Time-Dependent Response

The time response of the frequency dependence explained in the previous sections is calculated by a numerical Fourier or Laplace inverse transform in the following form [1,17]  

---

Olsen J and J0rgensen P 1995 Time-dependent response theory with applioations to self-oonsistent field and multioonfigurational self-oonsistent field wave funotions Modern Electronic Structure Theory vo 2, ed D R Yarkony (Singapore World Soientifio) pp 857-990... 

In a subsequent treatment from the time-dependent response point of view, connection with the Greens function... 

It is an unfortunate fact that many students and indeed design engineers are reluctant to get involved with plastics because they have an image of complicated materials with structures described by complex chemical formulae. In fact it is not necessary to have a detailed knowledge of the structure of plastics in order to make good use of them. Perfectly acceptable designs are achieved provided one is familiar with their perfonnance characteristics in relation to the proposed service conditions. An awareness of the structure of plastics can assist in understanding why they exhibit a time-dependent response to an applied force, why acrylic is transparent and stiff whereas polyethylene is opaque and flexible, etc., but it is not necessary for one to be an expert... 

J. Olsen and P. Jorgensen. Time-Dependent Response Theory with Applications to Self-Consistent Field and Multiconfigurational Self-Consistent Field Wave Functions, in Modern Electronic Structure Theory, edited by D. R. Yarkony, volume 2, chapter 13, pp. 857-990. World Scientific, Singapore, 1995. 

Time-dependent response theory concerns the response of a system initially in a stationary state, generally taken to be the ground state, to a perturbation turned on slowly, beginning some time in the distant past. The assumption that the perturbation is turned on slowly, i.e. the adiabatic approximation, enables us to consider the perturbation to be of first order. In TD-DFT the density response dp, i.e. the density change which results from the perturbation dveff, enables direct determination of the excitation energies as the poles of the response function dP (the linear response of the KS density matrix in the basis of the unperturbed molecular orbitals) without formally having to calculate a(co). 

Therefore the time-dependent response of C to the step disturbance in feed concentration is... 

When a polymer is extruded through an orifice such as a capillary die, a phenomenon called die swell is often observed. In this case, as the polymer exits the cylindrical die, the diameter of the extrudate increases to a diameter larger than the diameter of the capillary die, as shown in Fig. 3.9. That is, it increases in diameter as a function of the time after the polymer exits the die. Newtonian materials or pure power law materials would not exhibit this strong of a time-dependent response. Instead they may exhibit an instantaneous small increase in diameter, but no substantial time-dependent effect will be observed. The time-dependent die swell is an example of the polymer s viscoelastic response. From a simplified viewpoint the undisturbed polymer molecules are forced to change shape as they move from the large area of the upstream piston cylinder into the capillary. For short times in the capillary, the molecules remember their previous molecular shape and structure and try to return to that structure after they exit the die. If the time is substantially longer than the relaxation time of the polymer, then the molecules assume a new configuration in the capillary and there will be less die swell. 

When dash pot and spring elements are connected in parallel they simulate the simplest mechanical representation of a viscoelastic solid. The element is referred to as a Voigt or Kelvin solid, and it is shown in Fig. 3.10(c). The strain as a function of time for an applied force for this element is shown in Fig. 3.11. After a force (or stress) elongates or compresses a Voigt solid, releasing the force causes a delay in the recovery due to the viscous drag represented by the dash pot. Due to this time-dependent response the Voigt model is often used to model recoverable creep in solid polymers. Creep is a constant stress phenomenon where the strain is monitored as a function of time. The function that is usually calculated is the creep compliance/(f) /(f) is the instantaneous time-dependent strain e(t) divided by the initial and constant stress o. ... 

Time dependent response of preparation to crude toxin. 

Time-dependent response of a liquid or solid subjected to stress or strain. 

Imperato A, Cabib S, Pughsi-Allegra S Repeated stressful experiences differently affect the time-dependent responses of the mesolimbic dopamine system to the stressor. Brain Res 601 333-336, 1993... 

Then, to the linear order for 5Ja r,t), the mean-field Hamiltonian (4) can be decomposed into static and time-dependent response parts... 

This time-dependent response to pH of the swelling medium was modelled with a Boltzmann superposition type model shown in Eq, (46) ... 

Rivard GE, Infante-Rivard C, Dresse MF et al. Circadian time-dependent response of childhood lymphoblastic leukemia to chemotherapy a long-term follow-up study of survival. Chronobiol Int 1993 10 201-204. 

Puglisi-Allegra, Stephano, Assunta Imperato, Luciano Angelucci, and Simona Cabib. 1991. "Acute Stress Induces Time Dependent Responses in Dopamine Mesolimbic System." Brain Research 554 217-22. 

Fernandez-Martinez AB, Collado B, Bajo AM, Sanchez-Chapado M, Prieto JC, Carmena MJ. 2007. Vasoactive intestinal peptide induces cyclooxygenase-2 expression through nuclear factor-kappaB in human prostate cell lines Differential time-dependent responses in cancer progression. Mol Cell Endocrinol 270 8-16. 

Brannonpeppas L, Peppas NA. Time-dependent response of ionic polymer networks to pH and ionic-strength changes. International Journal of Pharmaceutics 1991,70,53-57. 

The theory of PCM calculation of the effective polarizabilities is based on a time-dependent response theory that describes the interaction between the molecular solutes and the Maxwell electric field. We will review the method in three separate sections, the... 

The next step is to consider the extra contributions related to the term involving the operator WQM/CM since they give rise to significant modifications of the terms that enter the procedure for solving the time-dependent response equations. Through the calculations of frequency-dependent response functions for the molecular subsystem we are able to investigate the effects of the structured environment on the molecular properties. 

To fully understand the behavior of biological materials we need to address the issue of viscoelasticity. When a weight is placed on viscoelastic material, there is an instantaneous elastic response and a time-dependent viscous response (see Figure 7.1). For polymers the elastic response reflects the change in macromoleular conformation, which is usually time independent if no bonds are broken. The viscous response is the flow of macromolecules by each other similar to what happens during the flow of fluids in a tube. Fluid flow is a time-dependent process. Polymers exhibit viscoelastic behavior because they have both a time-independent response and a time-dependent response. 

Figure 3 Brownian oscillator simulations for the ID (left) and 2D (right) Raman response for liquid CS2 at room temperature. (A) The response is modeled as a single oscillator represented by a sum of the three Brownian oscillators in (B). (B) The response is modeled by three independent Brownian oscillators. (C) The response is modeled by 20 randomly distributed Brownian oscillators. Note that all three cases reproduce the same ID time dependent response but exhibit clear differences in the 2D responses.

In discussing shear deformation, it is convenient to distinguish between the initial elastic and viscoelastic response of the polymer to the applied load and the subsequent time-dependent response. However, the distinction is somewhat arbitrary and is not as fundamental as that between elastic volume response and crazing. Viscoelastic shear deformation continues throughout the period under load. The observed time-dependence of lateral strain reflects both generalized viscoelastic relaxation and shear band formation. Since crazing consists simply of displacement in the tensile stress direction, it makes no contribution to lateral strain therefore —e specifically measures deformation by shear processes. 

Several authors have extaided the treatment of this model to determine its time-dependent response. - A particularly clear account, summarizing and extending earlier work on the subject, is given by Nee and Zwanzig. They obtain... 

The effect of coating thickness on the response time of the sensor was also evaluated. The time dependent response of a sensor coated with a 100 micron layer and that of a sensor coated with a 200 micron layer to a 10 ppm PMP solution at pH = 13 was measured. The fibre with a 200 micron coating reached a maximum response within 14 min. The response time of the 100 micron coated fibre was decreased to 8 min. For an on-line monitor, the time for initial response is the most important factor. Using pH = 13, a distinct response occurred within 1 min. 

The derivation of formulae for the frequency-dependent nonlinear susceptibilities of nonlinear optics from the time-dependent response functions can be found in a number of sources, (Bloembergen, Ward and New, Butcher and Cotter, Flytzanis ). Here it is assumed that the susceptibilities can be expressed in terms of frequency-dependent quantities that connect individual (complex) Fourier components of the polarization with simple products of the Fourier components of the field. What then has to be shown is how the quantities measured in various experiments can be reduced to these simpler parameters. 

In the above, quantities with no arguments are time-dependent, those with one argument, which is always a frequency, are time-independent Fourier coefficients. It is convenient to introduce one further type of S5mbol with two arguments, where the quantity defined contains the full nth order time-dependent response at frequency which will contain both positive and negative complex frequency components. The composite quantities, can always be expressed in terms... 

Olsen, J., Jorgensen. P. Time-dependent response theory with appUcations to self-consistent field and multiconfigurational self-consistent field wave functions. In Modern Electronic Structure Theory, vol. 2. World Scientific, Singapore (1995)... 

Abstract We review Kohn-Sham density-functional theory for time-dependent response func-... 

Sahara, T., Goda, T., and Ohgiya, S. 2002. Comprehensive expression analysis of time-dependent responses of yeast cells to low temperature. /. Biol. Chem. 51,50015-50021. Schadt, E.E., Li, C., Su, C., and Wong, W.H. 2000. Analyzing high-density oligonucleotide... 

VO2. Methodologic limitations of many of these studies included nonrandomized crossover periods, potentially leading to pharmacologic carry-over failure of patients to achieve a steady state before crossover, and the use of time-dependent response measures. It is also unclear whether patients were comparable at basehne—whether they had received the same or other vasoactive agents before the study period and for how long. ... 

---