obtain the estimates for the kernel of the resolvent of the direct operator in $W^1_{\infty}$ and to prove the reconstruction formula for the unknown coefficients of this perturbation

Born approximation for the magnetic Schrödinger operator

Abstract We prove the existence of scattering solutions for multidimensional magnetic Schrödinger equation such that the scattered field belongs to the weighted Lebesgue space $L_{{-}\delta}^2(\mathbb{R}^n)~(n \ge 2)$ with some $\delta > \frac{1}{2}$. As a consequence of this we provide the mathematical foundation of the direct Born approximation for the magnetic Schrödinger operator. Connection to the inverse Born approximation is discussed with numerical examples illustrating the applicability of the method

Scattering problems for perturbations of the multidimensional biharmonic operator

Abstract Some scattering problems for the multidimensional biharmonic operator are studied. The operator is perturbed by first and zero order perturbations, which maybe complex-valued and singular. We show that the solutions to direct scattering problem satisfy a Lippmann-Schwinger equation, and that this integral equation has a unique solution in the weighted Sobolev space $H_{-δ}^2$. The main result of this paper is the proof of Saito’s formula, which can be used to prove a uniqueness theorem for the inverse scattering problem. The proof of Saito’s formula is based on norm estimates for the resolvent of the direct operator in $H_{-δ}^1$

Inverse scattering problem for quasi-linear perturbation of the biharmonic operator on the line

Abstract We consider an inverse scattering problem of recovering the unknown coefficients of quasi-linearly perturbed biharmonic operator on the line. These unknown complex-valued coefficients are assumed to satisfy some regularity conditions on their nonlinearity, but they can be discontinuous or singular in their space variable. We prove that the inverse Born approximation can be used to recover some essential information about the unknown coefficients from the knowledge of the reflection coefficient. This information is the jump discontinuities and the local singularities of the coefficients

Guided TE-waves in a slab structure with lossless cubic nonlinear dielectric and magnetic material:parameter dependence and power flow with focus on metamaterials

Abstract The parameter dependence and power flow of guided TE-waves in a lossless cubic nonlinear, dielectric, magnetic planar three-layer structure is studied as follows. Using a travelling wave ansatz with stationary amplitude, Maxwell’s equations are transformed to a system of ordinary nonlinear differential equations. The solutions of the system are presented compactly (in terms of hyperbolic and elliptic functions).The nonnegative and bounded (“physical”) solutions are determined by using a phase diagram condition (PDC) that is applied to express the continuity (transmission) conditions at the interfaces leading to the dispersion relation (DR).Based on the PDC, the parameter dependence and stability of the solutions to the DR and corresponding power flow are studied numerically for permittivities and permeabilities that may be appropriate to describe metamaterial

Parameter dependence and stability of guided TE-waves in a lossless nonlinear dielectric slab structure

Abstract The nonlinear Schrödinger equation is the basis of the traditional stability analysis of nonstationary guided waves in a nonlinear three-layer slab structure. The stationary (independent of the propagation distance) solutions of the nonlinear Schrödinger equation are used as “initial data” in this analysis. In the present paper, we propose a method to investigate the dependence of these solutions on the experimental parameters and discuss their stability with respect to the parameters. The method is based on the phase diagram condition (PDC) and compact representation (in terms of Weierstrass’ elliptic function and its derivative) of the dispersion relation (DR). The problem’s parameters are constrained to certain regions in parameter space by the PDC. Dispersion curves inside (or at boundaries) of these regions correspond to possible physical solutions of Maxwell’s equations as ”start” solutions for a traditional stability analysis. Numerical evaluations of the PDC, DR, and power flow including their parameter dependence are presented

Comment on “Solitary waves in optical fibers governed by higher-order dispersion”

Abstract Mainly with respect to the mathematical part of the article by Kruglov and Harvey [Phys. Rev. A 98, 063811 (2018)] some (supplementary) remarks on the solution method, on the conditions of existence, and on the parameter dependence are presented. For elucidation, numerical examples are included

Inverse scattering for three-dimensional quasi-linear biharmonic operator

Abstract We consider an inverse scattering problem of recovering the unknown coefficients of a quasi-linearly perturbed biharmonic operator in the three-dimensional case. These unknown complex-valued coefficients are assumed to satisfy some regularity conditions on their nonlinearity, but they can be discontinuous or singular in their space variable. We prove Saito’s formula and uniqueness theorem of recovering some essential information about the unknown coefficients from the knowledge of the high frequency scattering amplitude